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

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

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.

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 birefringence — closed-form kinematic and gauge-sector anisotropy along \mathbf{V}_1+\mathbf{V}_2+\mathbf{V}_3, and their predicted multi-channel concordance (P9).
  • 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.

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 v1.01 and Paper II v1.01.