K4 Cell Framework·v2.0 public review, frozen 2026-07-08·1003 pages·Zhihua Liang, no institutional affiliation·not peer reviewed·errata open
This work is an attempt to compute them instead — off one finite object, with no dial to turn.
There are about twenty of them. They set the size of an atom and the rate the universe is flying apart. Physics measures each one — the electron's mass, how strongly light grips charge, how much of the sky is dark matter — writes it into the equations by hand, and moves on.
19 in the minimal Standard Model; 26 to 28 once neutrino masses are included, depending on whether neutrinos are Dirac or Majorana. Cosmology adds its own.
A calculation with no dial to turn cannot be rescued when it is wrong. So this page prints its worst row next to its best, numbers its own open gaps, and names the measurement that would end it. The freedom that remains here is discrete — which embedding, which channel — and those are the open questions listed further down.
the experiment stops resolving after the first 8 significant digits
m_μ/m_e · the experiment resolves 8 of these digits
a standing commitment nobody can currently check
CONDITIONAL on E8, an interface the author lists as open
A picture of an idea, not a picture of the sky. It was generated on the author's machine from a fixed random seed by a Zel'dovich toy model — the textbook first-order approximation that produces filaments, nodes and voids. No telescope data is shown, nothing in it was fitted, and no quantity from this framework enters it. Between the smallest length physics can name and the farthest thing we can see is about 61 factors of ten; this framework's single cosmological comparison sits at the far end of that span, and it is the worst row on this page.
The row above is conditional. It depends on a map from the object's few ingredients into the full particle content of the Standard Model, and that map is not proved — the author lists it as open in his own published errata, entry E8. The cosmological-constant problem is not solved here, and nothing on this page claims it is. Not peer reviewed: two carved-out papers are under review (CQG-116665, JGP13432); the 1003-page monograph is not submitted and is not on arXiv.
Every number below is read off one finite object. Here it is, in three steps.
Four points. Every pair joined — with four points that is six connections. On each point sits a small quantum degree of freedom with three settings. Every connection pushes its two ends to be unlike each other. Now the key fact: with three settings shared among four points, that is impossible. Some pair always collides. The object never settles. It is permanently strained, and the strain has structure.
Think of four singers holding a chord. What you hear is in no single voice; a held note alone is not a chord. Transpose all four together and nothing changes, because only the intervals are audible. Here it is the same and stronger: the absolute setting at any one point means nothing at all. Inside the object, everything there is to compute — every distance, every coupling — is carried by the six relations, and none of it by the four points. The points are only where the relations have to attach.
The space of this object's quantum states carries one natural geometric quantity. Its real part is a distance — a Fisher metric. Its imaginary part is a curvature — a Berry curvature. Call the distance the metric leg and the curvature the gauge leg. Gravity lives on the first; Yang–Mills theory — the kind of field theory the other three forces are built from — lives on the second. That both come out of the same object is settled. The bet is everything after that: that gravity and Yang–Mills therefore arrive together rather than being glued together afterwards. What has been written down so far is a conditional Einstein–Yang–Mills response, and its conditions are the open interfaces drawn in the route below.
Four sites, six edges, three local states per site: 3⁴ = 81 basis states before dynamics and constraints are applied.
81 is small enough to print. Below is every basis state of the starting space, drawn as a tetrahedron with one colour per site. Thick edges join two sites that share a colour.
Same-colour edges per state, averaged over all 81exactly 2= 6 edges × 1/3
0 of 81. Four sites, three colours means two sites must share one; K4 has every edge, so that edge exists. The frustration is not an assumption — it is arithmetic.
These are product basis states before dynamics and constraints. The ground state is an entangled superposition, not one of these 81 cells. Nothing here derives physics — it fixes the size of the object and shows the frustration is structural.
These eleven are the rows that already have something public to be checked against. The rest of the census is in the manuscript tables. The worst row is the BAO absolute distance scale: χ² = 34.40 for 13 degrees of freedom, 3.28 σ-equivalent. It is in the same list and on the same bar as the best one — one lane down, because a χ² over 13 degrees of freedom is a different kind of number from a single row's pull, not because it is being kept out of sight.
carried by an open interface
the experiment stops resolving after the first 2 significant digits
physical trace-arm gate readout conditional on E6
carried by an open interface
the experiment stops resolving after the first 3 significant digits
mass tower / mechanism-F
carried by an open interface
the experiment stops resolving after the first 2 significant digits
Casimir-flag readout conditional on E8
carried by an open interface
the experiment stops resolving after the first 3 significant digits
exact rational — the digits never stop
CKM typed readout conditional on E8
carried by an open interface
the experiment stops resolving after the first 8 significant digits
charged-lepton protocol conditional on E8
carried by an open interface
the experiment stops resolving after the first 4 significant digits
closed typed electroweak readout conditional on E3, E8
carried by an open interface
The framework commits no digits on this row. This is a scale-line comparison, and here the prediction is the blunter of the two sides.
Type-7 colour scale-line conditional on E5
These are shape and scale diagnostics. They do not average with the rows above.
computed 30.135
measured χ² = 34.40 / 13
absolute-scale diagnostic
computed frozen K4 CPL curve
measured shape-only comparison
shape-only diagnostic
Emitted as point values that sit below every current bound. Below a bound means untested, not confirmed.
computed ≈ 0.059 eV
selected normal-ordering branch
computed 3.69 meV
Majorana point emission
There is no single headline score here, and there will not be one. The three lanes are different kinds of number and averaging them would be a category error.
The full census is 31 primary predictions, 20 companion and readout refinements, a set of rare-B_s protocol rows, and one structural cosmology profile, κ₄(r). The manuscript tables are the authority on each row's status.
Measured values and their uncertainties are transcribed from the comparison table in the public-review repository; they are not independently sourced here. That transcription is the step worth auditing.
The Cabibbo parameter — how strongly the quark families mix — comes out of this framework not as a decimal but as an exact fraction: 9/40. Do the division. 9 ÷ 40 = 0.225, exactly, and it stays exactly 0.225 however far you carry it. The measured value is 0.22501 ± 0.00068. You have just checked one row of this ledger by hand.
What you have not checked is whether 9/40 is what the framework must produce. That step runs through the embedding of the seed content into the full Standard Model carrier, which the author lists as an open interface (E8) and which review Target 8 exists to attack. An exact rational landing on the measured value is striking. It is not yet a derivation.
measured, with its error bar0.22501 ± 0.00068
0.225 sits inside the bar
Continuous fitted parameters: 0. There is no dial. A parameter is a dial, and the Standard Model has about twenty-five of them, each turned into place by measurement. Here there are none. The object is four points, three states per point, the complete graph, one uniform antiferromagnetic coupling on all six edges. Even the overall coupling strength cancels out of a dimensionless ratio, and in the two upper lanes above — the comparable pulls and the diagnostics — every row is one. The two one-sided rows are not: Σ m_ν and m_ββ are given in eV, so they carry an absolute mass scale that this cancellation argument does not cover. That is the first place to look for a hidden input.
Physical postulates: one — the existence of the K4 cell lattice, taken as definitional data. Within its stated class, the cell's own shape (four sites, three colours, complete graph, uniform antiferromagnetic coupling, integral class-sum normalisation) is derived from internal consistency rather than assumed. The width of that stated class is itself a review target.
If you find a measured quantity entering on the left-hand side of any row, that is the disproof. Say which row and where. Open an issue
This is the route from the finite object to the comparison surfaces, drawn with its gaps as gaps. A solid link is exact or model-internal. A broken span is a named interface the author has published as open — the label in the gap is his own erratum code.
MAIN OPEN BRIDGE finite K4 substrate → faithful physical realization
electroweak lift — a named interface, not an implicit identification
carries: sin²θ_W(M_Z)
the non-abelian colour carrier is still a separate construction
carries: α_s(M_Z)
the geometric response scalar Λ_geo is not the stationary physical scalar Λ_eff
carries: Λ_eff ℓ_*²
generation extension, full normal embedding, real branch, 48-row current-symbol surjectivity
carries: sin²θ_W(M_Z) λ_C m_μ/m_e CKM J
relative lift and natural gluing (DC-G); underlying-class injectivity (DC-U)
no numeric row — this one carries the type-catalogue and sector claims
Now pull all of them at once. What is left is a theorem about a finite graph — true, machine-checked, and not a statement about nature. That is the honest floor of this project, and it is why the numbers above are offered as a target rather than as a result.
A theory with dials survives any experimental result, because you re-fit. This one has no dials, so after a miss there are exactly two moves: find a genuine mistake in the derivation and publish the correction, or say the framework is finished. There is no third move, because there is nothing to turn.
Normal ordering is derived. Inverted ordering is categorically excluded inside the model.
A confirmed inverted ordering ends the framework.
JUNO · DUNE · Hyper-K
sign(sin δ_CP) × sign(η_B) = −1, so with the observed baryon asymmetry the framework requires sin δ_CP < 0 in the standard matter convention.
A measurement of sin δ_CP > 0 falsifies it.
The orientation itself is deliberately not derived — it is spontaneously selected vacuum data. That is exactly what makes the lock a test rather than a fit.
DUNE · Hyper-K
Upper octant, 4/7.
A settled lower octant contradicts it.
DUNE · Hyper-K
m_ββ = 3.69 meV, emitted as a point value rather than a range.
Currently below every bound, which means untested, not confirmed.
next-generation 0νββ
The two-term readout gives Λ_eff ℓ_*² = 2.93×10⁻¹²² against an observed 2.89×10⁻¹²² (±1.5%) — conditional on E6, where the frozen PDF conflates the geometric response scalar Λ_geo with the stationary physical scalar Λ_eff.
A Λ determination at 0.5% precision or better separates the two-term readout from the leading-order value.
next-generation cosmology
sin²θ_W(M_Z) = 0.231219995 — conditional on the electroweak-lift and Standard-Model-carrier interfaces (E3, E8).
If the measurement sharpens and moves, no repair is available.
precision electroweak
transcribed from the frozen public-review release: 2026-08-29
updated 2026-08-29
The monograph itself has not been submitted to a journal and is not peer reviewed. Two papers carved out of it are under review:
Previously submitted to Physical Review D (2026-07-05) · desk-rejected at editorial screening, not sent to referees (2026-07-10)
The monograph is not on arXiv.
Lean 4 is a proof assistant: you restate a theorem in a language a computer can check, and the file does not compile unless every step follows. At the 2026-07-08 release, a row-by-row sign-off ran over all 771 labelled theorem rows of the manuscript: 727 lean_certified, 19 proved_core_only, 4 needs_lean_node, 21 prose_empirical_open. The root corpus is 313 modules. Every compiled statement rests on exactly the three standard logical axioms of the mathematical library — propext, Classical.choice, Quot.sound. The project contributes no axiom, no opaque declaration and no sorry of its own.
lean_certified 727proved_core_only 19needs_lean_node 4prose_empirical_open 2144 rows are not certified, and are labelled as such.
Certified means the Lean statement carries the same logical force as the written one at the granularity that statement declares. Most of these certificates are carrier-capped: an analytic ingredient the mathematical library does not yet supply — a clustering bound, a continuum-limit input — enters as an explicitly named hypothesis rather than as a hidden assumption. Certification is a claim about logical structure. It is not an empirical claim about nature. A machine-checked proof of the wrong statement is still a proof of the wrong statement, and the honest reading of these 727 rows is that the bookkeeping is clean, not that the physics is right.
The public-review PDF, and its checksum:
sha256sum K4_Cell_Framework_v2.0-public-review.pdf
727d7c1fd690655a7a487afd66ba39b12f5b0eae5a622e2a224005a02d27c479The PDF is deliberately frozen at 2026-07-08. Confirmed Chapter 3 corrections found by a later adversarial audit are published in the errata; the bytes were never silently replaced. That is the whole policy, and you can check it.
Every number on this page is written into it at build time from one data file, ledger.json, and the build recomputes from that file what it can — every pull, every resolved-digit count, the Lean bucket totals — then checks that the stored figures actually appear in the page. If a recomputation disagrees, the build fails rather than publishing the disagreement. What the build cannot do is check that file against the manuscript: the ledger is transcribed by hand. That transcription is the step worth auditing, and the file is served at /ledger.json for exactly that.
The most useful review is not agreement. A short comment identifying the first clear failure point, missing assumption, incompatible convention, or overstrong claim is worth more than applause.
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Zhihua Liang (梁植华)