Physics describes the world with remarkable precision, yet some of its most basic features are simply measured and used, never explained. Admissibility Physics asks whether they trace back to one limit: that any region of the world can hold only finitely many distinctions at once. Follow that idea carefully, and much of what we normally take as given begins to follow from it.
A1 — at every causally connected region, only finitely many distinctions can be held at once. Everything structural is meant to follow from taking that one limit seriously.
The enforceability of distinction — Paper 1 ↗No dials. A measured value enters only as a comparator at the very end, never as an input; every registered check declares what it consumes, and none of it is free.
The executable engine ↗Every load-bearing claim is a named check that runs in the verification suite and is tagged by how strongly it is established. Nothing on this page is asserted by hand.
Run the bank yourself ↗Outputs of constraint logic, compared with experiment — 39 tested so far, 32 within 3σ, median error 0.37%.
See the prediction table ↓The Bekenstein–Hawking law sets a black hole's entropy equal to a quarter of its horizon area — a thermodynamic quantity read off a geometric one, exactly, with no account of why the two domains should speak to each other. The holographic bound, the gauge–gravity correspondence, the CPT and spin–statistics theorems: each is a connection between branches of physics that we write down without deriving from anything deeper.
Alongside the connections sit the questions physics measures but never explains. They are taken as inputs — accurate, essential, and unexplained.
Admissibility Physics is a candidate for the layer underneath: one program among several attempts to name what these connections and open questions might share. It begins by taking a single limit seriously.
Measured, not explained —
Not taken as given here. Three carrier requirements, run against every compact simple Lie algebra, leave only this template — and cost minimization then fixes the three colours.The structure of admissible physics — Paper 2 ↗
A budget question: each generation costs a fixed slice of capacity, and three fit under the 61-channel ceiling while a fourth would overflow it.Admissibility constraints & field content — Paper 4 ↗
The stable fixed point of a two-sector capacity competition — the ledger share sin²θW = 3/13, within about 0.2% of the measured value.the full derivation — Paper 42 ↗ · the electroweak sector — Paper 18 ↗
Read off the same ledger: the 42 vacuum channels of 61 give ΩΛ = 42/61, and the absolute density lands roughly 120 orders down — without any tuning.The capacity ledger — Paper 8 ↗
Selected, not assumed — four dimensions are the setting in which the geometry closes consistently into Einstein's equations.Dynamics & geometry — Paper 6 ↗
Picture one of those animations that zooms into a fractal: every scale reveals another, without end. Mathematics permits this — a line divides forever, a smooth field varies at any wavelength. But the world does not seem to be endlessly zoomable. Every real distinction has to be held somewhere — a photon heading north, a spin pointing up in a field, the bound state of a hydrogen atom — and a finite region can hold only so many at once.
The move is to put a floor under physics: a positive cost to shifting one durable arrangement into another, and a finite budget for how many can be held side by side. Treat physical law as the bookkeeping of that limit, and the familiar puzzles stop looking separate.
Incompatible observables, gauge redundancy, the curve of spacetime, a crowded competition settling on one outcome — read this way, they are the same overspend, surfacing at different layers of one finite ledger.
Take the floor seriously, and structure follows —
Non-closure. A finite budget forces trade-offs. Not every observable can be simultaneously definite — the structural origin of quantum incompatibility.
Locality becomes gauge structure. Local enforcement means patches overlap. The equivalent descriptions of one state form a gauge bundle with a connection.
A gauge group from the budget. The capacity-optimal way to factor the enforcement dimensions selects SU(3) × SU(2) × U(1) — no other product group is admissible.
The weak mixing angle. Capacity competition between gauge channels has a single stable fixed point: a source ratio of 3/13, within about 0.2% of the measured Weinberg angle.
Gravity from shared load. When subsystems share enforcement cost, the feasibility penalty is quadratic, local, and universal. The unique object with those properties is a metric tensor.
One ledger, two interfaces. The 61-channel budget that fixes the Standard Model also sets the cosmic energy split: ordinary, dark, and vacuum as 3, 16, and 42 of 61.
The arrow of time. Recording a distinction spreads it irreversibly into the surroundings. That one-way step is the arrow of time, and the laws of thermodynamics follow as corollaries.
Action from a minimum step. The framework's partition function is Connes' spectral action; expand it and the cosmological constant, Einstein–Hilbert gravity, the gauge terms, and the Higgs potential fall out as coefficients.
Carried far enough, the bookkeeping outputs specific values — not fitted to data, but read off the ledger and then compared with experiment. Teal is what the framework derives; caramel is what nature measured.
Two gauge sectors draw on the same capacity. Written as a least-cost balance, that competition has a single stable fixed point — the ledger share sin²θW = 3/13 ≈ 0.2308, read off the channel counting and never fitted. Pinning the measured effective angle exactly takes a further, spelled-out bridge of scale, scheme, and running, which lands it about 0.2% away.
Full derivation — Paper 42 ↗ · the electroweak sector — Paper 18 ↗
The same budget of 61 channels that fixes the Standard Model also partitions the cosmos: 3 ordinary, 16 dark-matter, 42 vacuum. The 42 vacuum channels give the dark-energy fraction ΩΛ = 42/61 = 0.6885 — within 0.05% of Planck, one integer read two ways.
The capacity ledger — Paper 8 ↗ · the dark sector — Paper 35 ↗
Three carrier requirements — a complex trilinear interaction, a chiral sector that breaks time-reversal, and an abelian grading — are run against every compact simple Lie algebra. Only the SU(Nc) × SU(2) × U(1) template survives, and cost minimization then picks Nc = 3.
Each generation of matter costs a fixed slice of capacity. Three fit under the ceiling set by the 61-channel budget; a fourth would overflow it. The count is forced by the budget, not chosen — and the same accounting fixes the anomaly-free matter content.
See all 48 predictions in the table →
Each result is carried at a stated level of confidence — from analytically forced to structurally grounded — and the program names the measurements that would refute it. Read correctly, the claim is modest in form and large in consequence: physics has no parameters to fit here, only constraints to honour.
It is fair to ask what a program like this is allowed to assume. The honest answer is short. One assumption: at every causally connected region, only finitely many distinctions can be held at once. Everything structural is meant to follow from taking that seriously.
Three coherence conditions arrive with it, the moment a distinction is allowed to cost something — a positive floor, so nothing moves for free; a least-cost tie-break, so when several arrangements are admissible the cheapest is the one selected; and a non-degenerate cost spectrum, so the costs do not all collapse together. These are not extra physics. They are what it means for a cost to be a cost.
And one scale. The framework fixes every ratio it touches, but a ratio is not a size. Turning dimensionless structure into kilograms and metres takes exactly one external number — the Planck magnitude — and every mass rides it: the electroweak scale, the confinement scale, the cosmological constant, the mass of the top quark. That one number is not derived, and the program says so plainly. Assumptions that fix only dimensionless structure cannot hand you an absolute size.
One assumption, three coherence conditions, one scale. Nothing else is fed in — and the next section is how that is kept true.
Everything that goes in —
At every causally connected region, only finitely many distinctions can be held at once — the single substantive claim the whole framework rests on.The enforceability of distinction — Paper 1 ↗
Maintaining a distinction costs something bounded below — the floor that makes holding things in place load-bearing rather than free.Paper 1 ↗ · the minimal core — Paper 13 ↗
When several arrangements are admissible, the one realized is the cheapest — the argmin rule at the heart of the Principle of Least Enforcement Cost.What physics permits — Paper 0 ↗
The costs do not all collapse to one value, so the cheapest arrangement is unique up to gauge equivalence — what keeps the selection well-posed.The calculus of finite continuability — Paper 10 ↗
The framework fixes every ratio it touches, but a ratio is not a size. Turning dimensionless structure into kilograms and metres takes exactly one external number, and the program says so plainly.Absolute mass scales — Paper 28 ↗
A program that claims to derive measured constants faces one besetting temptation: to let the target value leak into the derivation, so that a “prediction” is really a fit in a derivation’s clothes. The defense here is mechanical, not a promise.
A measured value enters only as a comparator — at the very end, after the number is already fixed — never as an input. Every registered check carries an explicit guard recording that no measured target was consumed, and the verification suite refuses any derivation caught reading its own answer. Before a derivation even begins, an audit-first pass checks whether the result already sits in the bank under another name, so the framework does not quietly re-fit what it has already earned.
That is what the 0 means. There are no dials. A result is either forced by the constraints or it is marked open and left open. When the framework is wrong it cannot be tuned back into agreement — which is precisely what lets a failed prediction count against it.
How a number could cheat — and what stops it —
A measured value is admitted only at the very end, as a comparator after the number is already fixed. The derivation never sees its own answer, and every check records that no measured target was consumed.The executable engine ↗
Every registered check lists exactly what it consumes. There is no slot for a tunable constant — a hidden dial would surface as an undeclared input and fail the audit.The executable engine ↗
Before a new derivation begins, an audit-first pass greps the bank for the result under any name, so the framework cannot quietly re-fit something it has already earned.The executable engine ↗
Every claim carries an epistemic grade, and a result moves up the ladder only when a registered check earns it. A silent promotion has nowhere to hide.The executable engine ↗
One rule about what distinctions can coexist, carried forward until structure is forced. Nothing here is chosen to fit — each step is a registered theorem, and each links to the paper that proves it. Hover the map to trace how the results depend on one another, all the way down to the single assumption.
THE SAME CHAIN, IN WORDS — HOVER ANY STEP FOR MORE
This is the whole input. Everything below is forced from it; nothing is chosen to fit. Read it — Paper 1 ↗
The same crack gives the rest of quantum mechanics: Hilbert space over the complex numbers, the Born rule, and completely-positive evolution all follow as the cheapest consistent bookkeeping. Read it — Paper 5 ↗
Run against every compact simple Lie algebra, only this product group survives — the gauge group is selected, not assumed. Read it — Paper 2 ↗
The same accounting fixes three generations of matter: each costs a fixed slice of capacity, and a fourth would overflow the ceiling. Read it — Paper 4 ↗
Ordinary matter, dark matter, and dark energy come out as 3, 16, and 42 parts of 61 — roughly 5%, 26%, and 69%. Read it — Paper 8 ↗
Each lands within a fraction of a percent of measurement — and because no measured value was ever read as an input, the agreement counts as a test. Read it — Paper 42 ↗
Geometry is bookkeeping: distance is the least cost of correlating two things, curvature is where capacity varies from place to place. Read it — Paper 6 ↗
The program isn't only a set of papers — it's executable. Every derivation is a registered check that runs in a verification suite and is tagged by how strongly it's established. Nothing on this page is asserted by hand.
Every load-bearing claim is a named check function; importing the apf package registers them all at load time.
Run the bank yourself ↗The full suite runs in well under a minute, and the build refuses to ship if a single check fails.
One module per result, each declaring its dependencies and its epistemic grade.
Quantitative outputs compared against experiment — 39 tested so far, 32 within 3σ.
Across the tested predictions; the mean absolute error is 3.83%.
EPISTEMIC STATUS — HOW STRONGLY EACH RESULT IS ESTABLISHED
Those four tags are not decoration — they are how the program stays honest over time. Every claim carries one, and a result moves up the ladder only when a registered check earns it. The same tags let the framework track what is genuinely forced, what still rests on a named identification, and what is honestly open — so progress is visible, and a quiet downgrade has nowhere to hide. The bank is the ledger of record; nothing here is asserted by hand.
The predictions sit at the leaves of a deep funnel: one assumption at the top, widening into 48 testable numbers below. A single failed prediction at any leaf indicts the whole chain above it. Of 39 predictions with current experimental values, 32 fall within 3σ — mean error 3.83%, median 0.37%.
Counts are read from the bank's dashboard_data.json and reflect the current release.
A selection from the 48 quantitative predictions. The framework produces the left column from constraint logic; the right column is the measured world.
| Quantity | Predicted | Measured | Deviation | Status | Source |
|---|---|---|---|---|---|
| Weak mixing angle sin²θW | 3/13 = 0.23077 | 0.23122 | 0.19% | [P_structural] | P42 ↗ |
| Dark-energy fraction ΩΛ | 42/61 = 0.6885 | 0.6889 | 0.05% | [P] | P8 ↗ |
| Gauge group | SU(3)×SU(2)×U(1) | SU(3)×SU(2)×U(1) | exact | [P] | P2 ↗ |
| Fermion generations Ngen | 3 | 3 | exact | [P] | P4 ↗ |
| Spacetime dimension d | 4 | 4 | exact | [P] | P6 ↗ |
| Strong coupling αs(MZ) | 0.1179 | 0.1179 | 0.0% | [P_structural] | P18 ↗ |
| CKM mixing (6 elements) | capacity ratios | PDG values | 6/6 < 5% | [P_structural] | P4 ↗ |
Epistemic tags: [P] proved from the one assumption · [P_structural] forced up to one named identification. Full scorecard and falsifiability conditions are in the papers.
The spine of the program is ten short papers, each building on the one before. Here is the core of each in a few sentences — with a link to read it in full, and the code behind all of them on GitHub. After the ten sits the capstone — Paper 40 — where the separate threads converge into a single picture.
Start with a plain criterion: a physical difference is real only if the world can hold it in place against disturbance, and holding it costs something. Most differences can be defended one at a time. But some pairs cannot — defending both at once costs more than defending each alone, and the order you do it in changes what budget is left over.
That order-sensitivity is the crack quantum mechanics grows from. When the order of two operations changes the outcome, the accounting can no longer be ordinary commuting arithmetic; it has to be the non-commuting kind quantum theory uses. Paper 1 makes the link precise and shows where the familiar complex Hilbert space starts to appear.
Demands that are each affordable on their own can overspend when they meet at the same interface — the budget simply does not add up. Paper 2 calls this non-closure and shows it is the engine behind competition and structure throughout the framework.
Non-closure cannot be carried by simple additive symmetry; it forces the richer, non-abelian kind. Working through every compact simple Lie algebra leaves only SU(3) × SU(2) × U(1), and the cheapest version has three colours. A filtered scan of thousands of candidate matter contents leaves exactly one survivor: the Standard Model's 45 fermions. Counting the channels gives a fixed budget of 61 — which in turn sets the cosmic energy split, about 69% dark energy and the rest matter.
Paper 2 gave the space its rooms; Paper 3 gives it a direction. Once a distinction is recorded by spreading into its surroundings, no local action can pull it back. That irreversibility is the arrow of time — derived here, not assumed as a boundary condition.
Along the way entropy gets a concrete meaning: it is the capacity currently tied up in the correlations an interface is holding. The familiar laws of thermodynamics follow as corollaries, and the rule that physical evolution must be “completely positive” — usually taken as an axiom — becomes a theorem.
Why three families of matter, and not two or four? Paper 4 turns it into a budget question: each generation costs a fixed amount of capacity, and three fit under the ceiling while a fourth would overflow it.
The same accounting pins the weak mixing angle at 3/13 — within 0.2% of the measured value — as the stable point of a competition between two sectors, fixes the full Standard-Model matter content as the one anomaly-free option that survives out of thousands, and reframes dark matter not as a missing particle but as a geometric correlation the ledger requires.
Paper 1 showed why the accounting must be non-commuting; Paper 5 builds the rest of quantum mechanics on top of it. Hilbert space, the Born rule for probabilities, tensor products for combining systems, and the rules for how states evolve all come out as the cheapest consistent way to keep the books where joint distinctions cannot be separated.
Two payoffs stand out. The reason quantum theory uses complex numbers — rather than real or quaternionic ones — is derived, not chosen. And measurement stops being a mysterious “collapse”: it is simply a change in which bookkeeping scheme is in force.
Where do space, time, and gravity come from? Paper 6 treats geometry as bookkeeping: the distance between two things is the least cost of correlating them, and curvature is what appears where capacity varies from place to place. Run this in four dimensions and Einstein's equations emerge as the only consistent closure.
The picture also says where ordinary physics stops. Smooth equations of motion hold only in well-behaved regimes; at a horizon, at saturation, or the moment a record locks in, the equations give out — even though the underlying accounting still makes sense.
Physics is usually summarised by a Lagrangian — a single expression you write down and then take on faith. Paper 7 derives it instead. It first shows that any step leaving an irreversible record must cost at least a fixed minimum; identify that minimum with action and it is Planck's constant.
Then comes the central identity: the framework's partition function turns out to be the same object as Connes' spectral action from non-commutative geometry. Expanding it term by term hands back the cosmological constant, Einstein–Hilbert gravity, the gauge field terms, and the Higgs potential as separate coefficients. The Standard-Model Lagrangian is not postulated — it is read off.
Paper 8 is where the single ledger ties the very small to the very large. The same budget of 61 channels that fixes the Standard Model also partitions the cosmos: ordinary matter, dark matter, and dark energy come out as 3, 16, and 42 parts of 61 — roughly 5%, 26%, and 69%.
From the same accounting it reads off a value for the dark-energy density, a Hubble constant near 70 (sitting between the two clashing measurements), and a formula for the temperature of the cosmic microwave background that matches to a third of a percent. One integer, two interfaces — the particle world and the universe at large.
Paper 9 asks, carefully, what it would take to get general relativity's weak-field predictions out of the cost-of-comparison picture. It lays out a sequence of gates a derivation has to pass and shows that the “clock” part already recovers the gravitational redshift around a mass.
It is also candid about the gap: recovering the redshift alone does not yet fix the “ruler” part, and it names the exact remaining theorem that would close it. This is the framework showing its work — a real result paired with an explicit open target.
Paper 10 is the grammar underneath everything else. Its single primitive is a continuation: in a given context, one distinction is allowed to continue as another within a capacity budget. Everything is then phrased in that language — a field is an equilibrium pattern of where the substrate carries a continuation, gauge symmetry is relabelling that preserves it, entropy is its irreversible blurring, and dynamics is the selection among allowed continuations.
It does not prove the downstream theorems by itself. It supplies the common vocabulary and the discipline by which every later branch has to be checked.
If the first ten papers build the framework, Paper 40 is where it gathers. Treating temperature, entropy, and the laws of thermodynamics for a system whose distinctions are finite and costly to hold, it finds the program's separate threads — the cost floor, the 61-channel ledger, the arrow of time, the cosmological constant, the horizon — reappearing as faces of one bounded ledger, read thermodynamically.
Between perfect symmetry, where distinction has been spent away, and the void, where none has yet been drawn, sits the finite middle the whole framework has been describing. This is where the unification stops being a claim and becomes a single picture.
The ten papers above are the spine. A few more are the natural next stops: the plain-language overview, the self-contained core, the runnable engine, and the sharpest quantitative results. Everything is open-access in the admissibility_physics community on Zenodo.
Paper 0 — the narrative layer. What the framework takes physics to be built on, what each commitment does, and what the technical papers derive from it. The gentlest way in.
Not a manuscript but a program. Thousands of registered checks tie the one assumption to every derived constant — and you can run the whole verification suite yourself.
This is a candidate offered for scrutiny, not a finished edifice. If a derivation looks wrong, a prediction looks refutable, or a connection looks worth pursuing, I want to hear it — sharp disagreement included. Researchers interested in collaborating on the open frontiers (the dark-sector empirical program, the Yang–Mills continuum limit, the electroweak precision arc) are especially welcome.
The corpus is currently open-access on Zenodo, but not yet on arXiv. I am looking for an arXiv endorser in hep-th, hep-ph, or gr-qc to help bring the work to a broader audience. If you are eligible to endorse and the program is something you would be willing to vouch for, please reach out at brooke.ethan@gmail.com.