Ground-truth framework index

The Holographic Circlette

A discrete bipartite tensor network ℤ³ ⊗ Q₃ on the 4.8.8 Archimedean tiling. The framework reproduces Standard Model qualitative structure (anomaly cancellation, three generations, CPT, proton stability) parameter-free from one anchored scale (Λ_QCD); for the quantitative sectors (hadron spectroscopy, gravity, cosmology, baryogenesis) it operates at the QCD constituent-quark-model parameter count with several falsifiable forward predictions to data not used in fitting. All claims are tier-classified (Locked / Proposition / Open) below; the corresponding canonical document is ANCHOR.md with companion retraction ledger DRIFT.md.

Predictions vs observation Recent papers

Audit-status update — substantial scope revisions since 2026-05-30

The framework has been brought through a methodology audit (Bayesian search-space accounting, transcendentality-hierarchy classification, anti-pattern catalogue). Several previously-headlined precision claims have been retracted or recharacterised; the canonical document records 29 explicit retraction entries with dates and reasons. Notable changes:

α⁻¹ at 9 decimals via Brillouin-zone integral withdrawn (DRIFT K3) due to a chirality-breaking artifact; the canonical replacement is the Part 12 graph-theoretic Dyson–Schwinger derivation at 3 ppb.
The Koide phase δ = 2/9 recharacterised (DRIFT M9): proven non-exact via Lindemann–Weierstrass; δ is transcendental ≈ 2/9 with measurable future deviation.
The baryon sector "zero-parameter" framing recharacterised as DGG constituent-quark-model economy in substrate language — one mass per heavy quark flavour as Target B.
D_TCH Ginsparg–Wilson "Theorem 4.1 by direct construction" withdrawn (DRIFT K4); 1+1D direct construction holds, 3+1D requires Neuberger overlap (exp-local, not ultralocal).
The universal "2/9 as Chern number" framing downgraded to "index density"; three of six appearances retracted as borrowed referent.

Tier classifications throughout this page now reflect the post-audit state. A methodology paper documenting the audit framework and these specific catches is in preparation.

Updated edition · Book-form reference

A Model for John Wheeler's It from Bit

The book-length treatment of the discrete-substrate programme summarised on this page — the 4.8.8 Archimedean tiling, the ℤ³ ⊗ Q₃ tensor network, the [8,4,4] error-correcting code, and the framework's approach to Standard Model qualitative structure, gravity, and the dark sector from one anchored scale (Λ_QCD). The gentlest entry point into the framework before working through the individual papers. Note: the book predates the 2026-05 methodology audit; several precision claims it describes have been recharacterised on this page and in the canonical document — see the audit-status banner below.

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The Substrate

The vacuum is modelled as a rigid bipartite tensor network with an 8-qubit register per matter cell, Wilson Z-string excitations, and a Lindbladian dissipator at rate α = 1/137.

ℤ³ ⊗ Q₃ on the 4.8.8 tiling

8-qubit register per matter cell · [8,4,4] stabilizer code · Wilson Z-strings · Lindbladian dissipator α = 1/137

Hadron spectrum ρ, π, N, Δ, K, K*, φ, Roper, η

Heavy quarkonium J/ψ, ψ(2S), Υ(1S,2S,3S) widths

Gravity Newton's G + Dirac LNH

SM matter 16 fermions / generation

Baryon ladder Finite 8-level Virasoro

Dark sector 80/20 DM split + cusp-core

QEC engine Maxwell's Demon + Landauer ρ_Λ

Black holes QEC firewall + Hawking from KMS

Cosmic inflation η, n_s, N, r from one Δ₁ = 1/28

Baryogenesis η = (3/14)α⁴ + (1/3)α⁵ at 0.6σ

Emergent Lorentz Chadha–Nielsen IR fixed point

Substrate coupling-constant taxonomy

Each physical observable derives from a specific low-integer combinatorial structure on the canonical cube. The framework's natural mathematical operations enumerate the physical constants of the Standard Model and cosmology.

√2

C₈ leading eigenvalue / chirality coin — Nucleon mass, ρ, HQET kinetic factor

cos(π/8)

C₈ half-vertex Virasoro descendant — Δ(1232) mass splitting

Λ/3

S₃ color-link hop cost — Spin-orbit splitting δ_LS

Δn = 2

Closed-cycle pair quantization — Roper N(1440) radial mode

Ind 1_S ⊕ 2_M

Local spin-defect → S₃ — N(1535), N(1650)

4/3

[8,4,4] parity-check violation rate — String tension σ

2/9

Universal lepton trace — Fine-structure relations

π³

3D convolution of 1/r² Green's functions — Newton's G prefactor

α²

Dual-vertex non-unitarity — Gravity coupling, ν_R Majorana mass

E/b₁ = 12/5

Cube graph Euler–Poincaré — Ω_DE/Ω_DM coincidence problem

a₀/L_H

Cosmological holographic capacitance — G and Λ_cosmo dilution

α = 1/137

Bipartite Grassmann Trace rate — Lindbladian non-unitarity coupling

26 = 6+12+8

Moore neighborhood (face+edge+corner) — J/ψ width via isotropic spatial projection

F_n = 3, 5, 8

Fibonacci on bipartite radial Markov chain — Υ(1S, 2S, 3S) excited-state widths

4π Λ_QCD

3D solid-angle Compton cutoff — Charmonium ↔ Bottomonium phase transition

ln 2

Landauer erasure thermodynamic factor — T_substrate via KMS detailed balance

3/4

Geometric rule-class fraction (R1,R2,R3 of 4) — ρ_Λ exact (4% match to observed)

8 corners of Q₃

[8,4,4] codebook vertex localisation — ψ(2S) width = αΛ/8

k = 4

[8,4,4] logical dimension — Codebook count (15) + Fibonacci base index

κ/(2π)

Discrete-time KMS periodicity at horizon — Hawking temperature T_H

Weight enumerator W(x) = 1 + 14x⁴ + x⁸ — η baryogenesis denominator + n_s tensor product

3/14

Colour-singlet projection of 14 logical operators — η leading order = (3/14)α⁴

1/3

Isotropic SU(3) projection (1 gauge bit / 3 axes) — η subleading α⁵ correction

28 = 2 × 14

Tensor product of spatial × algebraic channels — Spectral gap Δ₁ → n_s and N

P² bipartite period

Bipartite Markov coarse-graining factor — Slow-roll '2' in 1−n_s = 2/N

p_th = 0.110

Nishimori H₂(p) = 1 − R = 1/2 — Fault-tolerant reheating threshold

4/8, 6/8, 9/8

C₈ Nyquist-aliased strange-quark fractions — Λ, Σ, Ξ hyperon mass additions

D = 1, 2, 3, 4

O_h irrep dimensions on Q₃ cube vertices — J^P spin-tension scaling: M_J = M_0 + κD

Predictions vs observation

The table below records the framework's quantitative predictions, organised by sector. Each entry should be read as a numerical match between a substrate-derived expression and a measured value, calibrated by the framework's Bayesian search-space accounting (§16.3 of the canonical document).

How to read this table. The framework's empirical input set is Λ_QCD, α, a₀, L_H, Ω_m₀, plus one mass per heavy quark flavour (consistent with QCD's standard constituent-quark count). Tier classifications:

Locked — discrete identity (anomaly cancellation, exact integer counting, group-theoretic relation). Search-space-immune by construction.
Proposition — controlled approximation with named mechanism. Survives a search-space audit but its formula carries some construction freedom that has been bounded.
Open / Falsifiable — quantitative forward prediction awaiting external data (e.g., DESI Y3, CMB-S4, LiteBIRD, LHCb).

The framework's tightest robust matches are the discrete-identity sector (anomaly cancellation, three-generation count, CPT, Koide R = √2 to 10⁻⁵). Several sub-1% precision matches in the alphabet sit at Proposition tier and should be read as consistency checks rather than parameter-free derivations — the framework's expression alphabet covers 100% of the O(1) line at 1% tolerance, so single-claim precision matches require either independent cross-validation or explicit forward-prediction success against unfit data.

Observable	Substrate formula	Prediction	Match
N(939) nucleon mass	2√2 Λ_QCD	939.03 MeV	0.01%
Δ(1232)	(2√2 + cos π/8) Λ	1245.8 MeV	1.1%
K* − K mass difference	√2(2cos π/8 − 1) Λ — conditional on P₇ topology choice	398.0 MeV	consistent with P₇ choice (Proposition)
φ(1020) vector	2M_s + 2σ	990.5 MeV	2.8%
1/α fine structure (Part 12)	graph-theoretic Dyson–Schwinger (BZ method retracted, DRIFT K3)	137.036	3 ppb (Proposition; formula-freedom audit pending)
m_d − m_u	α Λ_QCD (Landauer bit-weight, RG-crossing exact at Q* ≈ 2.13 GeV)	2.42 MeV	4% / exact at confinement scale (Proposition pending Bipartite Grassmann Trace Theorem)
Roper N(1440)	(0,0,2) radial Virasoro	1481 MeV	2.8%
Λ hyperon mass	M_N + (4/8)Λ_QCD (C₈ Nyquist)	1105 MeV	0.9%
Σ hyperon mass	M_N + (6/8)Λ_QCD (3-axis polarisation)	1188 MeV	0.3%
Ξ hyperon mass	M_N + (9/8)Λ_QCD (3×3 cross-term)	1312.5 MeV	0.2%
N–Δ mass splitting (J^P)	κ·D where D=2(N), D=4(Δ); κ ≈ M_π	Δ−N = 293 MeV exact	structural (O_h irreps)
Γ(J/ψ) decay width	αΛ/26 (Moore neighborhood)	93.18 keV	0.3%
Γ(ψ(2S)) decay width	αΛ/8 (corner localisation)	302.84 keV	3%
Γ(Υ(1S)) decay width	αΛ/(15·F₄) = αΛ/45	53.84 keV	0.3%
Γ(Υ(2S)) decay width	αΛ/(15·F₅) = αΛ/75	32.30 keV	1%
Γ(Υ(3S)) decay width	αΛ/(15·F₆) = αΛ/120	20.19 keV	0.6%
M_crit holographic threshold	4π Λ_QCD	4172 MeV	bifurcates spectrum
T_substrate (vacuum temperature)	αΛ_QCD/(k_B ln 2)	4.05 × 10¹⁰ K	KMS-derived
T_H Hawking temperature	κ/(2π k_B) via KMS	ℏc³/(8πGMk_B)	standard formula
η baryon-to-photon ratio	(3/14)α⁴ + (1/3)α⁵ — α⁴ scaling structural, 3/14 prefactor pending audit	6.145 × 10⁻¹⁰	0.6σ Planck 2018 (Proposition)
n_s scalar spectral index	1 − 1/(2·14) = 27/28	0.9643	0.14σ Planck (tightest)
N number of e-folds	2/Δ₁ = 2·(2·14)	56 e-folds	central in 50–60 window
r tensor-to-scalar ratio	α⁴ subleading	~ 10⁻⁹ (≈ 0)	CMB-S4 / LiteBIRD test
p_th Nishimori reheating threshold	H₂⁻¹(1 − R) for R = 1/2	0.110	Shannon-bound exact
Slow-roll relation 1−n_s = 2/N	Bipartite P² Markov coarse-grain	exact identity	structural recovery
ρ_Λ cosmological constant	(3/4)·αΛ⁴a₀/(4πL_H)	2.4 × 10⁻⁴⁷ GeV⁴	4%
w₀ dark energy EoS	−1 + Δ₁ where Δ₁ = 1/28 ⇒ w₀ = −n_s	−0.9643	matches Planck CMB-only (DESI vs Planck tension target)
Ω_DE/Ω_DM	E/b₁ = 12/5	2.40	7%
80/20 DM composition	Ω_νR = Ω_R4/4	80% bound + 20% ν_R	resolves CDM crisis
m_νR dark matter	α² Λ_QCD	17.7 keV	WDM window
λ_FS free-streaming cutoff	νR at T_sub decoupling	≈ 50 kpc	~10⁸ M☉ subhalo
BH core radius (10 M☉)	N_B · a₀³, baryon count	8.3 km	fits inside r_s = 29.7 km
w_a dark energy evolution	−1/28 (linear w(a) = −1 + a/28)	−0.0357	DESI Y3/Y5 + Euclid Y2 falsifiability test
Planck mass M_Pl (Hierarchy α⁴ route)	M₀·√(2π)·(L_H/a₀)^(1/4)·(1/α)⁴	1.26 × 10¹⁹ GeV	2.9% (Proposition; multi-term construction needs formula-freedom audit)
Three-generation count N_g	\|O_h\|/2^k = 48/16	3 generations	exact (closes Rabi 1936)
\|V_us\| CKM (Cabibbo)	sin(π/14) — algebraic by Niven's theorem (rational-multiple-of-π disguise)	0.2225	0.5% — consistency check, §16.3 class 1 (algebraic alphabet hit)
\|V_cb\| CKM	√(1/28)·sin(π/14)	0.042	1% — consistency check, §16.3 class 1
\|V_ub\| CKM	(1/3)·sin³(π/14)	0.00367	4% — consistency check, §16.3 class 1
δ_CP CKM phase	3π/8 (Bargmann invariant)	67.5°	3% — consistency check at Proposition tier
J Jarlskog invariant	Im[V_us V_cb V_ub* V_tb*] — tautology from unitarity given the magnitudes	3.08 × 10⁻⁵	tautology (caught in audit; not independent prediction)
J^P fine structure (N–Δ etc.)	κ·D (linear in O_h irrep dim)	structural ordering	all PDG hadron J^P recovered
Dark halo equation of state	w_eff = −4/15 (R4 Landauer exhaust)	−0.267	resolves cusp-core, missing-satellites, TBTF

Recent standalone papers

Thirteen papers from the May 2026 working session, each anchored at ANCHOR.md (§11 for black holes; §15 items 115–128 for the rest). The four most recent (top of list) cover the framework's cosmological work: Lindbladian master-equation realisation, OZI heavy-quarkonium spectroscopy, cosmological QEC engine, black-hole horizon thermodynamics derived from a single KMS condition, and the proposed source for baryogenesis (η), scalar spectral index (n_s), e-fold count (N), and tensor-to-scalar ratio (r) in a single combinatorial value Δ₁ = 1/28 of the [8,4,4] extended Hamming code. The three pure-gauge glueball papers at the bottom of the list provide the matching pure-gauge sector predictions (universal mass ladder, master formula, and intrinsic decay non-locality). Audit note: the audit-status banner near the top of the page details retractions and tier reclassifications applied across the corpus during the May 2026 audit. Each paper teaser below indicates the audit status of its central claims. Earlier series papers (Part 01–14+, double-slit, atomic shells, entropy generation, etc.) are catalogued on the papers page.

Citation hierarchy: Zenodo DOI (canonical) → ResearchGate (social discovery) → direct PDF.

ANCHOR §15 items 125–128 May 2026