Most of a proton’s mass is not in its parts. About nine-tenths of it is the energy of the connection that binds them. Most of the gravitating mass of the universe is also unseen. This paper asks whether those two facts could be one: whether the unseen mass around galaxies could be a fabric of connection energy, of the same type that makes up ordinary matter, and whether the same principle of connection could carry further, to abstract thinking and consciousness.
This is a first report of work in progress, not a finished theory. So far the idea has been put to twenty-seven tests on public astronomical data, each written down with its pass and fail criteria before the data were opened. Many versions failed, and each failure narrowed the search. What stands today: one rule with one fixed threshold describes the unseen pull in 147 galaxies; a fabric locked point by point to ordinary matter gives the measured vertical pull near the Sun with nothing fitted; and a two-state formula with no adjusted number passed, weakly, on 17 groups and clusters of galaxies not seen before. At six points, the behaviour found at the large scale matches in form what is established inside the atom.
One prediction is on record, dated 12 November 2026: wide pairs of stars should pull on each other 1.335 times more strongly than Newton’s law gives. The star catalogue that will test it is due on 2 December 2026.
The law that would join these findings is still missing, and the link to the mind is untested. The paper sets out what was found, what failed and what comes next, and it invites discussion.
Status of this paper. This is a hypothesis and a theory with limited testing. It is not a proof. It contains:
This paper used AI assistance in the evaluation of this theory and hypothesis and in drafting the text. The hypothesis, judgements, formulations and the final wording are the author’s.
The theory proposes one thing, a fabric of connection, and two links that run through it. The first is between the two great theories of physics. The second is between that physics and the mind.
Why they may be related. The two theories meet in one word: mass. The standard model says where mass comes from. General relativity says what mass does. The standard model’s answer is not what most people expect. Only about a tenth of a proton’s mass is tied to the masses of its parts (Yang et al., 2018). The rest is the energy of their motion and of the connection that binds them. So most of the ordinary mass in the universe is already energy of connection, not substance.
General relativity makes no distinction. All energy gravitates, whatever its kind. That leaves one question, and it is the question of this paper: if connection energy is most of the mass at the small scale, could it also be the unseen mass at the large scale?
What correlates between the micro and the macro.
| Behaviour | Micro: established | Macro: found in the tests reported here |
|---|---|---|
| Most of the mass is in the connection, not the parts | About nine-tenths of the proton (Yang et al., 2018) | About five-sixths of the matter in the universe is unseen (Planck Collaboration, 2020) |
| The connection is invisible to light | Light probing a proton sees only the quarks (Aschenauer et al., 2024) | The unseen mass is seen only through gravity (Clowe et al., 2006) |
| It grows stronger, relative to the simple law, with distance | The bond between quarks (Huston et al., 2024) | The unseen pull around a galaxy |
| Bound, until surroundings or heat free it | Quarks in a proton; electrons in an atom | Locked to stars and cold gas; free around hot gas |
| The whole is not the sum of the parts | The proton’s bond acts on itself (Huston et al., 2024) | The one rule that passed is not a sum; the sums failed |
| The unit is fixed by the constants of nature | The atom | The star: about 10⁵⁷ particles, from the same constants (Burrows & Ostriker, 2014; Carr & Rees, 1979) |
How the fabric continuum could bring the two together. The hypothesis is that the unseen mass is a fabric: mass of the connection type, the energy of the exchange between bodies and between places. It forms a web in which everything is connected and nothing is external. It has two states. Around cohesive matter it is locked to that matter by one rule. Around diffuse matter it is free.
This places one thing in both theories. Its type comes from the standard model. Its effect is the one general relativity describes. In Einstein’s equation it is a single added term: the energy of the exchange.
The theory in one formula.
The left side is the shape of space and time. The right side is what shapes it. Einstein’s equation has the first two terms on the right: ordinary matter and radiation. The theory adds the third: the energy of the exchange between bodies and between places, which is the fabric. Everything else in the equation is unchanged.
Why they may be related. This is where the theory began. A mind is not its cells. What is learned is held, in large part, in the strength of the links between them, and abstract thinking is the linking of links: relations among relations (Takeuchi et al., 2014). A mind is mostly connection, as a proton is, and as, on this hypothesis, a galaxy is.
The author’s starting observations were about the limits of that mind:
“we are aware of what we are aware… not more”
“continuity… how we are creating continuity during existence and are not aware”
What correlates. Three of the behaviours in the table above carry over. The thing is its connections more than its parts. The whole is not the sum of the parts. And nothing stands alone: what a thought means depends on everything it is connected to, as a body’s motion in the fabric depends on the whole web.
How the fabric continuum could enable abstract thinking. The author’s hypothesis, in his words:
“the same principles that define matter and space… and the inter connectivity creates the model of abstract learning without or in combination with the chemical processes in the brain… and this inter connectivity expands with a type of entanglement or superposition or energy to others… waves become signals with information… energy does not die… and this is in essence conscience”
It is held in two strengths.
Two steps are involved, and they stand differently. The first is the connection itself: a relation between things. Established physics allows this, and says that a relation of this kind cannot by itself carry a message (Ghirardi et al., 1980). The second is the author’s further proposal: that waves in the fabric can become signals that carry information, and that because energy does not die, what is carried is not lost. That second step is new. It is not part of established physics and it has not been tested. The author holds the two in that order: the relation first, the signal second.
The question. Two theories describe the physical world. General relativity describes gravity and the large scale. The standard model describes particles and the small scale. They do not join. Separately, most of the gravitating mass in the universe is unseen and is known only as a difference: the gravity that is observed, minus the gravity of everything visible (Planck Collaboration, 2020).
The hypothesis. The unseen mass is a fabric: mass of the connection type, the energy of the exchange between bodies and between places, and not a substance of its own. It is the same type of mass that makes up most of a proton (Yang et al., 2018). The fabric is a non-linear quantum matrix in which nothing is external. It has two states. Around cohesive matter, such as stars and cold gas, it is locked to that matter by one rule. Around diffuse hot gas it is free. The star is the unit of the fabric, and the same principle of connection carries down to the atom and, as a further hypothesis, to abstract thinking and consciousness.
The hypothesis in formulas. The added term of section 1.1 takes a different form in each of the fabric’s two states.
Locked, around cohesive matter. The total pull follows from the pull of the ordinary matter alone:
Here is the share the fabric adds, and is the one fixed threshold. Where the ordinary pull is strong, is close to zero and Newton’s law holds. Where it is weak, the fabric supplies most of the pull. This rule was found by others from the motions of galaxies; the tests here confirm it (McGaugh et al., 2016).
Free, around diffuse hot gas. The fabric takes its cosmic share:
The number 5.36 is the measured ratio of unseen to ordinary matter in the universe as a whole (Planck Collaboration, 2020). It is not fitted to any system in this paper.
Together, for a group or cluster of galaxies:
The locked part is the rule applied around each galaxy of ordinary mass , out to a reach set by its neighbours. The free part is the cosmic share of the hot gas. No number in it is adjusted. Section 6 gives the tests of each formula.
The evidence, at two scales. The hypothesis stands on two legs, and this paper gives them equal weight.
The micro side: what is established. These are results of particle and atomic physics, confirmed by others over many decades. The paper draws on them and does not test them again.
The macro side: what was tested. Twenty-seven tests were declared in writing, with pass and fail criteria, before the data were opened. Each was run to answer one question, and each answer set the next question (section 6.2). Many versions of the idea failed, and each failure narrowed the search. What they led to, and what now stands, is:
Where the two sides meet. Each macro finding has a micro counterpart in the table of section 1.1: mass that is mostly connection, invisible to light, stronger with distance, bound until freed, not a simple sum, and built from a unit fixed by the constants of nature. That is a match of form at six points. It is not yet a match of fact.
The prediction. If the star is the unit of the fabric, two stars orbiting far apart near the Sun should pull on each other 1.335 times more strongly than Newton’s law gives, and so orbit about 15.5% faster. This was computed and placed on record on 12 November 2026, before the release of the catalogue that will test it (2 December 2026) (European Space Agency, n.d.-a). This is the place where the micro and the macro are tested together: the star is the characteristic body that gravity builds from particles, and the prediction asks whether the fabric begins there.
What is not shown. No test here separates the hypothesis from ordinary dark matter in a single galaxy, or from the existing minority theory that uses the same rule (Milgrom, 1983a). No derivation of the rule from the hypothesis is offered. No experiment shows that the micro connection and the macro fabric are one thing and not two alike. The link to abstract thinking and consciousness is untested.
The author’s starting point, in his words:
“how do we interact with the universe… not from a conscience variable… from the forces that could be construed as abstract… quantum is abstract”
Stated in the terms of physics, the question is how gravity and quantum theory fit together: what space is made of, how energy moves in it, and how the micro and the macro world fit in one quantum matrix, the fabric continuum.
Physics defines the unseen mass only by what is missing:
In words: the gravity that is observed, minus the gravity of everything that can be seen. The formula says how much and where. It does not say what. The author’s position is that the search has been aimed at the wrong thing:
“you are trying to measure something you are measuring wrong… that is the first step… how to measure”
“dark matter is part of the fabric”
“atomic photons are part of the fabric”
“energy can travel through fabric… in all directions… without moving”
“exchanging… like entanglement”
Read together, these say that the fabric is one thing at every scale: the exchange that connects. Section 4.1 sets out what that means inside the atom, between bodies and places, and in the way the fabric works.
The model is stated in five formulas. For each one, the text says what it means and how it stands.
Formula 1. The theory.
The left side is the shape of space and time. The right side is what shapes it. The first term on the right is ordinary matter. It already contains the micro fabric: the energy of the exchanges inside every nucleus and atom is most of the mass of ordinary matter (Yang et al., 2018). The second term is radiation. The third is the addition: the energy of the exchange between bodies and between places, which is the macro fabric.
Standing: this is the hypothesis. The equation without the third term is Einstein’s and is established. The third term is named here, and it is not yet derived. Formulas 2 and 3 say what it must amount to in the two states.
Formula 2. The locked state, around cohesive matter.
Here is the total pull, is the pull of the ordinary matter, is the share the fabric adds, and is the one fixed threshold. Where the ordinary pull is strong, is close to zero and Newton’s law holds. Where it is weak, the fabric supplies most of the pull.
Standing: tested. The rule was found by others from the motions of galaxies (McGaugh, Lelli and Schombert 2016, written there in an equivalent form). It is confirmed here on 147 galaxies and over about 10 billion years (Genzel et al., 2020; Lelli et al., 2016; Nestor Shachar et al., 2023). The value of was fixed by declaration and not fitted.
Formula 3. The locked state, point by point.
This says where the locked fabric is, and not only how hard it pulls. At each point its density follows from the ordinary pull at that point. Formula 2 is what this gives for the total pull in a galaxy.
Standing: tested in one place. It gives the measured upward pull near the Sun with nothing fitted (64.1 predicted against 67.9 ± 3.8 measured), and a round fabric of the size the rule implies does not (Bienaymé et al., 2014; Bovy & Rix, 2013; Eilers et al., 2019; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; McKee et al., 2015; Nitschai et al., 2021; Zhang et al., 2013). The formula exists in the literature (Milgrom 2010), where its output is called a “phantom” density, a device for calculation. Here it is read as real mass of the connection type.
Formula 4. The free state, around diffuse hot gas.
The fabric takes its cosmic share. The number 5.36 is the measured ratio of unseen to ordinary matter in the universe as a whole (Planck Collaboration, 2020).
Standing: 5.36 is established and is not fitted to any system here. That the fabric around hot gas sits at this share is the hypothesis, tested through Formula 5.
Formula 5. The two states together, for a group or cluster of galaxies.
The locked part is Formula 2 applied around each of galaxies of typical mass , out to a reach of half the spacing between neighbours inside the radius . The free part is Formula 4. No number is adjusted to the data.
Standing: tested, with a weak pass. On 17 systems not seen before, observed mass over predicted mass was 0.88, inside the declared range (Lin et al., 2003; Zhang et al., 2011). On 290 systems seen earlier it passed 9 of 11 checks and predicted about 27% too much in the most massive clusters (Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019; Gonzalez et al., 2013; Laganá et al., 2013; Lovisari et al., 2015; Sanderson et al., 2013; Sun et al., 2009).
What the formulas do not yet give. Formula 1 names the exchange term. Formulas 2 to 5 describe what it does. Nothing yet derives the second from the first: there is no expression for the exchange term from which the rule, the threshold and the two states follow. That derivation is the missing law, and it is the main open problem of the theory.
Each statement below is the author’s, quoted from the working record. The wording between the quotations is a plain restatement.
The fabric is one thing at every scale: the exchange that connects.
The author holds to this order: the relation first, the signal second.
“what if we replace dark matter with another type of mass… one that has the properties that work in the micro and macro world”
The type chosen is mass that is the energy of a connection. It is established at the micro scale: in the standard calculation only about a tenth of a proton’s mass is tied to the masses of its quarks, and the rest is the energy of their motion, of the field that binds them, and of a quantum effect of that field (Yang et al. 2018). Most ordinary mass is already of this type. The hypothesis is that the fabric is the same type at the macro scale: the energy of the exchange between bodies and between places.
The author accepted that this needs new physics. Inside the proton the energy of the connection is positive and large. The ordinary gravitational binding between the bodies of a galaxy is negative and, as their speeds show, about a millionth of the mass or less (Eilers et al., 2019). The hypothesis needs a connection that is positive and about five times the ordinary mass.
“a non-linear quantum matrix… has no linear path… actually connected at all times to all places and can take any of those paths”
Asked what one entry of the matrix stands for:
“two bodies and two places”
Bodies are connected to bodies, and places are connected to places, including places with nothing in them. From this follows a statement about motion. In the matrix, nothing is external. A body’s motion depends on the whole web, and Newton’s law holds for a body taken together with its connections, not for the body alone.
“Non-linear” has an exact meaning here: the whole is not the sum of its parts. This is true of the connection inside the proton, which acts on itself (Huston et al., 2024). It is also true of the one rule that passed its tests at the macro scale (section 6). Almost every formula that failed there was built as a sum.
“we need to add distance and cohesion”
“I believe hot and cold gases are the culprit”
“the surroundings… the fabric… that is the missing piece”
“the gravity of galaxies do stretch”
Put together: the fabric is locked around cohesive matter, which is matter bound into stars and cold gas. It is free around diffuse matter, which is thin hot gas. The reach of the lock around a galaxy is limited by its surroundings, which stretch it.
The micro scale shows the same pattern. An atom holds its electrons until heat or a strong outside force strips them, and the hot gas of a cluster is matter in exactly that stripped state (Gary, n.d.; MIT Atomic and Optical Physics Wiki, n.d.). A proton holds its quarks until far greater heat frees them (Bazavov et al., 2019). Bound until freed, then free, is how connection behaves at each scale.
“the star is a different version of the atom of the fabric… a different scale… the atom is the child of the star”
“our star is the link to the universe and galaxies”
The star stands between the two scales. Its mass is fixed by the constants of the micro world set against the strength of gravity (Burrows & Ostriker, 2014; Carr & Rees, 1979). Apart from a trace of lithium, every nucleus heavier than helium was made in stars or in their deaths (Fields et al., 2024). And on the hypothesis the star is the unit of the fabric, as the atom is the unit of ordinary matter. In its strong form this says that each star carries its own share of the fabric. That form has a test (section 8).
“the same principles that define matter and space… and the inter connectivity creates the model of abstract learning without or in combination with the chemical processes in the brain… and this inter connectivity expands with a type of entanglement or superposition or energy to others… waves become signals with information… energy does not die… and this is in essence conscience”
(“Conscience” is used throughout the record in the sense of consciousness.)
The author added that the level he means is not the chemical one:
“not the chemical disposition of activity… the nuclear level of activity”
This part of the hypothesis is stated in two strengths, set out in section 1.2 and examined in section 10.
This paper puts forward a possibility. It is that the large-scale universe, the macroverse, is a form of the small-scale one, the microverse: that the two are built on the same model, and that the fabric continuum is what runs through both.
We stand in the microverse. That is meant literally. Counted in powers of ten, a person is about ten steps larger than an atom and about twenty-six steps smaller than the observable universe (Davis & Lineweaver, 2004; National Institute of Standards and Technology, n.d.). Everything that can be taken apart and measured in a laboratory lies at the small end of that ladder. The large end can only be watched from inside. So the model of the microverse is known in detail, and the model of the macroverse is only beginning to be discovered. If the possibility is right, the macroverse is the larger part of the fabric continuum, and what has been learned at the small scale is a guide to it.
The two scales do show similar models. Section 1.1 lists six behaviours that the connection inside the proton and the atom shares with the unseen mass around galaxies. Section 9 sets them out in full.
The work on this hypothesis and theory has only started. What is reported here is a first examination: the model stated, the micro side checked against its sources, the macro side put to tests, and one prediction placed on record. It found glimpses of possible validation, listed in section 5.4, and it found a larger number of versions that failed, listed in section 6. Neither amounts to a verified model.
The author intends, together with partners, to report further updates as new tests are made, until a verified model that connects the two scales is found or the possibility is ruled out.
The microverse: established results, checked against their sources. Nothing at the micro scale was measured for this paper. The micro side rests on results of particle and atomic physics that others have established over many decades. Each such statement used here was checked against a published source. Thirty-nine statements were checked. Thirty were confirmed as worded. Nine were corrected, and the corrected wording is the one used.
The macroverse: tests declared in advance. For each test a short declaration was written first. It stated the formula, the constants, the data to be used, the pass and fail criteria, and what was already known to the person drawing up the test. The declaration was given a checksum and a time. Only then were the data opened. Each test was run once, and every result is reported, whichever way it fell. A formula adjusted after a result until it fits has shown nothing; the declarations are there so that a pass means something and a fail is not explained away.
Results were then re-derived by a separate check that wrote new code from the declaration alone, compared the inputs with the published sources, and was instructed to look for errors, not to confirm. Tests 1, 10 and 15 to 26 have been checked in this way; Test 27 has not. No check found a wrong number. Several found that a summary had been worded more strongly than the result allowed, and those wordings are corrected here.
Joining the two. The claim that one fabric runs through both scales was judged in three steps, in rising order of strength.
Each row is a place where the macroverse was found to behave as the model drawn from the microverse says it should. Each is labelled with how firmly it stands and with what would turn the glimpse into a validation.
| What the model expects | What was found in the macroverse | How firmly | What would make it a validation |
|---|---|---|---|
| The connection follows one law with a fixed constant, as the bonds of the microverse do | One rule with one fixed threshold describes 147 galaxies, unchanged for about 10 billion years (Tests 1 and 7) (Genzel et al., 2020; Lelli et al., 2016; Nestor Shachar et al., 2023) | Firm. It confirms a relation found by others (McGaugh et al., 2016) | A derivation of the rule and its threshold from the fabric |
| The connection is locked to matter point by point | In our own galaxy the same factor gives both the Sun’s orbit and the pull up out of the disc, with nothing fitted (Test 19) (Bienaymé et al., 2014; Bovy & Rix, 2013; Eilers et al., 2019; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; McKee et al., 2015; Nitschai et al., 2021; Zhang et al., 2013) | Passed, and confirmed by an independent check. One place in one galaxy | The same result at greater heights and in other galaxies |
| Bound matter and freed matter carry the connection differently, as atoms and ionised gas do | A formula with two states, locked to the stars and free around the hot gas, with no fitted number, passed on 17 systems not seen before (Tests 18 and 20) (Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019; Gonzalez et al., 2013; Laganá et al., 2013; Lin et al., 2003; Lovisari et al., 2015; Sanderson et al., 2013; Sun et al., 2009; Zhang et al., 2011) | A weak pass. The sample is small | A larger sample of clusters with stars and hot gas measured separately |
| The connection is invisible to light and still bends it | The rule that gives the motions of stars also gives the bending of light around spiral galaxies (Test 2b) (Brouwer et al., 2021) | Firm for spirals | The same for ellipticals once their hot gas and neighbours are accounted for |
| The whole is not the sum of the parts | The rule that passed is non-linear. The formulas built as sums failed (Tests 10, 11, 13) (Gopika & Desai, 2020; Li et al., 2020; Salucci et al., 2012) | Firm as a pattern | A non-linear law that also covers clusters |
| There is no preferred size | The core of the fabric has the same surface density at every core size measured, from 0.3 to 26 thousand parsecs (Test 13) | A finding inside a failed test | An explanation of why that density takes the value it does |
| The unit of the fabric carries more of it than loose matter does | Places supplied by stars show more unseen pull than places supplied by cold gas, at 3.5 sigma (Tests 24 and 26) | Open. Reproduced independently; may be an effect of the data | The same result in galaxies with the best-measured distances |
| The unit is fixed by the constants of nature | The mass of a star follows from the constants of the microverse set against gravity (Burrows & Ostriker, 2014; Carr & Rees, 1979) | Established physics | The prediction of section 8: that each star carries its own share of the fabric |
These are glimpses. None of them, alone or together, separates the fabric from ordinary dark matter in a single galaxy, or from the existing theory that uses the same rule. They show that the possibility has not been closed, and they show where to look next.
Data. All macro data are public: rotation curves of 147 nearby galaxies (the SPARC sample), gravitational lensing around a very large sample of galaxies (the KiDS-1000 survey), rotation curves of distant galaxies seen as they were up to 10 billion years ago, published X-ray and lensing measurements of several hundred groups and clusters of galaxies, and published measurements of the motions of stars near the Sun (Bienaymé et al., 2014; Bovy & Rix, 2013; Brouwer et al., 2021; Chiu et al., 2016; Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Eckmiller et al., 2011; Eilers et al., 2019; Ettori et al., 2019; Genzel et al., 2020; Ghirardini et al., 2019; Gonzalez et al., 2013; Gopika & Desai, 2020; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Humphrey et al., 2011; Humphrey et al., 2012; Kuijken & Gilmore, 1991; Laganá et al., 2008; Laganá et al., 2013; Lelli et al., 2016; Lin et al., 2003; López-Corredoira, 2025; Lovisari et al., 2015; Nestor Shachar et al., 2023; Nitschai et al., 2021; Pratt et al., 2016; Sanderson et al., 2013; Sun et al., 2009; Vikhlinin et al., 2006; Zhang et al., 2013; Zhang et al., 2011).
Constants. The acceleration threshold is not fitted. It is fixed throughout as
This value was chosen by declaration and is close to the value others obtain by fitting () (McGaugh et al., 2016). Test 7 shows that the threshold does not follow the expansion rate as it changes over time, so the agreement with today’s expansion rate is recorded here as a coincidence of numbers and not as an explanation.
What was examined in the microverse. The model of the microverse is known in detail, so nothing there needed to be measured again. Its part in this work was to be checked and then used as the guide. Thirty-nine established statements of particle and atomic physics were verified against their sources. One direct comparison of numbers was made, between the threshold of the macro rule and the pull at the surface of an electron, a proton and a pion. It did not match. The published work on whether the atomic nucleus plays a part in the brain was reviewed.
What was tested in the macroverse. Twenty-seven tests were declared in advance and run on public astronomical data: on single galaxies, on our own galaxy, on galaxies seen as they were 10 billion years ago, on elliptical galaxies, and on several hundred groups and clusters of galaxies.
Why the work concentrated on the macroverse. Because it is the unknown. The microverse can be taken apart in a laboratory. The macroverse can only be watched from inside, and it raised question after question: what the unseen mass is, why it follows ordinary matter so closely in one kind of system and not in another, what part the stars play, and what the surroundings do. Each test answered one question and raised the next.
What is hoped for. One of those questions may be answered soon. The star catalogue due on 2 December 2026 will show whether two stars far apart pull on each other as the fabric predicts (section 8) (European Space Agency, n.d.-a). The prediction is on record.
What stands whatever that outcome is. Two things were met again and again in the test results and are not settled by that one measurement.
The author’s proposal is that these two, taken together, could explain many of the anomalies in the test results. There could be other explanations, and that proposal has not yet been tested. It is the part of the theory and hypothesis that most needs research.
What comes next. The work on these anomalies will continue, with the aim of confirming or denying the hypothesis and theory. Section 6.9 lists them and the test each one calls for.
The tests were not a list drawn up at the start. Each was run to answer one question, and each answer, pass or fail, set the next question.
1. Does one rule describe the unseen pull in a galaxy? Yes (Tests 1 and 7). One rule with one fixed number does it for 147 galaxies, and the number has not changed in about 10 billion years (Genzel et al., 2020; Lelli et al., 2016; Nestor Shachar et al., 2023). This gave the search its fixed point: inside a single galaxy the fabric follows the ordinary matter by this rule.
2. Is the rule the whole story? No (Test 2). In clusters of galaxies and around elliptical galaxies there is more pull than the rule gives (Brouwer et al., 2021; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019). So the question became what those systems have that a single spiral galaxy does not.
3. Does the fabric have a size or a shape of its own? No (Tests 4, 5, 6 and 13) (Gopika & Desai, 2020; Li et al., 2020; Salucci et al., 2012). It is not a wave of one length, and it is not an atom writ large. What these tests did find is that the core of the fabric has the same surface density at every core size. The fabric has no preferred scale.
4. Does it change with heat, age or cosmic time? No (Tests 7 and 8). The fabric behaves like a standing property of matter in space, and not like a product of a galaxy’s history.
5. What do the systems that depart from the rule have in common? The excess grows outward around ellipticals and grows with the amount of ordinary matter in groups and clusters (Tests 9 to 12, 14, 16 and 27) (Chiu et al., 2018; Eckert et al., 2016; Eckmiller et al., 2011; Gonzalez et al., 2013; Laganá et al., 2013; Lovisari et al., 2015; Pratt et al., 2016; Sanderson et al., 2013; Sun et al., 2009; Vikhlinin et al., 2006). It is not a sum over member galaxies (Tests 10 and 11). The author concluded that the law is not linear and that the surroundings matter.
6. Is anything missing inside a galaxy? No (Test 15). Frequency and distance add nothing once the pull is known. The rule is complete inside a single galaxy, and the missing piece lies outside it.
7. Is the missing piece the depth of gravity, or the point where gas can no longer cool? Depth: no (Test 17). The cooling point: not shown (Tests 16 and 27) (Rees & Ostriker, 1977). Both of those tests ran into the same obstacle, which is itself a finding: the two ways of weighing a group of galaxies do not yet agree (Akino et al., 2022; Pratt et al., 2019).
8. Is it the state of the ordinary matter? This was the turn. Clusters are mostly thin hot gas; galaxies are stars and cold gas. A formula with two states, locked to the stars and free around the hot gas, with no fitted number, described groups and clusters across the whole range of mass (Test 18) and then passed on systems not seen before (Test 20) (Lin et al., 2003; Zhang et al., 2011).
9. Does the lock hold up inside one galaxy, point by point? Yes, where it could be tested (Test 19) (Bienaymé et al., 2014; Bovy & Rix, 2013; Eilers et al., 2019; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; McKee et al., 2015; Nitschai et al., 2021; Zhang et al., 2013). The number that explains the Sun’s orbit also gives the pull up out of the disc.
10. What part do the stars play? Heavier stars account for the inner excess of ellipticals (Test 21) (Cappellari et al., 2013; Treu et al., 2010). Old and young stars lock the fabric alike, and cold gas appears to lock less (Tests 22, 24 and 26). The star emerged as the candidate unit of the fabric.
11. Can that be tested without hindsight? Yes. The prediction for wide star pairs (Test 25, section 8) was placed on record before the data exist.
In a single galaxy the total pull is given by the pull of the ordinary matter through one rule (Formula 2 of section 3.3):
Where the pull of the ordinary matter is strong, is nearly zero and Newton’s law holds. Where it is weak, the fabric supplies most of the pull.
What the tests add:
What this means for the search. The rule is a relation found by others, and these tests confirm it (McGaugh et al., 2016). It is the fixed point of the model: any account of the fabric must give this rule in a single galaxy. What comes next: a derivation of the rule and its threshold from the fabric.
If the fabric is locked point by point, its density at each place follows from the ordinary pull there (Formula 3). The test (Test 19) uses the pull straight up out of the disc of our galaxy, 1.1 thousand parsecs above the plane near the Sun. It is measured from the motions of stars and owes nothing to the rule (Bienaymé et al., 2014; Bovy & Rix, 2013; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; Nitschai et al., 2021; Zhang et al., 2013). The factor by which the rule boosts the Sun’s own orbit is 1.46, and it comes from the Sun’s distance from the centre and its orbital speed alone (Eilers et al., 2019; GRAVITY Collaboration, 2018). A point-by-point lock says the same factor must boost the upward pull.
| Predicted | Measured (nine published studies, 1991 to 2024) | Verdict | |
|---|---|---|---|
| Point-by-point lock | 64.1 ± 5.0 | 67.9 ± 3.8 | Pass |
| Round fabric of the size the rule implies | 54.1 ± 3.4 | 67.9 ± 3.8 | Fail |
(Units: solar masses per square parsec.)
The result was re-derived independently and stands. Its limits: this is one place in one galaxy; the nine measurements disagree with each other by more than their stated errors, some of them share data, and they are not all quite the same quantity; and an ordinary round dark halo of the usual density also passes (McKee et al., 2015). Higher above the disc the published measurements disagree among themselves, and one published study using a full calculation of this lock finds it fits as well as a round halo up to 4 thousand parsecs (Bienaymé et al., 2024; Bovy & Tremaine, 2012; Moni Bidin et al., 2012; Zhu et al., 2023).
What this means for the search. This is the first test here in which a prediction of the fabric, beyond the rule itself, passed. What comes next: the same comparison at greater heights and in other galaxies, where the lock and an ordinary halo part ways.
The rule alone falls short in systems of many galaxies. The observed mass is 1.5 to 2 times what it gives, and the gap grows with the amount of ordinary matter (Tests 2, 11, 16 and 27) (Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Eckmiller et al., 2011; Ettori et al., 2019; Ghirardini et al., 2019; Gonzalez et al., 2013; Laganá et al., 2013; Lovisari et al., 2015; Pratt et al., 2016; Sanderson et al., 2013; Sun et al., 2009; Vikhlinin et al., 2006).
The two-state formula (Formula 5) has no fitted number: the fabric is locked around each galaxy by the rule, out to a reach of half the spacing between neighbours, and it is free around the hot gas at the cosmic share of 5.36 (Planck Collaboration, 2020).
This pass is weak. Seventeen systems is a small sample, 16 of them are clusters, and two forms that differ by 35% both pass, so the data cannot choose between them. The second form passes by a thin margin; it was also declared with a cut-off formula meant for a compact host, where a spread-out host such as a cluster calls for a somewhat longer reach (Gajda & Łokas, 2016). The first form passes under every variation tried. In single galaxies all the ordinary matter is cohesive, so the formula reduces to the rule and every galaxy result is unchanged.
What this means for the search. For the first time one formula with nothing adjusted describes groups and clusters, and it does so by using the state of the ordinary matter, which is a distinction taken from the microverse. What comes next: a larger sample with stars and hot gas measured separately. No more such data could be found at present.
Ellipticals show more pull than the rule gives, and the excess grows outward (Tests 2b and 9) (Brouwer et al., 2021). Test 21 asked whether their stars are simply heavier than their light suggests. With a published correction the excess close to the galaxy disappears (Cappellari et al., 2013; Treu et al., 2010). The excess far out does not: about half of it remains.
Two points from the checks. The published star-mass correction applies mainly to the centres of ellipticals, so even the inner agreement is partly generous (La Barbera et al., 2019; Smith, 2020; van Dokkum et al., 2017). And the far-out region lies where a published study judges ellipticals not reliably isolated, so part of what remains may be the pull of neighbours (Mistele et al., 2024). A published analysis that raises the star masses, adds the hot gas around ellipticals and applies a stricter test of isolation finds no significant difference between ellipticals and spirals (Mistele et al., 2024).
What this means for the search. In the author’s terms the elliptical anomaly is three things together: the characteristics of the stars, the hot gas, and the surroundings. What comes next: a test with all three accounted for at once.
At the same total ordinary pull, places where the pull comes from cold gas show less total pull than places where it comes from stars (Test 24: −0.165 ± 0.047, or 3.5 sigma) (Lelli et al., 2016). An independent check reproduced the number exactly and removed two explanations: the shape of the rule at weak pull, and an excess of gas mass. A heavier star mass is disfavoured (Test 26): the data prefer almost no change in star mass, and the difference remains.
What is left is a choice the data cannot yet make. Either a unit of stars carries more fabric than a unit of cold gas, or the difference comes from the data: it is concentrated in galaxies whose distances are less well measured, and in the 66 galaxies with the best distances it falls to 1 sigma.
What this means for the search. If it is real, it is the first sign that the star is special to the fabric, as the author holds. What comes next: the same test on galaxies with the best-measured distances, and the prediction of section 8.
Many versions of the idea were tested and set aside. Together they show that the fabric is not:
Every one of these treats a system as standing alone, and most are sums. That is what the failures have in common, and it is why the author’s reading is that the missing piece is the surroundings and that the right law is not linear. Each failure removed a wrong turning. None of them closed the road.
These are the places where the results do not yet fit, each with the author’s proposal for what could be its cause and the test it calls for. Other explanations are possible in every row, and none of these tests has been run.
| Anomaly in the results | The author’s proposal | The test it calls for |
|---|---|---|
| The rule falls short in groups and clusters, and more so the more matter they hold | The state of the matter: the fabric is free around hot gas. The surroundings stretch the lock | A larger sample with stars and hot gas measured separately |
| Ellipticals show an excess that grows outward | The characteristics of their stars, their hot gas, and their neighbours | One test with all three accounted for |
| Stars and cold gas differ in the pull they carry | The star is the unit of the fabric | Galaxies with the best distances; the wide-pair prediction |
| The two ways of weighing a group disagree (Akino et al., 2022; Pratt et al., 2019; Sereno et al., 2020; Umetsu et al., 2020) | What is measured depends on how it is measured | Systems weighed both ways, compared one by one |
| Results shift with the assumed mass of the stars | The life and death of stars: faint stars and dead stars carry mass with little light | Star masses measured by an independent method |
| No test here could include what lies around each system | The surroundings are part of the fabric | Data on the surroundings of each galaxy and cluster |
| Not yet examined: the time when a galaxy’s rotation speeds up | That period, with the characteristics of the stars, could shape the fabric a galaxy carries | Galaxies caught at that stage, and the history of spin of each galaxy, set against its departure from the rule |
The work on these will continue, with partners, and the results will be reported whichever way they fall.
| # | What was tested | Result |
|---|---|---|
| 1 | Three forms of the rule on 147 galaxies (2,696 points) (Lelli et al., 2016) | The “thermal” form matches the best fitted curve (scatter 0.133). It is the known empirical relation (McGaugh et al., 2016) |
| 2 | The rule in 12 clusters of galaxies (Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019) | Fail. Observed mass is 1.5 to 2 times what the rule gives |
| 2b | The rule in lensing around spiral and elliptical galaxies (Brouwer et al., 2021) | Spirals pass (offset −0.006). Ellipticals fail (+0.18 to +0.21) |
| 3 | A cross-check using heat | Void |
| 4 | The fabric as a wave of one fixed wavelength; one surface density from dwarfs to clusters (Gopika & Desai, 2020; Li et al., 2020; Salucci et al., 2012) | Fail; marginal in galaxies, fail in clusters |
| 5 | Two phases with a floor (Lelli et al., 2016) | Fail |
| 6 | The atom’s equation copied unchanged to a galaxy | Fail |
| 7 | Threshold constant in time, against a threshold that follows the expansion rate (Genzel et al., 2020; Nestor Shachar et al., 2023) | Constant passes in every bin back about 10 billion years. Evolving fails |
| 8 | Heat breaks the connection (Lelli et al., 2016) | Fail |
| 9 | The elliptical excess grows with distance from the galaxy (Brouwer et al., 2021) | Declared fail; the outward growth itself is seen (+0.14 to +0.15) |
| 10 | A head-count sum of member galaxies, 12 clusters (Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019) | Outer radius passes, inner radius fails |
| 11 | The same on 133 new systems (Chiu et al., 2018; Gonzalez et al., 2013; Laganá et al., 2013; Sanderson et al., 2013) | Fail |
| 12 | An empirical trend with mass, fitted on half and tested on the rest | Two of three parts pass |
| 13 | A surface term plus a volume term (Gopika & Desai, 2020; Li et al., 2020; Salucci et al., 2012) | Fail |
| 14 | One switch-on distance for all galaxy masses | Fail / inconclusive |
| 15 | Does frequency or distance add anything at fixed pull, inside galaxies? (Lelli et al., 2016) | Adds nothing detectable. The test is not sharp |
| 16 | A switch at the mass where gas can no longer cool (Eckert et al., 2016; Lovisari et al., 2015; Rees & Ostriker, 1977; Sun et al., 2009) | Declared fail. The fail rests on one of three samples; on the other two all parts would pass. Unresolved |
| 17 | The depth of a system’s own gravitational well as the single variable | Fail on galaxies and on clusters |
| 18 | Two states with three forms of reach, no fitted numbers, 290 systems (Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019; Gonzalez et al., 2013; Laganá et al., 2013; Lovisari et al., 2015; Sanderson et al., 2013; Sun et al., 2009) | All three fail. One form passes 9 of 11 checks |
| 19 | The upward pull near the Sun: point-by-point lock against a round fabric (Bienaymé et al., 2014; Bovy & Rix, 2013; Eilers et al., 2019; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; McKee et al., 2015; Nitschai et al., 2021; Zhang et al., 2013) | Lock passes (0.6 sigma). Round fabric fails (2.7 sigma). Confirmed independently |
| 20 | Two-state formula on 17 systems not seen before (Lin et al., 2003; Zhang et al., 2011) | Both forms tested pass. The pass is weak |
| 21 | Are the stars in ellipticals heavier than their light suggests? (Brouwer et al., 2021; Cappellari et al., 2013; Treu et al., 2010) | Fail overall. The inner excess is explained; the outer is not |
| 22 | Do stars act on the fabric directly, in single galaxies? | Mixed. No clear effect, and none excluded below about 12% |
| 23 | Two-state formula on a larger unseen sample (Chiu et al., 2016; Humphrey et al., 2011; Humphrey et al., 2012; Laganá et al., 2008) | Incomplete. Only 8 further systems exist with the needed measurements |
| 24 | Do old bulge stars, disc stars and cold gas lock the fabric alike? (Lelli et al., 2016) | Bulge and disc stars alike. Cold gas differs at 3.5 sigma. Confirmed independently; cause unresolved |
| 25 | Prediction for wide star pairs | On record. To be decided after 2 December 2026 (European Space Agency, n.d.-a) |
| 26 | Does a higher star mass remove the gas difference? (Lelli et al., 2016) | Inconclusive. Heavier stars are disfavoured as the cause |
| 27 | Test 16 again, on 17 unseen systems weighed by X-ray gas pressure only (Eckert et al., 2016; Eckmiller et al., 2011; Lovisari et al., 2015; Pratt et al., 2016; Rees & Ostriker, 1977; Sun et al., 2009; Vikhlinin et al., 2006) | Fail. The rule falls short even in the smallest groups (1.72, seven systems, all with masses extended beyond the measured radius). The rise with mass is seen at 1.9 sigma. Not independently re-checked |
The fabric continuum is one fabric of connection running through the microverse and the macroverse. In the microverse it is the exchange that binds the parts of the nucleus and the atom, and it is most of the mass of ordinary matter. In the macroverse it is the unseen mass. There it is locked, point by point, to cohesive ordinary matter by one rule, out to a reach set by the surroundings, and it is free around diffuse hot gas, at the cosmic share. The star is its unit.
| Part of the model | From the microverse (established) | From the macroverse (section 6) | How it stands |
|---|---|---|---|
| The fabric is mass of the connection type | Most of the proton’s mass is the energy of its connection (Yang et al., 2018) | Most of the matter of the universe is unseen and acts only through gravity (Planck Collaboration, 2020) | A likeness. The hypothesis |
| It follows one law with a fixed constant | The bonds of the microverse are fixed by constants. The one that has been tested, for the electric bond, has not changed over billions of years (Damour & Dyson, 1996; Murphy et al., 2022) | One rule and one threshold in 147 galaxies, unchanged for about 10 billion years (Genzel et al., 2020; Lelli et al., 2016; Nestor Shachar et al., 2023) | Firm at the macro scale. Not yet derived |
| It is locked point by point | A bond belongs to the particles it joins | The upward pull near the Sun, with nothing fitted (Bienaymé et al., 2014; Bovy & Rix, 2013; Eilers et al., 2019; Guo et al., 2020; Holmberg & Flynn, 2004; Horta et al., 2024; Kuijken & Gilmore, 1991; López-Corredoira, 2025; McKee et al., 2015; Nitschai et al., 2021; Zhang et al., 2013) | Passed in one place, and checked |
| It has two states, locked and free | Bound matter and freed matter: the atom and ionised gas; the proton and free quarks (Bazavov et al., 2019; Gary, n.d.) | The two-state formula in groups and clusters, with no fitted number (Chiu et al., 2018; Eckert et al., 2016; Eckert et al., 2017; Eckert et al., 2022; Eckert et al., 2019; Ettori et al., 2019; Ghirardini et al., 2019; Gonzalez et al., 2013; Laganá et al., 2013; Lin et al., 2003; Lovisari et al., 2015; Sanderson et al., 2013; Sun et al., 2009; Zhang et al., 2011) | A weak pass on unseen systems |
| The surroundings set its reach | An atom in dense matter keeps its outer electrons only as far as its neighbours allow (Pethick, 2019) | Galaxies in clusters are cut short by the cluster’s pull; ellipticals show an excess that grows outward (Brouwer et al., 2021; Limousin et al., 2007) | Supported in form. Two forms of reach pass, and the data cannot yet choose |
| The whole is not the sum of the parts | The connection inside the proton acts on itself (Huston et al., 2024) | The rule that passed is non-linear, and the sums failed | Firm as a pattern |
| The star is its unit | The mass of a star follows from the constants of the microverse (Burrows & Ostriker, 2014; Carr & Rees, 1979) | Stars appear to carry more of the fabric than cold gas does, at 3.5 sigma | Open. The prediction of section 8 tests it |
The five formulas of section 3.3 state the model. Formula 1 adds one term to the source of gravity in Einstein’s equation: the energy of the exchange. Formulas 2 and 3 give the locked state, Formula 4 the free state, and Formula 5 the two together.
Two statements go with them. Radiation meets the fabric only through gravity: light is bent by the fabric and is not otherwise absorbed, emitted or scattered by it. And matter and the fabric are conserved together, because the fabric is the energy of the exchange between bodies.
Work by others over the last three decades relates the area of a surface in space, the entanglement across it, and the energy within it:
Jacobson (1995) derived Einstein’s equation from the thermodynamics of such surfaces. Ryu and Takayanagi (2006) proposed, and checked in simple cases, that in a class of model universes the entanglement across a surface is given by an area. Lashkari, McDermott and Van Raamsdonk, and Faulkner and co-authors (2013, published 2014) showed that in such model universes, close to the simplest one, the relation above gives Einstein’s equation to first order. These results are established for those models. They are not established for our universe, and they are credited here as the ground the hypothesis starts from.
The author’s addition is that the entanglement has a part that belongs to the exchange itself and not to the matter, and that this part gravitates.
Two conditions follow from established measurements, and the model has to meet both. The energy of the exchange must thin out as space expands in the same way that matter does (Planck Collaboration, 2020). And the fabric must already have been free of ordinary matter about 380,000 years after the beginning, before the first stars, because the pattern in the oldest light shows that most of the gravitating mass was not being pushed about by light as the ordinary matter then was (Bromm, 2013; European Space Agency, n.d.-b; Glover & Klessen, 2026; Hu & Dodelson, 2002; Planck Collaboration, 2020; Scott & Smoot, 2024).
So the star is not the origin of the fabric. On the model it is the unit through which the fabric is locked and through which it is revealed. The free state came first. That fits the place of the microverse in the model: its exchanges were at work from the beginning, and stars came later.
Three things would complete it, and each is work to be done.
Whatever the answer to the third, the first two remain to be researched, and the author intends to continue that work with partners and to report the results whichever way they fall.
If each star carries its own share of the fabric, locked point by point, then two stars orbiting each other at a very large separation should pull on each other more strongly than Newton’s law gives. The effect appears at separations of a few thousand times the Earth–Sun distance and is complete by about ten thousand, where the pull between the two stars has fallen to the order of the threshold.
This is the place where the microverse and the macroverse are tested together. The star is the characteristic body that gravity builds from particles, and its mass is fixed by the constants of the microverse (Burrows & Ostriker, 2014; Carr & Rees, 1979). The prediction asks whether the fabric begins there.
The prediction was computed from the rule exactly as used in the tests above, with nothing fitted, and placed on record at 13:18 UTC on 12 November 2026.
| Separation (thousands of Earth–Sun distances) | Pull compared with Newton |
|---|---|
| 1 | 1.00 |
| 3 | 1.05 |
| 5 | 1.18 |
| 7 | 1.30 |
| 10 and beyond | 1.335 |
(For a pair with a total mass of 1.5 Suns. The orbital speed is higher by the square root: about 15.5% for wide pairs.)
If the fabric does not reach the scale of single stars, the pull is Newton’s at every separation.
How it will be decided. By published analyses of the next release of the Gaia star catalogue (due 2 December 2026) from at least two independent groups (European Space Agency, n.d.-a). The hypothesis passes if they find the pull of wide pairs between 1.235 and 1.435 times Newton’s and each excludes Newton at 3 sigma. It fails if they find Newton’s value and each excludes 1.335 at 3 sigma. Anything else is undecided. The release date itself decides nothing; the analyses will follow it.
Three things the reader should know. First, the formula used is the standard one for the published theory that uses the same law (Milgrom, 2010). With that theory’s own inputs the published value is about 1.37; the value here, 1.335, comes from the inputs of this paper (Banik & Zhao, 2018). A pass would confirm the point-by-point lock at the scale of stars. It would not by itself separate this hypothesis from that theory. Second, analyses of the earlier release of the catalogue disagree, and the latest are still divided: some find the extra pull and some find Newton’s value (Banik et al., 2024; Chae, 2023; Chae, 2024; Chae et al., 2026; Chae & Yoon, 2026; Cookson et al., 2026; Hernandez, 2023; Pittordis & Sutherland, 2023; Saad & Ting, 2026). Third, a fail would mean that the fabric begins at a larger scale and that the star is its unit in form only.
Whatever the outcome, it will be reported. Checksums of the declaration and of the prediction file are given in section 15.
Section 5 put forward the possibility that the macroverse is a form of the microverse. This section sets the two side by side: what is alike, where they meet, how far the likeness goes, and what it would take to go further.
The left column is established physics. The right column is what the tests of section 6 found.
| The microverse | The macroverse | |
|---|---|---|
| Where the mass is | In the standard calculation about nine-tenths of a proton’s mass is the energy of the motion and binding of its parts, not the mass of the parts (Yang et al., 2018) | About five-sixths of the matter of the universe is unseen. It is known only through its pull (Planck Collaboration, 2020) |
| What light sees | Light and electrons fired at a proton meet only its quarks. The quarks carry only part of its momentum, roughly 60% in a recent calculation at the usual reference scale; the rest is in the connection, which light does not see (Alexandrou et al., 2020; Aschenauer et al., 2024) | The unseen mass neither gives off nor absorbs light. Light is bent by it, and that is the only way light shows it (Clowe et al., 2006) |
| How it changes with distance | Around an atom, empty space partly hides the electric charge, so it looks weaker from far away. Inside the proton the opposite holds: the connection grows stronger with distance (Erler & Freitas, 2024; Huston et al., 2024) | Around a galaxy the unseen pull, compared with Newton’s, grows with distance. That is the direction of the proton, not of the atom |
| Whether the parts add up | The connection inside the proton acts on itself, so the whole is not the sum of the parts (Huston et al., 2024) | The one rule that passed is not a sum. The formulas built as sums failed |
| Whether it has a size of its own | The connection has no fixed length; its energy grows with distance until, at about the size of a proton, it breaks (Bali et al., 2005) | The core of the fabric has the same surface density at every core size measured |
| Whether it changes with time | The constant that sets the strength of the electric bond, the one that has been tested, has not changed, to parts in a million or better, over billions of years (Damour & Dyson, 1996; Murphy et al., 2022) | The threshold of the rule has not changed over about 10 billion years |
A thing stays bound to its centre until its surroundings stretch it or heat frees it. Each row is established, except the last entry of the last row, which is the hypothesis.
| Scale | What is bound | Freed by the surroundings | Freed by heat | The free state |
|---|---|---|---|---|
| Quarks | Quarks in a proton | Pulled far enough apart, the connection breaks and makes new particles (Bali et al., 2005) | At about 1.8 trillion degrees, by a gradual change (Bazavov et al., 2019) | A hot soup of free quarks |
| Atoms | Electrons around a nucleus | A strong outside field strips the outer electron. In dense matter an atom keeps an outer electron only if there is room for its orbit between the neighbours (Ebeling et al., 2012; MIT Atomic and Optical Physics Wiki, n.d.; Pethick, 2019) | At around ten thousand degrees in a star’s outer layers (Fraknoi et al., 2022; Gary, n.d.) | Hot ionised gas |
| Galaxies | Stars, and on the hypothesis the locked fabric | The pull of a cluster cuts each galaxy short, at a distance set by the galaxy’s mass and its orbit (Gajda & Łokas, 2016; Limousin et al., 2007) | — | Stars, and on the hypothesis fabric, spread between the galaxies |
Two details stand out. The rule in the middle row, that an atom reaches only as far as its neighbours allow, has the same form as the reach that did best in the two-state formula of section 6.5. And the hot gas that fills a cluster of galaxies, around which the fabric was found to be free, is itself matter in the freed state of the middle row.
The star belongs to both.
The claim that one fabric runs through both scales was judged in three steps (section 5.3).
What this means for the search. The two scales share a model in form. That is a real finding, and it is what makes the possibility worth pursuing. It does not show that they are one thing: the forces differ at each scale, and no experiment yet shows one mechanism beneath them. What comes next: the prediction for the star; a derivation that gives the threshold from the constants of the microverse; and the question raised in section 6, whether the time when a galaxy’s rotation speeds up, together with the characteristics of its stars, could account for what the simple likeness leaves out.
The author asked how any such likeness can be measured “when we can see such a finite piece of time”. The question is exact. A person stands about ten powers of ten above the atom and about twenty-six below the observable universe, and sees a few decades of a history of billions of years (Davis & Lineweaver, 2004; National Institute of Standards and Technology, n.d.).
No slow process of the macroverse has ever been watched from start to finish. Three things stand in for time.
The microverse is measured in the same way: every atom of a kind is identical, so watching a great number for a short time stands in for watching one for a very long time.
All three rest on one assumption: that things are alike in other places and at other times. It has been checked within stated limits, in the light of distant gas and in a natural nuclear reactor that ran about 2 billion years ago (Damour & Dyson, 1996; Murphy et al., 2022). Where it cannot be checked, the science stops. The beginning of the fabric, before the oldest light, lies beyond all three. That is the present limit of the view from inside, and it is part of what the author means by a continuum.
This part of the hypothesis has not been tested. It is included because, for the author, it is where the theory began and what it is for.
“we are aware of what we are aware… not more”
“we have no reference of time”
“continuity… we are creating continuity during existence and are not aware”
The last of these is the heart of it: the possibility that we are creating our existence in a form we do not understand or see.
This section sets out what science has established that bears on that possibility, with the experiments and their figures, and marks plainly what is shown, what is disputed and what is not shown.
A mind is connection. What is learned is held, in large part, in the strength of the links between nerve cells (Takeuchi et al., 2014). This was first shown in 1973, when links in the brain were found to stay strengthened for hours after use (Bliss and Lømo), and the work on how memories are stored in such links was recognised by a Nobel Prize in 2000 (Kandel, 2000; Nobel Prize Outreach, n.d.-b). Reviews still call it a hypothesis broadly supported, with critical experiments remaining (Takeuchi et al., 2014). Abstract thinking, on this view, is the linking of links: relations among relations.
It runs on very little. The brain uses about 20 watts, about a fifth of the body’s oxygen for a fiftieth of its mass (Balasubramanian, 2021; Raichle & Gusnard, 2002). That energy ends as heat (Wang et al., 2014).
The author’s hypothesis is that the same principle of connection that runs through the microverse and the macroverse is at work here, at the level of the atomic nucleus and not only of chemistry, and that it reaches beyond the single mind (sections 1.2 and 4.6).
Two things can share one state, so that what is found at one is tied to what is found at the other, with nothing passing between them. This is entanglement. A single thing can also be in two states at once. This is superposition. Neither is in doubt.
| Experiment | What was shown | Figures | Standing |
|---|---|---|---|
| Three laboratories, 2015 (Vienna, Boulder, Delft) (Giustina et al., 2015; Hensen et al., 2015; Shalm et al., 2015) | Entanglement is real and cannot be explained by hidden local causes, with the known loopholes closed | Stations 58 m, 184 m and 1.3 km apart. The Vienna result stands at 11.5 sigma (National Institute of Standards and Technology, 2015) | Replicated |
| Nobel Prize in Physics, 2022 (Aspect, Clauser, Zeilinger) (Nobel Prize Outreach, n.d.-a) | Awarded for experiments with entangled photons | — | Established |
| Satellite, 2017 | Entanglement shared between two ground stations (Yin et al., 2017) | 1,203 km apart | Repeated by the same group in 2020 over 1,120 km (Yin et al., 2020) |
| Satellite, 2017 | The state of a particle of light sent from the ground to orbit by means of entanglement (Ren et al., 2017) | Up to 1,400 km | Single study |
| Large Hadron Collider, 2023 and 2024 (ATLAS Collaboration, 2024; CMS Collaboration, 2024) | Entanglement between the heaviest known particles, at the highest energies reached | More than 5 sigma in two separate experiments | Replicated. What it implies is debated (Bechtle et al., 2025) |
What entanglement does not do. It cannot be used to send a message (Ghirardi et al., 1980). That is an established theorem, and every experiment above respects it. A protocol exists by which energy can be drawn out at one place using entanglement and an ordinary signal from another, and it has been demonstrated in the laboratory; it, too, needs the ordinary signal and sends nothing faster than light.
This is the author’s order exactly (section 4.1): the relation first, the signal second. The relation is established. The signal is the proposal.
Quantum connection was first seen in single particles. The question for the fabric continuum is how far up in size it can be carried. The record so far:
| What | How large | Figures | Standing |
|---|---|---|---|
| Molecules in two places at once (Fein et al., 2019) | Up to 2,000 atoms each | More than 25,000 times the mass of a hydrogen atom | One laboratory with a long record |
| Two small mechanical objects entangled with each other (Kotler et al., 2021; Mercier de Lépinay et al., 2021; Ockeloen-Korppi et al., 2018; Riedinger et al., 2018) | In one experiment, a pair of metal drums of about a trillion atoms each (Kotler et al., 2021; National Institute of Standards and Technology, 2021) | About 70 trillionths of a gram each, held a few thousandths of a degree above absolute zero (Kotler et al., 2021; Mercier de Lépinay et al., 2021; Ockeloen-Korppi et al., 2018) | Four groups, 2018 to 2021 |
| Two diamonds entangled at room temperature (Lee et al., 2011) | 3 mm across, 15 cm apart (Belli et al., 2016) | The shared state lasted about a trillionth of a second (Belli et al., 2016) | Single study |
| A crystal in two states of motion at once (Bild et al., 2023) | 16 millionths of a gram | The two states differed by about a billionth of a billionth of a metre and lasted about ten millionths of a second | Single study |
| Mirrors cooled almost to stillness (Whittle et al., 2021) | 10 kg | Brought close to their lowest quantum state. Not a superposition | Single study |
Two things are plain from this table. The reach of quantum connection has grown, in thirty years, from single particles to objects that can be seen. And the larger the object, the colder and more isolated it must be and the more briefly the state lasts. Between a millionth of a gram and a brain, or a galaxy, lies a very great distance that no experiment has crossed.
Gravity and the quantum world. This is where physics is now trying to join the two scales by experiment, and it is the scientific form of the connection this paper proposes.
If such an experiment succeeds, it will show for the first time a quantum connection carried by gravity: the microverse and the macroverse joined in one measurement. That has not happened yet.
| Claim | What the evidence is | Standing |
|---|---|---|
| Enzymes use quantum tunnelling | Hydrogen passes through barriers it could not cross classically (Klinman & Kohen, 2013) | Established |
| Plants use long-lived quantum states to move energy | Reported in 2007. A 2020 reassessment found the states last less than a tenth of a trillionth of a second at room temperature, too short to matter (Cao et al., 2020; Engel et al., 2007) | Largely resolved against |
| Migrating birds sense magnetism through a quantum effect in a protein of the eye | The protein from a migratory bird is magnetically sensitive in the test tube (Xu et al., 2021) | Single study. Not shown in a living bird |
| Quantum states in the brain are destroyed at once | Calculated for ions and for the cell’s protein scaffolding. The calculation does not cover the spins of atomic nuclei | Established for what it covers |
| Nuclear spins in the brain could hold quantum states long enough to matter | Proposed in 2015. Later calculations give far shorter lifetimes than first claimed (Agarwal et al., 2023; Fisher, 2015; Player & Hore, 2018) | Proposal only. Contested |
| Isotopes, which differ only in the nucleus, change behaviour or anaesthesia | Reported for lithium in rats (1986, 2020) and for xenon in mice (2018) | Each a single study, none repeated. None separates the effect of nuclear spin from that of mass |
| The scaffolding inside nerve cells shows a collective quantum effect of light | Measured in purified protein in solution (2024) (Babcock et al., 2024) | Single study. Not shown in cells |
| A drug that stiffens that scaffolding delays anaesthesia | Eight rats; loss of consciousness delayed by about 69 seconds (2024) (Khan et al., 2024) | Single study |
| Consciousness arises from quantum collapse in that scaffolding (Hameroff & Penrose, 2014) | No positive evidence. A 2021 experiment ruled out the simplest form of the collapse it relies on (Derakhshani et al., 2022; Donadi et al., 2021) | Proposal only. Contested (McKemmish et al., 2009; McQueen, 2023) |
| The brains of people interacting fall into step | Well documented, through the ordinary senses (Burgess, 2013; Czeszumski et al., 2020; Dumas et al., 2010; Hamilton, 2021) | Established |
| The brains of people shielded from each other are correlated | One positive report in 2003; a later repeat found nothing (Ambach, 2008; Wackermann et al., 2003) | Not replicated |
The plain position. No experiment has shown entanglement in a living brain, and none has shown a link between quantum connection and consciousness. At the level of the atomic nucleus the question has not been closed, because the experiment that would decide it has not been done.
“energy does not die”
Physics agrees, and says something further.
So what a mind does is not erased from the universe. Its energy, and in principle its information, go on. They go on dispersed, as heat, in a form no instrument could gather back. What that information is in the form it then takes, and whether it could ever be understood, by energy or in any other form, is not known. The author’s hypothesis is that it is not lost to the fabric. Physics does not yet say whether that is so.
What this means for the search. The possibility of a connection running from the microverse to the macroverse is not a fringe idea. It is being pursued in laboratories now, through experiments on gravity and quantum states (Bose et al., 2025; Fuchs et al., 2024; Westphal et al., 2021). What this paper adds is the proposal that the mind belongs to the same continuum. That could be so. There could be other explanations of everything in this section, and nothing here shows it.
Energy does not die. This much is established physics, and it has been put plainly for a wide audience. The astrophysicist Neil deGrasse Tyson has pointed out that when a body is cremated, the energy held in its molecules does not disappear. It becomes heat, leaves as infrared light, and travels outward into space at the speed of light (IFLScience, 2026). The energy of a life goes on. What established physics does not say is that the pattern goes with it: what was known, thought and remembered. Whether anything of that is carried, by energy or in another form, is the question the author raises here. It is open, and this paper does not claim an answer.
The author was moved to this thought by the story of a child who loved the stars and hoped to study them.
These are for those qualified to run them. The author’s aim is to state the question precisely enough that it can be answered.
The work on this hypothesis and theory has only started. This section says what is not yet known, what would count for the hypothesis, what would count against it, and what the author and partners intend to do next.
In the model.
In the macroverse.
At the joint between the two scales.
On the other side.
Each of these can be decided by measurement. That is the test of whether a hypothesis is worth holding.
The author intends to carry this forward with partners and to report further updates as tests are made, whichever way they fall, until a verified model that connects the microverse and the macroverse is found or the possibility is ruled out.
Each ingredient of the hypothesis has a published relative. The author has drawn on them, and they are named here so that a reader can see what is new and what is not. Each of them, taken alone, has a known difficulty.
| Published idea | What it gets right | Its known difficulty |
|---|---|---|
| A change to the law of motion or of gravity below a threshold of acceleration (Milgrom 1983, three papers, and much later work) | The rule that single galaxies follow | Clusters of galaxies; colliding clusters (Angus et al., 2007; Clowe et al., 2006) |
| The radial acceleration relation (McGaugh, Lelli and Schombert 2016) | The rule in the same form as used here, found from 153 galaxies, with a fitted threshold of 1.20 × 10⁻¹⁰ m/s² where this paper fixes 1.08 × 10⁻¹⁰ | It is a relation found in the data, with no account of its cause |
| Dark matter as a medium that is polarised by gravity, as an insulator is by an electric field, but with the opposite sign (Blanchet 2007, and later work with Le Tiec and others) (Blanchet, 2009; Blanchet & Le Tiec, 2008; Blanchet & Le Tiec, 2009) | Gives the galaxy rule | Its equilibrium in a galaxy has been shown to be unstable (Stahl and co-authors 2022) |
| Dark matter that takes a connected, frictionless state in galaxies and an ordinary state in clusters (Berezhiani and Khoury 2015) | Galaxies, and the masses of clusters (Hodson et al., 2017) | Fits to a large sample of galaxies need unlikely star masses and do not behave as the rule does, and there is conflict with lensing far out (Mistele and co-authors 2022, 2023) |
| Gravity and the dark sector arising from entanglement (Verlinde, published 2017) | Agrees with lensing around galaxies (Brouwer et al., 2017) | Its prediction for the Solar System is far from what is measured (Hees and co-authors 2017) |
| Gravity strengthened in galaxies by the interaction of its own field with itself (Deur 2009 and later) (Deur et al., 2020) | Aims at the galaxy rule without unseen mass | The mechanism is disputed (Barker, Hobson and Lasenby 2023; Deur has replied) (Deur, 2023) |
| Extra apparent matter arising in a matrix model of space (Steinacker 2026) | A matrix in which everything is connected | The extra matter around a mass has negative net mass, and it has not been compared with data |
| Quantum states of atomic nuclei at work in the brain (Fisher 2015) | Names something in the brain that is shielded from its surroundings: the spin of a phosphorus nucleus inside a molecule | The lifetimes it needs are contested by later calculations, and no experiment has confirmed it (Agarwal et al., 2023; Player & Hore, 2018) |
How the fabric continuum differs.
What it does not yet do that some of them do. Several of the works above are complete mathematical theories from which predictions follow. The fabric continuum is not yet that. It has a model, five formulas, and a body of tests, and it lacks the law that would join them. Until it has that law it should be judged as a hypothesis with limited testing, which is how this paper presents it.
The table below takes the open gaps in present physics that this paper touches, and says for each what is established, what the fabric continuum offers, and how far the first stage of the work has taken it.
| The gap | What is established | What the fabric continuum offers | Where the first stage stands |
|---|---|---|---|
| General relativity and the standard model do not join | Each is confirmed in its own domain. No accepted theory contains both | One meeting point: mass. The connection energy that the standard model finds inside the proton is proposed as the unseen mass that general relativity needs at the large scale. One term is added to Einstein’s equation (Formula 1) | A proposal with a match of form at six points (section 1.1). No derivation yet. Work on a match of number is continuing |
| The nature of the unseen mass | Its gravity is measured on every scale from galaxies to the oldest light. No particle of it has been detected | It is not a new substance. It is mass of the connection type, in two states | Not separated from ordinary dark matter by any test here. The prediction of section 8 could begin to separate them |
| Why single galaxies follow one rule | The rule is measured (McGaugh, Lelli and Schombert 2016). In the standard account it has to emerge from how galaxies form; in the minority theory it is a new law of motion. Neither is settled | The rule is the lock of the fabric to cohesive matter, point by point | The rule and its fixed threshold were confirmed here on 147 galaxies and over about 10 billion years. The lock gave the measured pull near the Sun with nothing fitted. An ordinary round halo of the standard kind passes that test as well |
| Why the same rule falls short in clusters of galaxies | A known difficulty of every theory built on the rule: clusters need about 1.5 to 2 times more | A second state. Around diffuse hot gas the fabric is free, at the cosmic share, with no number adjusted | Passed its declared test on 17 systems not seen before. The pass is weak, a larger test is incomplete, and two forms of the reach cannot yet be told apart |
| Why the threshold is close to the speed of light times the expansion rate | A numerical coincidence noted since 1983. No accepted explanation | The threshold is fixed at that value in advance and not fitted | The fixed value works on the galaxies. The threshold does not change with the expansion rate over time (Test 7), so the link is to today’s value only, and it remains unexplained |
| Whether the unseen pull reaches down to single stars | Analyses of wide pairs of stars are divided | The star is the unit of the fabric, so the pull should be there | One dated prediction on record. To be decided by analyses of the catalogue due 2 December 2026 |
| Whether physics has a place for abstract thinking and consciousness | No accepted physical account. Quantum effects in the brain are proposed and contested | The same principle of connection, in form, and as a further hypothesis in fact, at the level of the nucleus | Untested. An experiment is described in section 10 |
What this comparison shows. On each gap the fabric continuum offers one idea where the works in the table above each address one or two. That breadth is what the author puts forward for discussion. On each gap the first stage has produced a declared test, a prediction, or a stated next step, and on none of them a proof.
The author’s statement about the fabric is a statement about transport:
“energy can travel through fabric… in all directions… without moving”
Transport phenomena is the established field that studies how momentum, energy and mass move. This section sets the hypothesis beside that field. It is a first-stage comparison: it says what is established, where the fabric continuum meets it, what the established results ask of the hypothesis, and what work comes next.
One form for three kinds of transport. Momentum, heat and mass each flow in proportion to a gradient: Newton’s law of viscosity, Fourier’s law of heat conduction and Fick’s law of diffusion (Bird et al., n.d.).
Energy can travel while the medium stays in place. Energy moves by conduction, by convection and by radiation (Ling et al., n.d.-a). A wave carries energy and momentum while each part of the medium only oscillates about its resting position (Moebs et al., n.d.). In a wire carrying a current, the charges drift at well under a millimetre a second, and the energy flows through the field in the space around the wire (Feynman et al., n.d.-b; Ling et al., n.d.-a).
Some transport loses nothing. Below 2.1768 K liquid helium flows with a viscosity at least 1,500 times lower than ordinary liquid helium, and heat travels through it as a wave (Balibar, 2006; Donnelly, 2009). A current in a superconducting ring has been watched for weeks, with an inferred decay time of about 100,000 years (File & Mills, 1963).
The two kinds of ordinary matter in a cluster transport differently. The stars of a galaxy form a collisionless system. For a galaxy of about 10¹¹ stars the time for encounters between stars to change their orbits is about 10¹⁷ years, millions of times the age of the universe, so each star moves in the smooth pull of the whole (Leiden University, n.d.). The hot gas of a cluster is a collisional plasma, with electron free paths of the order of 20 kiloparsecs (Markevitch & Vikhlinin, 2007; Nath, 2003). When a galaxy moves through that gas, the gas of the galaxy can be stripped away while its stars are left in place (Boselli et al., 2022; Gunn & Gott, 1972).
What collisions of clusters show. When two clusters pass through each other, the hot gas is slowed and the galaxies are not. The unseen mass is found with the galaxies. This limits how strongly the unseen mass interacts with itself to below about 1 cm² per gram (Markevitch et al., 2004; Randall et al., 2008). One study of 72 collisions gave a tighter limit of 0.47, which a later reanalysis relaxed to about 2 (Harvey et al., 2015; Wittman et al., 2018).
Nothing outruns light. Gravitational waves carry energy, and they travel at the speed of light to about one part in 10¹⁵. Entanglement alone carries neither energy nor a message. Teleporting a quantum state needs two classical bits for each quantum bit, and those travel no faster than light (Bennett et al., 1993).
At the smallest scale. When heat frees quarks and gluons from the proton, the fluid they form has the lowest friction for its entropy of any substance measured: a ratio between 0.08 and 0.23, against a conjectured lowest possible value of about 0.08 (Auvinen et al., 2020; Bernhard et al., 2019; Kovtun et al., 2005).
| Established transport result | The statement of the hypothesis it bears on | How it stands at this stage |
|---|---|---|
| A wave or a field carries energy while the medium stays in place | Energy travels through the fabric “without moving” | Consistent in form. The author’s statement describes a known kind of transport |
| Superfluids and superconductors transport without loss | The fabric as a connected state without friction | A likeness. Not tested |
| Stars are collisionless; hot gas is collisional and can be stripped | Two states: locked to cohesive matter, free around diffuse hot gas | The same two kinds of matter separate in transport as separate in the tests of section 6. Cold gas is collisional and yet counts as locked in the tests, so the two dividing lines are close but not the same |
| The freed state inside the proton is nearly frictionless | The free state of the fabric | A likeness of form between the micro and the macro. Not a match of number |
| In collisions the unseen mass stays with the galaxies and passes through | The free fabric, at 5.36 times the hot gas | A condition on the model: see 13.3 |
| No signal outruns light | “Waves become signals with information” | A condition on the model: see 13.3 |
Three conditions follow. The hypothesis has to meet each, and none is yet shown.
A proton, an atom, a star, a galaxy and a cluster of galaxies are all composite systems: wholes made of parts. The hypothesis makes a claim about every one of them, that the whole is not the sum of its parts and that nothing is external. The dynamics of composite systems is the established field that says when that is true and when it is not. This section sets the hypothesis beside it, as a first-stage comparison.
The mass of a whole is not the sum of its parts. The mass of a bound system is the mass of its parts plus the energy of their motion and of their interaction. Binding by an attractive force lowers it: a helium nucleus is 0.75% lighter than its two protons and two neutrons taken apart, and a hydrogen atom is lighter than its proton and electron by about one part in 100 million (Ling et al., n.d.-b; National Institute of Standards and Technology, n.d.). Confinement does the opposite: most of the proton’s mass is the energy of its fields (section 1.1).
In Newton’s mechanics the inside and the outside separate. The forces between the parts of a composite cancel in pairs, so its centre moves as a single body of the total mass under the outside forces alone, and its internal motion goes on separately (Feynman et al., n.d.-a).
A bound system can be weighed from its motions. For a bound system in balance, the energy of motion and the energy of binding are tied together, so the speeds and the size give the mass. Zwicky applied this to the Coma cluster in 1933 and found far more mass than its light accounts for. This was the first inference of unseen mass (van den Bergh, 1999; Zwicky, 1933).
Gravity treats a composite as it treats its parts, where this has been tested. The Earth and the Moon fall toward the Sun at the same rate to about 2 parts in 10¹³, although the Earth holds more gravitational binding energy (Williams et al., 2004). A neutron star and a white dwarf fall toward a third star at the same rate to about 2 parts in a million (Archibald et al., 2018; Voisin et al., 2020).
The separation fails when the outside pull is uneven. Tides stretch a composite and can strip its outer parts. Galaxies inside clusters have lost their outer halos in this way, and the stars stripped from them form a faint light between the galaxies, of the order of 10 to 20% of a cluster’s starlight depending on the method of measurement (Montes, 2022).
A composite can change its parts. The quarks inside a proton or neutron that is bound in an iron nucleus are distributed differently from those in a free one, by up to about 20%. This is established by experiment, and its cause is still debated (Hen et al., 2013; Hen et al., 2017).
The whole can differ in kind from the parts. An electron in a crystal moves as if its mass were anything from 0.07 to about 200 times its free mass, depending on the crystal (Stewart, 1984). Anderson (1972) argued that new properties appear at each level of complexity and cannot simply be read off from the level below.
Many bodies under gravity cannot be solved exactly. There is no general exact solution even for three, and the method is numerical simulation (Dehnen & Read, 2011).
| Established result | The statement of the hypothesis it bears on | How it stands at this stage |
|---|---|---|
| Mass of a whole = parts + energy of motion and interaction | The fabric is mass of the connection type | The principle is established. That the unseen mass is of this type is the hypothesis |
| Attractive binding lowers mass; confinement raises it | The fabric is positive, about five times the ordinary mass | The fabric could not be the energy of gravitational binding, which is negative and, for a cluster, of the order of one part in 100,000 (an estimate computed for this paper from the speeds of the galaxies). It would have to be of the confinement kind. This needs new physics (section 4) |
| In Newton’s mechanics the inside and outside separate, and pulls add | “The whole is not the sum of the parts” | The rule that passed is not a sum, and every version tested as a sum failed (section 6). Under such a rule the separation no longer holds |
| Tides strip a composite; galaxies in clusters lose their outer halos | The surroundings set the reach of the lock | Supported in form. Two forms of the reach passed the test on unseen systems, and the data cannot yet choose (section 6.5) |
| A nucleus changes the protons and neutrons inside it | The surroundings change what a body carries | A micro counterpart of the same behaviour. A likeness of form |
| New properties appear at each level | One principle of connection from the proton to the galaxy to the mind | Consistent with the weaker reading of the hypothesis, same in form (section 1.2) |
The author’s statement that nothing is external has a precise meaning in this field. Under the locked rule, the fabric at each point depends on the total pull of ordinary matter there. So the inside of a system is affected by the even pull of the larger system that holds it, which Newton’s mechanics and general relativity do not allow. The published theory that uses the same rule has the same property, known as the external field effect.
Two things follow.
The precise tests of how composites fall, quoted in 14.1, were made where the pull is strong. The Sun’s pull on the Earth and Moon is about 6 × 10⁻³ m/s², some 50 million times the threshold of the rule (computed for this paper), where the rule gives Newton’s law. They do not test the regime of the fabric. Wide pairs of stars do.
Everything reported in this paper can be checked.
For each of the twenty-seven tests the record holds:
It also holds the prediction of section 8, the reviews of the published literature, and the verification of the established statements against their sources.
| Item | Checksum (SHA-256) | Time (UTC) |
|---|---|---|
| Declaration 25: the star as the unit of the fabric | d42869637ae297077bad3eba9e1a966319d245a3ae914ca3d62484063db86ce9 | 12 November 2026, 13:10 |
| Prediction 25: the pull between wide star pairs | 430af72e50bfb17f0044679553ac4c7cd4923ebc07531a38a03fe9db222bcb63 | 12 November 2026, 13:18 |
A checksum is a fingerprint of a file. If one character of the file is changed, the checksum changes. Anyone who is later given the two files can confirm that they are the ones recorded here, and so that the prediction was made before the data that will test it.
The complete record is held by the author as one package and is available on request through maynardldokken.com.
| Package | Contents | Checksum (SHA-256) |
|---|---|---|
| fabric-continuum-record-2026-11-12.zip | 264 files: the declarations, results, code, independent checks, literature reviews and source verifications for Tests 1 to 27, with an index and a checksum for every file | a15e68b7cbecaa9b5c324ca89b1053a5ae2b4967e23cfd6b3f2c2610ae35c7f4 |
A reader who is sent the package can confirm it is the one recorded
here by computing its checksum. On most computers the command is
sha256sum fabric-continuum-record-2026-11-12.zip, and the
result should match the value above exactly.
The appendices, the two sections on transport and on composite systems, and the reference checks were added after the package was sealed. They were prepared from the package and from published sources, and they will be added to the next sealed version of the record.
Note on this list. 230 entries in one alphabetical list (APA 7). Of these, 189 were verified in full against a primary record. 37 were added with sections 13 and 14 and with section 10; where a title, year or author list was not confirmed from a page read for this paper, the entry says so. Four earlier entries remain marked “to confirm”.
Each test followed the same steps. A short declaration was written first. It stated the formula, the constants, the data to be used, the pass and fail criteria, and what the person drawing up the test already knew. The declaration was given a sha256 checksum and a UTC time before the data were opened. The test was then run once, and every number was reported. Most later tests (15 to 26) were re-derived independently, with new code from the declaration alone and compared the inputs with the published tables. Test 27 was not re-checked. Tests 2 to 9 and 11 to 14 have no independent check in the record.
Uncertainties come, in most tests, from a bootstrap: whole galaxies or whole systems are drawn again with replacement (usually 2,000 draws, with a fixed seed) and the statistic is recomputed. The standard error is the standard deviation of those draws. Points inside one galaxy are not treated as independent.
Fixed throughout, never fitted: the threshold a_c = c·H0/(2π) with H0 = 70 km/s/Mpc, which gives 1.0824 × 10⁻¹⁰ m/s². H0 = 67.4 and 73 were reported beside it in some tests. The rule is g = g_b / (1 − exp(−√(g_b/a_c))). For the SPARC galaxies the stellar mass-to-light ratios at 3.6 μm are 0.5 (disc) and 0.7 (bulge). The SPARC cuts are quality flag Q < 3, inclination ≥ 30°, and velocity error under 10 percent. These give 147 galaxies and 2,696 points.
Notes on reading the entries. “Verdict” is the declared verdict as the result file states it. “Check” names the independent check and quotes its headline. Where a number is not in any file of the record, the entry says “not in the record”. Numbers are copied from the files named. File names refer to folders of the record (section 15). Checks are named by their label in the record (for example W90, W100).
Estimates and standard errors are copied from the record. The z values and p-values were computed for this appendix with w110/stats.py; the full output is in w110/stats_out.txt and w110/B1_table.csv. No declared test was rerun or changed.
Formulas:
The normal p-value is an approximation. It assumes the bootstrap SE describes a normal sampling distribution. Where the record gives a bootstrap interval or a tail fraction, that is quoted as well and should be preferred.
| Test | Quantity | Estimate | SE | Reference | z | p (normal) | Bootstrap interval or tail in the record |
|---|---|---|---|---|---|---|---|
| 1 | H0 implied by the fitted threshold (check W74) | 75.10 | 4.85 | 70 | +1.05 | 0.29 | bootstrap interval of fitted threshold 1.024–1.318 × 10⁻¹⁰ (level not stated in W74) |
| 1 | rms of thermal form minus rms of fitted curve | 0.00047 | – | 0 | – | – | 95% [0.00000, 0.00373] |
| 4 | slope log ρ0–log r0, OLS (B predicts −1) | −1.16 | 0.10 | −1 | −1.60 | 0.11 | |
| 4 | same, orthogonal fit | −1.57 | 0.13 | −1 | −4.38 | 1.2e−5 | |
| 5 | P2 slope below 100 km/s (needs ≈ 0) | +0.87 | 0.23 | 0 | +3.78 | 1.6e−4 | |
| 6 | slope log r0–log Vflat (atom carry −1) | +0.86 | 0.28 | −1 | +6.64 | 3e−11 | |
| 7 | EVOLVING offset, z > 1.8 (RC100) | −0.120 | 0.029 | 0 | −4.14 | 3.5e−5 | Monte Carlo −0.115 ± 0.016 |
| 7 | CONSTANT offset, z > 1.8 (RC100) | +0.009 | 0.023 | 0 | +0.39 | 0.70 | |
| 7 | CONSTANT offset, z < 1.2 (RC100) | +0.052 | 0.029 | 0 | +1.79 | 0.073 | |
| 7 | EVOLVING, z > 1.8, RC41 cross-check | −0.081 | 0.039 | 0 | −2.08 | 0.038 | |
| 8 | within-bin Spearman ρ, heat against residual | −0.042 | – | 0 | – | 0.334 (one-sided, permutation) | from record |
| 11 | median ratio, accumulation formula (133) | 1.328 | 0.025 | 1 | +13.1 | ≪ 10⁻⁶ | 68% [1.290, 1.343] |
| 11 | slope of log(obs/rule) on log M500 | +0.169 | 0.0145 | 0 | +11.7 | ≪ 10⁻⁶ | |
| 12 | half-2 residual slope (T2) | +0.030 | 0.028 | 0 | +1.07 | 0.28 | |
| 13 | ρ_v from galaxies | 0.0011 | 0.0016 | 0 | +0.69 | 0.49 | |
| 14 | slope log R_on on log M_b | +0.240 | 0.244 | 0 | +0.98 | 0.33 | (against 0.5: −1.07) |
| 15 | b, frequency at fixed g_bar | −0.0129 | 0.0435 | 0 | −0.30 | 0.77 | 95% [−0.101, +0.069] |
| 15 | b, quality-1 only (information) | +0.0578 | 0.0511 | 0 | +1.13 | 0.26 | 95% [−0.045, +0.156] |
| 16 | P3 slope of log q on log M_b (140) | +0.1426 | 0.0314 | 0 | +4.54 | 5.6e−6 | no draw ≤ 0 (W101) |
| 16 | the same, X-ray samples only (found after the data) | +0.111 | 0.029 | 0 | +3.83 | 1.3e−4 | |
| 17 | 17A P1(b) observed minus law | −0.1612 | 0.0197 | 0 | −8.18 | 3e−16 | |
| 17 | 17B P1(b) observed minus law | −0.0781 | 0.0215 | 0 | −3.63 | 2.8e−4 | |
| 17 | 17A / 17B residual slope on 140 groups | +0.0512 / +0.0580 | 0.0311 / 0.0300 | 0 | +1.65 / +1.93 | 0.10 / 0.053 | |
| 18 | VA slope S1 / S3 | −0.006 / +0.056 | 0.023 / 0.027 | 0 | −0.26 / +2.07 | 0.79 / 0.038 | |
| 19 | L: OBS − prediction (67.90 − 64.29) | 3.61 | 6.28 | 0 | +0.57 | 0.57 | leave-one-out 0.20–0.96σ |
| 19 | G: OBS − prediction (67.90 − 54.11) | 13.79 | 5.11 | 0 | +2.70 | 0.0070 | leave-one-out 2.15–3.44σ |
| 20 | VT / VA slope (17 new) | −0.033 / +0.003 | 0.090 / 0.095 | 0 | −0.37 / +0.03 | 0.71 / 0.98 | |
| 22 | X1 / X2 / X3 / X4 slope b | +0.0965 / +0.0347 / +0.0400 / −0.0090 | 0.0560 / 0.0178 / 0.0154 / 0.0053 | 0 | +1.72 / +1.95 / +2.60 / −1.70 | 0.085 / 0.051 / 0.0094 / 0.090 | 95%: X2 and X3 exclude 0; X1 and X4 include 0 |
| 23 | VA slope (8 new) | +0.076 | 0.149 | 0 | +0.51 | 0.61 | |
| 24 | b_gas, all 147 | −0.1654 | 0.0470 | 0 | −3.52 | 4.3e−4 | |
| 24 | b_gas, quality-1 (92) | −0.1740 | 0.0617 | 0 | −2.82 | 0.0048 | |
| 24 | b_bul, all | +0.0160 | 0.0486 | 0 | +0.33 | 0.74 | |
| 24 | b_gas, distances not from Hubble flow (66; W98) | −0.066 | 0.068 | 0 | −0.97 | 0.33 | 3.2% of random 66-galaxy subsets give b_gas ≥ −0.066 |
| 24 | b_gas, Hubble-flow distances (81; W98) | −0.237 | 0.063 | 0 | −3.76 | 1.7e−4 | |
| 24 | difference between the two (W98) | −0.171 | 0.091 | 0 | −1.88 | 0.060 | |
| 26 | b_gas on B with f_A / on A with f_B | −0.1760 / −0.1298 | 0.0515 / 0.0851 | 0 | −3.42 / −1.53 | 6.3e−4 / 0.13 | |
| 27 | P3 slope of log q on log M_b (17 new) | +0.0531 | 0.0277 | 0 | +1.92 | 0.055 | 3.1% of draws ≤ 0 (one-sided) |
Lensing (Tests 2b, 9, 21). The record gives χ² with the published covariance for 15 bins. The p-values below were computed for this appendix, with p = P(χ²₁₅ > value), using the PLAIN rule at H0 = 70:
| Sample | Mean offset (dex) | χ²_cov / 15 bins | p | Normal-equivalent |
|---|---|---|---|---|
| Main isolated (KiDS) | +0.119 | 146.3 | 1.3e−23 | 10.0σ |
| GAMA isolated | +0.037 | 19.3 | 0.20 | 1.3σ |
| Late, Sérsic n < 2 | −0.006 | 12.9 | 0.61 | 0.5σ |
| Early, Sérsic n > 2 | +0.179 | 144.1 | 3.5e−23 | 9.9σ |
| Blue (late) | −0.054 | 24.2 | 0.062 | 1.9σ |
| Red (early) | +0.207 | 195.0 | 2.2e−33 | 12.0σ |
Results with no standard error in the record: Test 2 medians (only the scatter is given), Test 3, Test 9 inner/outer medians (per-bin errors only), Test 10, the Test 12 X-COP residual (−0.097), the Test 18/20/23 median ratios, and the Test 21 corrected medians. Test 25 has no data yet.
Threshold. 27 tests were declared. At an overall 5 percent level, Bonferroni gives a per-test level of 0.05/27 = 1.85 × 10⁻³. For a two-sided normal statistic that is |z| ≥ 3.11. This count is generous. Most tests report several sub-statistics, so the true number of comparisons is larger than 27.
Which positive findings clear it. A positive finding here means a non-zero effect that the record reports as found.
| Finding | z | Clears 3.11? | Comment |
|---|---|---|---|
| Gas against disc stars, Test 24, all 147 galaxies | −3.52 | Yes, narrowly | p ≈ 4.3e−4 |
| Same, quality-1 galaxies (92) | −2.82 | No | Same sign and size |
| Same, galaxies with distances not from the Hubble flow (66; W98) | −0.97 | No | Not distinguishable from zero. The difference from the Hubble-flow galaxies is itself only 1.88σ |
| Rise of the cluster shortfall with ordinary mass, Test 16 P3 | +4.54 | Yes | The declared test failed overall. The rise itself repeats the trend of Tests 11 and 12 (+0.169 ± 0.0145 on the earlier 133) |
| The same rise, Test 27 P3 (X-ray masses, 17 new) | +1.92 | No | Slope +0.0531 ± 0.0277, about a third of Test 16’s |
| The same rise after the depth law, Test 17 P3 | +1.65 / +1.93 | No | |
| Lensing excess around early types (Tests 2b, 9) | χ² p ~ 10⁻²³ (shape), 10⁻³³ (colour) | Yes | A departure from the rule, not support for it. After the star-mass correction of Test 21 about 0.1 dex remains, and all five outer bins lie below 10⁻¹³ m/s², where isolation is doubtful (W103) |
| Evolving threshold rejected, Test 7 (z > 1.8) | −4.14 | Yes | A rejection. In the smaller RC41 cross-check: −2.08 |
| Round fabric rejected, Test 19 (G) | −2.70 | No | Leave-one-out range 2.15–3.44σ. The chi-square among the nine inputs is 81.4 for 8 d.o.f. |
| Star variables, Test 22 (largest: X3) | +2.60 | No |
Also clearing the threshold, but as rejections of declared candidate formulas: Test 4 orthogonal slope (−4.38), Test 5 P2 (+3.78), Test 6 (+6.64), Test 17 P1(b) (−8.18, −3.63), and Test 18 VB S1 slope (−3.27).
Test 19 in detail. - Lock: prediction 64.1 ± 5.0, measurement 67.9 ± 3.8. Difference 3.61 ± 6.28, which is 0.57σ. - Round fabric: prediction 54.1 ± 3.4. Difference 13.79 ± 5.11, which is 2.70σ, p ≈ 0.007. - The lock’s pass is agreement within errors. It is not a detection of anything. The round fabric’s fail does not clear 3.11. - An ordinary round dark halo of the published local density gives 72.4 ± 7.4 and also passes. - So this test does not separate the lock from ordinary dark matter. It separates the lock only from the declared “round fabric of the size the rule implies”.
Test 7 (constant against evolving threshold). - The evolving threshold misses by −0.120 ± 0.029 at z > 1.8 (4.1σ) and −0.062 ± 0.015 over all 100 galaxies. Both clear the threshold as rejections. - The constant threshold sits at +0.009 ± 0.023 at z > 1.8. Its largest bin offset is +0.052 ± 0.029 at z < 1.2 (1.8σ). That is agreement, not a detection. - The two models differ by a median 0.148 dex at z > 1.8. No standard error of that difference is in the record.
Lensing, spirals and ellipticals (Tests 2b, 9, 21). - Late types by shape agree with the rule (χ² 12.9 for 15 bins, p = 0.61). Late types by colour sit at −0.054 dex (p = 0.062). - The main isolated sample, which Declaration 2 named, does not agree: +0.119 dex, p ~ 10⁻²³. The pass for spirals rests on a split by type that is not named in Declaration 2. - Early types depart strongly. The outer-minus-inner growth of Test 9 (+0.148, +0.140) is given without a standard error.
A pass by agreement is not a detection. Several results here are passes because a prediction, with nothing fitted, fell inside a range set in advance. Examples: Test 19 L, Test 7 CONSTANT, Test 2b late types, Test 20 VT and VA. Such a pass shows that the data do not contradict the prediction. Its strength comes from the declaration having been fixed first, so the window could not be moved to meet the data. It does not come from a significance level. A wide window, a small sample or large errors make a pass easy. A pass of this kind therefore cannot be counted as a positive finding in the Bonferroni sense. It also cannot be combined with other passes into a “number of sigma”.
Test 15.
Test 22. The 95% bootstrap intervals of b, multiplied by each variable’s middle range, give these upper ends for the effect E (computed for this appendix):
| Variable | Upper end of E (dex) | Factor |
|---|---|---|
| X1 | 0.111 | 1.29 |
| X2 | 0.103 | 1.27 |
| X3 | 0.091 | 1.23 |
| X4 | 0.093 | 1.24 |
Test 20 (17 systems). What a pass can and cannot exclude:
Test 23. 8 systems were found; 30 were required. No M_b bin holds 5 systems, so the bin criterion tested nothing. Slope SEs are 0.11–0.15. The test has essentially no power.
Galaxies. The rms of log10(g_obs/g_rule) over 2,696 points of 147 galaxies is 0.133 dex (0.1331; mean +0.0121). The fitted empirical curve gives 0.1327. The difference is 0.00047, with 95% bootstrap interval [0, 0.0037] (W74). Weighting each galaxy equally gives 0.1276 (W74).
Groups and clusters. The scatter is the standard deviation of log10(observed/predicted), in dex. Values marked † were computed for this appendix from per-system files of the record. COSMIC = M500/(6.364·M_b). RULE = M500/M_rule.
| Systems | n | Two-state V0 | VA | VT or VB | RULE | COSMIC |
|---|---|---|---|---|---|---|
| Test 18 S1 (the 138) | 138 | 0.085 | 0.091 | VB 0.090 | 0.096† | 0.092† |
| Test 18 S3 (the 140 groups) | 140 | 0.160 | 0.126 | VB 0.174 | 0.147† | 0.195† |
| Test 20 (17 new) | 17 | 0.099 | 0.108 | VT 0.101 | 0.083† | 0.105† |
| Test 23 (8 new) | 8 | 0.122 | 0.133 | VT 0.079 | 0.229 | 0.069 |
RULE medians, also computed here: 1.909 (S1), 1.923 (S3), 1.430 (17 new). The RULE scatter on S1, 0.096, agrees with the 0.0958 reported in Test 17.
Reading. The two-state formula mainly moves the median ratio toward 1. It does not consistently reduce the scatter. On the 138 it reduces it slightly (0.085–0.091 against 0.096). On the 140 groups VA reduces it (0.126 against 0.147), but V0 and VB do not. On the 17 unseen systems the plain rule has the smallest scatter (0.083). On the 8 of Test 23 the plain cosmic share is smallest (0.069). The declared criterion “STRENGTHENED” (Test 23) asked for lower scatter than both RULE and COSMIC. On Test 20’s data, computed here, neither VA nor VT would meet it.
Firm. The rule, with the threshold fixed by H0 = 70, describes the 147 SPARC galaxies with the same scatter as the fitted empirical curve (0.133 dex). This repeats a known relation. A threshold that follows the expansion rate is disfavoured at about 4σ in the RC100 sample, while a constant threshold is consistent with the data. The rule falls short in groups and clusters by a factor of about 1.5 to 2, and the shortfall rises with mass in several samples. The rise is not the same in every sample: one sample (Chiu et al. 2018) shows the opposite sign. Lensing around early-type galaxies departs from the rule. Many declared candidate formulas are rejected.
Suggestive. The gas-versus-disc-star difference of Test 24 clears the 27-test Bonferroni level only narrowly (3.52σ against 3.11). It does not clear it in quality-1 galaxies, and it is not distinguishable from zero in the 66 galaxies with the best distances. Its cause is unknown, and the check reads it as more likely a data or galaxy-property effect. The point-by-point lock of Test 19 agrees with one local measurement. The alternative it was set against fails at 2.70σ, which does not clear the Bonferroni level, and an ordinary round halo also passes.
Not established. That the two-state formula describes groups and clusters on unseen data: Test 20 is a weak, fragile pass on 17 systems that cannot choose between two forms, and Test 23 is incomplete. That stars act on the fabric directly (Test 22: nothing detected, effects up to about 25 percent not excluded). That frequency adds nothing inside galaxies (Test 15 lacks the power to exclude the effect size it named). Any link of number between the micro and macro scales (Appendix C3). No result here is a proof of the theory, and none separates the fabric from ordinary dark matter in single galaxies.
Section C1 copies correlations that were measured inside declared tests. Section C2 is new. It is descriptive, not a declared test, and was computed after the tests, for this appendix. Its code is w110/corr.py and its full output is w110/corr_out.txt. Sections C3 and C4 state what exists between the micro and macro scales, and what the study shows.
Test 15. Leftover error against orbital frequency at fixed pull (SPARC, 147 galaxies, 2,696 points). - Slope b = −0.0129 ± 0.0435 dex per dex; 95% bootstrap range [−0.101, +0.069]. - Spearman ρ of residual against W_bar inside six g_bar bins: +0.127 (p 7.1e−3), +0.023, +0.044, −0.011, −0.031, −0.165 (p 4.4e−4). The signs split 3 and 3. - Pearson r(log W_bar, log g_bar) = +0.906. At fixed pull, frequency is nearly fixed, which is why the test is not sharp. - Undeclared extras: within-galaxy b = +0.111, which the check (W100) puts at 1.6σ. Quality-1 galaxies: b = +0.058 (1.1σ).
Test 22. Four star variables (SPARC).
| Variable | Slope b ± σ | Spearman ρ (per-galaxy mean residual) | p |
|---|---|---|---|
| X1 star share | +0.0965 ± 0.0560 | +0.044 | 0.60 |
| X2 log SBeff | +0.0347 ± 0.0178 | +0.108 | 0.19 |
| X3 log SBdisk | +0.0400 ± 0.0154 | +0.165 | 0.045 |
| X4 Hubble type | −0.0090 ± 0.0053 | −0.114 | 0.17 |
The four variables are tied to each other and to g_bar: Spearman |ρ| 0.65–0.87. Point-level Pearson r with log g_bar is +0.696, +0.691, +0.404 and −0.650.
Test 24. Shares of bulge, disc and gas (SPARC). - b_bul = +0.0160 ± 0.0486. b_gas = −0.1654 ± 0.0470. In quality-1 galaxies: −0.1740 ± 0.0617. - The shares track the pull: corr(s_bul, log g_bar) = +0.68; corr(s_gas, log g_bar) = −0.73; corr(s_bul, s_gas) = −0.42. - Without the g_bar term, b_gas = −0.100.
Test 26. corr(s_gas, log g_bar) = −0.734 at f = 1, and −0.733 at the best-fit f. b_gas on the two halves: −0.1911 ± 0.0501 (B) and −0.1363 ± 0.0844 (A), both at f = 1.
The check of Test 24 (w98/CHECK-of-declaration-24.txt).
| Variant | b_gas |
|---|---|
| No g_bar control | −0.100 ± 0.037 |
| Linear control (declared) | −0.165 ± 0.047 |
| Cubic control | −0.199 ± 0.057 |
| 20 g_bar bins | −0.190 ± 0.058 |
| Within galaxies | −0.143 ± 0.043 (3.3σ) |
| Between galaxies | −0.120 ± 0.083 (1.4σ) |
| f_D = 1 (81 galaxies) | −0.237 ± 0.063 |
| f_D ≠ 1 (66 galaxies) | −0.066 ± 0.068 |
| Difference between the two | −0.171 ± 0.091 (1.9σ) |
| D > 16.9 Mpc | −0.302 ± 0.079 |
| D ≤ 16.9 Mpc | −0.154 ± 0.061 |
Cluster trends with ordinary-matter or total mass.
| Test | Sample | Statistic | Value |
|---|---|---|---|
| 11 | 133 systems | slope of log(obs/rule) on log M500 | +0.169 ± 0.0145 |
| 11 | 133 systems | slope, accumulation formula | +0.203 ± 0.020 |
| 12 | half 1 (68) | B on log M_b | +0.098 ± 0.031 |
| 12 | half 2 (70) | B on log M_b | +0.129 ± 0.028 |
| 12 | C18 (84) | B | −0.195 ± 0.045 |
| 12 | G13 (12) | B | +0.033 ± 0.043 |
| 12 | L13 (37) | B | +0.119 ± 0.018 |
| 12 | nearby, z < 0.2 (38) | B | +0.113 ± 0.017 |
| 16 | 140 new | slope of log q on log M_b | +0.1426 ± 0.0314 |
| 16 | S09 / L15 / E16 | slope | +0.085 / +0.155 / +0.054 |
| 16 | S09 + L15 (35; check W101) | slope | +0.111, z 3.9 |
| 17 | 140, after the depth law | residual slope, 17A / 17B | +0.0512 ± 0.0311 / +0.0580 ± 0.0300 |
| 27 | 17 new, X-ray masses | slope of log q on log M_b | +0.0531 ± 0.0277 |
| 27 | E11 / V06 | slope | +0.020 / −0.001 |
Test 16 binned medians of q against M_b for the 140 new systems: 1.410, 1.577, 2.090, 2.025.
Declaration 12 notes a built-in bias. M500 sits in the ratio, so a slope against M500 is pushed upward by the measurement error of M500 alone. For that reason Tests 12, 16 and 27 used M_b on the horizontal axis.
Lensing, early against late types. - Test 9, outer minus inner: early by shape +0.148, late +0.032; early by colour +0.140, late +0.042. - Test 21, early minus late over all 15 bins: shape +0.219 before and +0.108 after the 0.22 dex star-mass correction; colour +0.240 and +0.128. - W103’s other readings of D3, after the correction: shape +0.042 / +0.072 / +0.071; colour +0.190 / +0.148 / +0.111. - Test 2b sample means: early +0.179 / +0.207; late −0.006 / −0.054. The isolated sample is +0.119 and the non-isolated mass bins +0.128 to +0.233 (Test 14 declaration: +0.13 to +0.23).
Other within-test correlations. - Test 8 (RC100, within redshift bins, against the EVOLVING residual): heat h −0.042 (one-sided p 0.33), baryonic surface density +0.044, baryonic mass +0.085, bulge share −0.096, size +0.042, star-formation offset +0.060, σ0 alone +0.343 (p 0.001). The declaration warned that σ0 enters the authors’ own modelling. - Test 4: r(log ρ0, log r0) = −0.80. ρ0·r0 rises with luminosity (+0.155 ± 0.032 per dex) and with Vflat (+0.82 ± 0.15).
Descriptive, not a declared test, computed after the tests.
Galaxies. The SPARC data are prepared exactly as in Declaration 1 (w73/code/rar_test.py build(), loaded as in w83/code/freq.py): 147 galaxies and 2,696 points. The point rms is 0.1331 dex and the mean +0.0121, as in the record. The per-galaxy mean of log10(g_obs/g_rule) is ranked against each galaxy variable.
| Variable | ρ | p | n |
|---|---|---|---|
| star share 0.5L/(0.5L + 1.33 MHI) | +0.044 | 0.60 | 147 |
| log SBeff | +0.108 | 0.19 | 147 |
| log SBdisk | +0.165 | 0.045 | 147 |
| Hubble type T | −0.114 | 0.17 | 147 |
| log Vflat (where given) | +0.128 | 0.16 | 120 |
| log baryonic mass | +0.036 | 0.67 | 147 |
| distance D | +0.028 | 0.74 | 147 |
| inclination | −0.018 | 0.83 | 147 |
| quality flag Q (1 or 2) | −0.253 | 0.0020 | 147 |
The first four values reproduce Test 22 exactly. Among the variables themselves the ranks are strongly tied: - log Vflat with log baryonic mass: +0.95 - star share with log Vflat: +0.85 - T with log SBeff, log Vflat and log M_bar: −0.84 to −0.85 - distance with log baryonic mass: +0.65
Full matrix: w110/corr_galaxies_rho.csv (with _p and _n files).
Clusters and groups. Two sets are used: - A: w79/out/per_system.csv. 138 rows, of which the 5 S13 rows repeat G13 systems. The unique-133 version is reported in corr_out.txt as a sensitivity check. It changes no conclusion. - B: w84/out/new_systems.csv. 140 systems. Their stellar masses come from a relation in M500, so the gas-to-star ratio there is not an independent measurement.
The leftover errors are log(observed/rule), and log(observed/VA) with VA from w88/out/per_system_18.csv (the formula of w92/code/cutoff.py).
| Leftover | Variable | ρ (A, n = 138) | p (A) | ρ (B, n = 140) | p (B) |
|---|---|---|---|---|---|
| obs/rule | log M_b | +0.112 | 0.19 | +0.436 | 7.0e−8 |
| obs/rule | log M500 | +0.374 | 6.2e−6 | +0.775 | 3.0e−29 |
| obs/rule | log(gas/star) | +0.333 | 6.7e−5 | −0.040 | 0.64 |
| obs/rule | redshift | +0.818 | 1.7e−34 | +0.631 | 6.6e−17 |
| obs/rule | R500 | −0.017 | 0.84 | +0.673 | 9.0e−20 |
| obs/VA | log M_b | −0.208 | 0.015 | +0.196 | 0.020 |
| obs/VA | log M500 | +0.106 | 0.22 | +0.593 | 1.2e−14 |
| obs/VA | log(gas/star) | +0.275 | 1.1e−3 | −0.286 | 6.3e−4 |
| obs/VA | redshift | +0.490 | 1.0e−9 | +0.440 | 5.2e−8 |
| obs/VA | R500 | −0.141 | 0.098 | +0.558 | 7.5e−13 |
Bold marks correlations that survive the primary Bonferroni level below.
Count and correction. - Correlations of a leftover error with a variable (the primary family): 9 for galaxies + 20 for clusters = 29. Bonferroni at an overall 5 percent: p < 1.72 × 10⁻³ (|z| ≥ 3.13). - Correlations among the explanatory variables themselves: 36 (galaxies) + 20 (clusters). Counting everything computed gives 85, and p < 5.9 × 10⁻⁴. - 13 of the 29 survive the primary level, and 11 survive the stricter one. All 13 are cluster correlations. No galaxy correlation survives. The strongest galaxy one, with the quality flag (ρ = −0.253, p = 0.0020), misses narrowly. Q takes only the values 1 and 2.
What the surviving cluster correlations reflect (from the within-sample sensitivity in corr_out.txt, section C2d): - Redshift (A, ρ = +0.82). This is mostly a difference between samples. The 84 distant SPT clusters (C18, median obs/rule 2.04, SZ-calibrated masses) sit above the nearby samples (1.47–1.53). Inside C18 alone the correlation with z is +0.70, while the correlation with M_b turns negative (−0.50). Mass method, sample and redshift cannot be separated here. - M500 and R500. M500 is in the numerator of the ratio, and R500 grows as M500^(1/3). Part of these correlations is built in, as Declaration 12 warned. In B, R500 for the XXL systems is derived from M500. - log M_b in B (+0.44). This is the rank form of the Test 16 P3 rise. In A it is weak (+0.11) because the C18 sample runs the other way. - Gas-to-star ratio for VA (+0.28 in A, −0.29 in B). The signs disagree between the two sets, and in B the star mass is not measured. No single reading follows. - After VA, the correlation with log M_b falls to about ±0.2 (p 0.015 and 0.020) and does not survive. This matches Test 18 (VA slope on S1 −0.006 ± 0.023). The correlations with redshift and M500 remain.
Files: w110/correlations.png (figure), corr_galaxies_rho.csv / _p / _n, corr_clusters_A_rho.csv / _p, corr_clusters_B_rho.csv / _p, corr_primary.csv (the 29 with Bonferroni flags), galaxy_variables.csv, cluster_variables.csv.
Work on a numerical correlation between the micro and the macro is ongoing. The tests declared so far were first-stage. What they produced is set out below.
Sets of that kind could be:
With data of this kind the link between the micro and the macro can be tested as a correlation and not only as a likeness.
It shows that inside single galaxies the leftover error of the rule is not linked, at any corrected level, to star share, surface brightness, type, flat speed, baryonic mass, distance or inclination. This agrees with Tests 15 and 22. It shows that in groups and clusters the shortfall of the rule is linked to total mass, size and redshift, and that much of this is a difference between samples and mass-measurement methods, not one trend.
It does not show that any variable causes the shortfall. The variables are strongly tied to one another (|ρ| up to 0.95), and the analysis was chosen after the tests had been seen. The 13 surviving correlations are descriptions of these data sets, not findings. A correlation that matters would have to be declared in advance and tested on systems not yet opened, as the main tests were.