Claim map

Reviewer-facing claim map for Papers I and II of the A=1 Discrete Causal Lattice series: every claim labelled proven vs. conjectured, with its native PASS / PART / STUB / FAIL audit tag.

A one-page, reviewer-facing summary of what the series proves and what it only conjectures. Each claim carries two labels: a plain-language status (Proven / Conjectured / Disconfirmed) and its native audit tag from the paper’s own audit table. This page surfaces the canonical audit tables; it does not replace them — the authoritative tables travel with the papers in their repositories (Paper I · dcl; Paper II · dcl-sm-derivation).

This map is read in light of the program’s Statement of Intent: the goal is to chart the expressive power of the A=1 lattice, not to assert that it is the literal microscopic structure of reality. “Proven” below means proven about the object — a theorem, or a no-free-parameter experiment — not a claim about nature.

NoteHow to read the labels
Status Audit tag Meaning
Proven PASS Theorem, or no-free-parameter experiment, that holds.
Conjectured PART Mechanism established; full numerical / long-horizon closure pending.
Conjectured STUB Predicted with closed-form structure; not yet tested.
Disconfirmed FAIL Tested at the discrete level and not recovered.

“Backed by” names the experiment (exp_NN) or verification script that carries the row in the paper’s audit table.

Paper I — Geometry First

The substrate-priority paper: a bipartite octahedral causal lattice under the single axiom \mathcal{A}=1, from which quantum mechanics, special relativity, and Newtonian gravity are derived as consequences.

Proven (PASS)

Sector Claim Status Audit Backed by
Kinematics Speed-of-light limit c=1 Proven PASS exp_00
Kinematics Inertial persistence Proven PASS exp_01
Kinematics 1/r^2 discrete path-count correction Proven PASS exp_06
Kinematics Dirac equation and spin-\tfrac12 Proven PASS analytic
Kinematics Equivalence principle m_g = m_i Proven PASS exp_01, exp_02
Quantum Interference Proven PASS exp_03
Quantum Decoherence Proven PASS exp_04
Quantum Measurement / irreversibility Proven PASS exp_05
Quantum Born rule Proven PASS exp_03–exp_05
Quantum Mass quantization (Arnold-tongue) & photon dispersion Proven PASS exp_09
Gravity Gravitational attraction Proven PASS exp_02
Gravity Gravitational time dilation Proven PASS exp_02, exp_07
Gravity Clock-density conservation / continuity equation Proven PASS exp_07
EM EM-vs-gravity force geometry & photon emission at lock-in Proven PASS exp_08
Atomic Hydrogen E_n \sim -1/n^2 Proven PASS exp_10
Atomic Spontaneous quantization at n=1 Proven PASS exp_11
Atomic Two-body hydrogen to 4 sig figs (k=0.0970 vs 0.0971) Proven PASS exp_12
Atomic Bound state requires an active proton Proven PASS exp_11, exp_12
Atomic Three-body helium-like system Proven PASS exp_13
Atomic Two-electron helium Proven PASS exp_14

Conjectured — mechanism shown (PART)

Claim Status Audit Backed by
Black-hole horizon + Hawking temp. & Bekenstein–Hawking entropy (analytic, stated modeling assumptions) Conjectured PART analytic
Photon emission as an \mathcal{A}=1 necessity & joint-\mathcal{A}=1 beam-splitter emission operator Conjectured PART exp_19c, exp_20
Induced gauge action in Sakharov form Conjectured PART analytic
Two-body long-horizon stability & escape mechanism Conjectured PART exp_12b, exp_12c
Lock-in grid-independence Conjectured PART exp_12d_tight
Proton-mass lower bound Conjectured PART exp_16

Conjectured — predicted, untested (STUB)

Claim Status Audit
Kinematic lattice birefringence along (1,1,-1) Conjectured STUB
Zitterbewegung-source dual hypothesis Conjectured STUB
Gauge-sector birefringence Conjectured STUB
Multi-channel concordance prediction (P9) along (1,1,-1) Conjectured STUB

Update — the two birefringence rows above are since carried out and resolved in Paper IV v1.0 (DOI 10.5281/zenodo.21435951): optical-axis birefringence is forbidden — the polarization split cancels (a passed null, conditional on the geometric blocks). The accompanying single-domain dispersion construction is a no-go (gauge and matter sectors both excluded as constructed), with an open structural escape. See Standing falsifiable predictions below.

The SM-gauge-group-as-lattice-automorphism conjecture is posed here and advanced in Paper II; it appears under Paper II below at its latest status.

Paper II — Geometry Forces Physics

Characterises the Standard Model gauge group as the factor-product projection of the lattice’s 71-dimensional automorphism algebra. Every row is backed by a sympy verification script in src/utilities/.

Proven (PASS)

Claim Status Audit Backed by
Discrete spatial automorphism group has order 48 (O_h) Proven PASS automorphism_discrete.py
RGB sublattice contributes only \mathbb{Z}_3 \subset SU(3) Proven PASS automorphism_rgb_su3.py
SO(3,1)\times U(1) acts on \mathbb{C}^2=(\psi_R,\psi_L) — dim 7 Proven PASS automorphism_direct_product.py
Direct-product structure on extended \mathbb{C}^{12} — dim 18 Proven PASS automorphism_direct_product_extended.py
Tick-rule consistency on \mathbb{C}^{12} Proven PASS tick_rule_extended_consistency.py
Wilson-plaquette gauge invariance Proven PASS tick_rule_gauge_invariance.py
SU(3) branch consistency — only Branch A commutes with tick rule Proven PASS su3_branch_consistency.py
Non-abelian SU(3) dynamically generated from \mathbb{C}^3 color memory Proven PASS su3_generation_from_colour_memory.py

Conjectured — mechanism shown (PART)

Claim Status Audit Backed by
Exact equality vs. containment in the dim-71 centralizer Conjectured PART automorphism_centralizer_extended.py
SM-chirality coupling alignment (vector-like SU(2), spatial-parity \mathbb{Z}_2) Conjectured PART chirality_parity_alignment.py
Explicit 1/g^2 prefactor — ratio g_3^2/g_2^2 = 3/2 derived, universal c open Conjectured PART induced_gauge_action_nonabelian.py

Disconfirmed (FAIL)

Claim Status Audit Backed by
Modified (antilinear) tick rule for Branch B SU(3) / CP — no color matrix anticommutes with every Gell-Mann generator Disconfirmed FAIL tick_rule_cp_modified.py
Single-domain gauge viability (the three-diagonal substrate the derivation is carried out on) Disconfirmed FAIL Paper IV v1.0
ImportantPaper II v2.0 — the substrate is superseded

Paper II’s derivation is carried out on the three-diagonal, single-domain substrate that Paper IV excludes as constructed. The author’s position is stronger than “read conditionally”: the derivation is obsolete — the architecture leaves an optical axis that is observable but not observed, so the lattice geometry will have to change, and the successor architecture is not birefringent. \mathcal{A}=1 conservation is not falsified and the algebraic results are unaffected.

Open, and the single largest question about how much of Paper II survives: colour SU(3) arises from a per-site \mathbb{C}^3 index recording which of \mathbf{V}_1,\mathbf{V}_2,\mathbf{V}_3 carried the most recent tick — colour space is the three-diagonal set. A successor geometry that adds \mathbf{V}_4 reads naturally as \mathbb{C}^4 \to SU(4), not SU(3). Paper IV’s parked escape (a four-orientation vacuum while matter keeps its axis) would preserve colour, but that is unresolved foundational research. v2.0 makes no claim either way.

Not falsified: the coupling ratio g_3^2/g_2^2 = 3/2 is open under the successor geometry, not withdrawn — the Q-tensor and the universal one-loop prefactor cancel in the ratio (which is why it is independent of c), though the spectator counting it rests on could change.

Caveat: Paper II v2.0’s own abstract and conclusion are knowingly unreconciled with its changes table — they still present the coupling ratio and the (1,1,-1) birefringence as unconditional testable consequences. That rework was deferred by the author; this map states the corrected status.

Central claim — Eq. (137): Conjectured (PART). Containment \supseteq of SO(3,1)\times SU(3)\times SU(2)\times U(1) is established; strict equality = does not hold at the discrete level, and chirality / CP are explicitly not recovered.

Paper III — Tidal Ionization and the Quantum Roche Limit (in preparation)

Paper III (in progress) adds a third (gradient-detuning) ionization channel and an atomic ISCO, with two observational signatures. Its claims will be mapped here at first Zenodo deposit; until then this section is a placeholder, and no Paper III row should be read as audited.

Paper IV — Optical-Axis Anisotropy: Birefringence Cancellation and a Single-Domain No-Go (v1.0)

Published 2026-07 · concept DOI 10.5281/zenodo.21435951. An honest no-go: the three-diagonal, single-domain construction is excluded as constructed in both the gauge and matter sectors, while \mathcal{A}=1 conservation itself is untouched.

Claim Status Audit
Adjugate closure Q_B=\operatorname{adj}(P) and null optical-axis birefringence Retained, conditional on the geometric blocks PASS / blocks PART
Single-domain gauge viability (induced-photon common-mode speed) Disconfirmed — order-unity, dimension-four anisotropy, excluded by cavity / Michelson–Morley bounds FAIL
Matter sector “dimension-six-suppressed, therefore safe” Retracted — also excluded as constructed FAIL
\mathcal{A}=1 conservation principle Unresolved, not falsified by this result —

The root of both exclusions is the omission of the fourth cube body diagonal \mathbf{V}_4 — the same omission that defines the optical axis. The escape is open structural work: an O_h-restoring four-orientation vacuum, and a token\tomatter emergence map. Scope: this does not touch the adjugate theorem, the Bell-test results, or the rest of the program.

What these papers do not claim

A reviewer’s fastest orientation is often the negative space:

  • Not that the A=1 lattice is the literal microscopic substrate of the universe — see the Statement of Intent.
  • Not strict equality of the SM gauge group with the lattice automorphism group — only containment holds (Paper II, PART).
  • Not chirality or CP from the discrete substrate — tested and not recovered (Paper II, FAIL).
  • Not the absolute gauge-coupling scale — only the dimensionless ratio g_3^2/g_2^2 = 3/2 is fixed; the universal prefactor c is open (deferred to the planned discrete-probability paper).
  • Not the STUB predictions as confirmed — they carry closed-form structure but are untested.

Standing falsifiable predictions

The claims most useful to a skeptical reviewer are the ones that could kill the framework:

  • (1,1,-1) optical axis — a passed null and a single-domain no-go (Paper IV v1.0, DOI 10.5281/zenodo.21435951). Two results, stated honestly. First, vacuum birefringence is a passed test, not a standing prediction: the framework forbids optical-axis birefringence (the doubled transverse root cancels the polarization split), which corroborates the framework and excludes the dimension-5, CPT-odd birefringent rivals that generic discrete / Lorentz-violating models predict — though this null is conditional on the geometric constitutive blocks (their derivation as the full dynamical response is PART). Second, the forward-testable dispersion delivers a no-go for the single-domain construction: the induced-photon common-mode speed anisotropy is order-unity and dimension-four (a factor-$$2 anisotropic speed of light, excluded by Michelson–Morley / cavity bounds), and the matter sector is likewise excluded as constructed (the earlier “dimension-six-safe” reading is retracted). Both trace to one root: the omission of the fourth cube diagonal \mathbf{V}_4 that also defines the optical axis. The escape is open, structural future work — an O_h-restoring four-orientation vacuum and a token\tomatter emergence map. The result is honest and negative, cleanly scoped: it does not touch the adjugate theorem, the Bell-test results, or the rest of the program.
  • Short-range 1/r^2 discrete correction — a calculable departure from the exact inverse-square law at lattice range.
  • Coupling ratio g_3^2/g_2^2 = 3/2 at the lattice scale — open under the successor geometry, not withdrawn: the Q-tensor and the universal one-loop prefactor cancel in the ratio, but the spectator counting it rests on could change once the substrate does.

Provenance

This page is reconciled against, and subordinate to, the audit tables in the paper repositories. Where this summary and a paper’s audit table disagree, the paper’s table is authoritative. Last reconciled against Paper I v2.0 (10.5281/zenodo.21464971), Paper II v2.0 (10.5281/zenodo.21477781), and Paper IV v1.0 (concept DOI 10.5281/zenodo.21435951) — birefringence forbidden (a passed null, conditional on the geometric blocks); the single-domain dispersion construction is a no-go (gauge and matter both excluded as constructed), with an open structural escape.

Paper I v2.0 is itself a corrective re-version: it carries a revision notice withdrawing the phenomenological viability of the three-diagonal single-domain vacuum. Earlier Paper I deposits (v1.0–v1.02) remain available and unwithdrawn, but their viability claims are superseded — cite v2.0.