PDF-only public-review release of the K4 cell framework monograph.
This public-review repository supports technical review of the manuscript Microscopic Algebraic Theory of Holographic Emergence: Zero-Parameter Derivation of the Standard Model, Cosmology, and Emergent Gravity from a Four-Site SU(3) Substrate.
The primary review artifact is the manuscript PDF. The public repository is a stripped release surface: it contains the PDF, reader/review metadata, rights notices, issue templates, and a public review log, but not the private authoring tree or full reproduction workspace.
- Current public-review version:
2.0-public-review - Release date in citation metadata:
2026-07-08 - Primary PDF:
K4_Cell_Framework_v2.0-public-review.pdf - Citation metadata:
CITATION.cff - Concept DOI (resolves to the latest version):
10.5281/zenodo.18892076 - v1.0 version DOI (archived):
10.5281/zenodo.20314752 - Focused review targets:
REVIEW_TARGETS.md
Relative to the 1.0 public-review PDF (2026-05-20), the 2.0 manuscript (1003 pages) adds, among other results:
- Prediction census: 31 primary numbered predictions plus twenty companion refinements (two Yukawa anchor rows promoted to primary), backed by a machine-audited row-level corpus.
- Cosmological constant: a two-term readout of the gate exponent
placing
Lambda ell_*^2within0.9 sigmaof the observed value, with the subleading term shared verbatim with two laboratory observables. - Neutrino sector: normal ordering derived (inverted ordering
categorically excluded); the Majorana phase emitted as a point value
(
m_bb = 3.69 meV); thetheta_23octant selected; the leptogenesis sign lock, giving the standing falsifiersin(delta_CP) < 0for DUNE/Hyper-K. - Structure theorems: CP orientation shown to be spontaneously selected vacuum data (a layer-wise machine-exact blindness theorem); the readout conservativity theorem closed, including a complete census of the substrate's topological memory; and a cell-bootstrap theorem — within its stated class, the structure of the K4 cell (four sites, three colours, complete graph, uniform antiferromagnetic coupling) is derived from internal consistency, so the monograph's axiom base is the existence of the cell lattice.
- Lean 4 formalization: a 313-module root corpus with a global axiom-purity certificate, and a release-grade row-by-row sign-off ledger over all 771 monograph theorem rows (727 rows Lean-certified at full granularity; the remainder explicitly tiered, not advertised as certified).
- The corrections announced for v1.0 (the Part 1 operator-norm
reconstruction chain, found by the project's internal adversarial
audit on 2026-06-02) are incorporated in the 2.0 text; see
ERRATA.md.
This is a scholarly public-review surface for a monograph-scale theoretical physics manuscript. It is intended for reading, citation, technical criticism, proof checking, numerical/protocol review, and public issue discussion.
It is not a peer-reviewed journal publication, an OpenReview venue, a general
software distribution, or a full reproduction package. Public access to this
repository does not imply that unreleased source, code, internal notes, or
working directories are part of the citable v1 release package, nor does it
change the rights layout described in LICENSE and
LICENSES/OPEN-REVIEW.md.
As a statement of scholarly purpose, this project is shared in the spirit of human inquiry and a common future for humanity. Scientific truth, if found, belongs to humanity; the structures of nature are not private property.
That ethos concerns the facts, ideas, mathematical structures, physical methods, and experimental comparisons presented for study, testing, criticism, and citation. It does not replace the repository's rights notices, which govern the authored expression, figures, tables, release materials, and redistribution of substantial portions of the work.
The manuscript develops a K4 four-site SU(3) substrate as a candidate microscopic source for:
- quantum geometric tensor structure and the Fisher/Berry split;
- emergent spacetime geometry and Yang-Mills curvature;
- a full-order Einstein-Yang-Mills package;
- K4 representation data and multi-cell tensor-network structure;
- typed laboratory, cosmological, and interaction readout functors;
- Standard Model, cosmology, and branch-selection comparison surfaces.
The comparison discipline is typed throughout: source-side values, laboratory readout protocols, cosmological transfer diagnostics, one-sided bounds, and branch-selection tests are not treated as interchangeable numbers.
Start with the PDF unless you are auditing a specific release artifact.
| Reader profile | Suggested path | Main focus |
|---|---|---|
| General theoretical physics | Overview, Technical Synopsis, Introduction, emergent geometry, Grassmannian/QGT structure, K4 and multi-cell construction, predictions, Conclusion | Physical route and falsifiable surfaces |
| Mathematical physics | Emergent geometry, Grassmannian geometry, proof-detail appendices, readout-functor appendices, arithmetic-stratified prediction object | Fisher metric, Berry curvature, Schur-Weyl structure, Lovelock/Chern-Weil rigidity, typed functors |
| Collider and flavor physics | Introduction, K4 cell construction, multi-cell/vacuum structure, prediction tables, laboratory readout appendix | Electroweak readouts, CKM geometry, charged-lepton and quark mass ratios, rare leptonic B_s protocols |
| Cosmology | Introduction, cosmology section, prediction tables, cosmological readout appendix, release notes | kappa_4(r), horizon entropy-curvature gate, Lambda, inflation, neutrinos, BAO, Planck-side diagnostics |
| Open-review audit | Theorem statements, proof dependencies, prediction tables, comparison protocols, appendices, errata/review log | Claim provenance, closure status, reproducibility, conditional or bound-only rows |
K4 complete graph + SU(3) Heisenberg dynamics
-> Schur-Weyl and topological selection
-> quantum geometric tensor on the state/parameter manifold
-> Fisher metric / Berry curvature split
-> emergent spacetime + Yang-Mills curvature
-> full-order Einstein-Yang-Mills package
-> K4 representation data and multi-cell tensor networks
-> Standard Model readouts
-> Read_lab, Read_cosmo, and Read_int typed comparison functors
-> experimental branch-selection surfaces
This table is a compact orientation aid only. The complete status, assumptions, and proof/readout classes are in the manuscript's prediction sections and appendices.
| Surface | K4 readout | Public comparison status | Type |
|---|---|---|---|
sin^2 theta_W(M_Z) |
0.231219995 |
0.23122(6) |
closed typed EW readout |
alpha_s(M_Z) |
~0.1180 |
0.1180(9) |
Type-7 color scale-line |
Wolfenstein lambda_C |
9/40 = 0.22500 |
0.22501(68) |
CKM typed readout |
CKM J |
~3.085e-5 |
3.08(13)e-5 |
Casimir-flag readout |
m_mu/m_e |
206.768282688691 |
206.7682827(46) |
charged-lepton protocol |
m_b/m_s |
53.97 |
53.94(12) |
mass-tower / mechanism-F |
sum m_nu |
~0.059 eV |
below current cosmological bounds | selected NO branch / bound |
Lambda ell_*^2 |
2.93e-122 |
2.89e-122 (1.5%) |
two-term gate readout, 0.9 sigma |
m_bb |
3.69 meV |
below current 0nubb bounds |
Majorana point emission |
| BAO shape | frozen K4 CPL curve | 0.44 sigma_eq |
shape-only diagnostic |
| BAO absolute scale | c/(H0 r_d)=30.135 |
chi^2=34.40/13 (3.28 sigma_eq) |
absolute-scale diagnostic |
The current manuscript distinguishes primary numbered predictions from companion/readout refinements and structural profiles. In short form:
31 primary predictions
+ 20 companion/readout refinements
+ rare B_s protocol rows
+ 1 structural cosmology profile, kappa_4(r)
The manuscript tables and appendices are the authority for the current status of each row.
The v1 public-review release is PDF-first. It provides the manuscript for scholarly reading, citation, and technical criticism while keeping the initial public surface narrow.
This release includes:
- the public-review PDF;
- English and Chinese README files;
- citation metadata;
- rights and contribution notices;
- release notes and public review log;
- errata and curated review records;
- GitHub issue and pull-request templates;
- SHA256 checksums generated at export time.
This release intentionally does not include LaTeX manuscript source, software source code, numerical scripts, raw working directories, internal planning cards, private audit ledgers, or a full reproduction package. Separate manuscript-source, software-code, numerical-script, and reproduction packages may be released later if their scope, license, and stability are ready.
Use GitHub Discussions for conceptual questions, reader-route questions, and
broad technical discussion. Use GitHub Issues for actionable reports.
If you do not have time to read the whole manuscript, start with the focused
questions in REVIEW_TARGETS.md.
Good issue reports identify the exact location and the technical nature of the concern, for example:
- a proof gap, invalid dependency, or missing theorem status;
- a numerical value, comparison protocol, or reproduction concern;
- an experimental-data or timeline update with dated sources;
- a conditional/open result stated too strongly;
- a citation, prior-work, duplication, clarity, or typographical issue.
Please cite PDF page numbers, sections, theorem labels, equation labels, table rows, figure captions, appendix names, or release-note entries whenever possible.
Confirmed corrections are tracked in ERRATA.md. Curated open
questions and responses live under review/. Public-review updates
are also recorded in PUBLIC_REVIEW_LOG.md.
If you use the framework, cite the manuscript release and the exact archived
version or public repository commit consulted. See CITATION.cff
for the machine-readable citation record.
The manuscript PDF, release text, review materials, citation metadata, figures, tables, and other research content are manuscript/research content covered by the public-review rights notice unless a more specific file-level notice applies. Software files are MIT-licensed only when they are expressly identified as MIT-licensed software.
Authoritative rights and contribution terms: