Papers

Papers in the A=1 Discrete Causal Lattice series, with Zenodo DOIs, arXiv links, and repositories — discrete spacetime, emergent Lorentz invariance, and the Standard Model gauge group from geometry.

Every paper in the A=1 Discrete Causal Lattice series. Each entry points to the canonical Zenodo deposit (where applicable), the working repository, and the current version.

New to the series? The Claim map is a one-page, reviewer-facing summary of what the series proves versus what it conjectures — every claim labelled and tied to its audit tag, reconciled to Paper IV’s single-domain no-go.

The series is collected in the author’s A=1 Discrete Causal Lattice community on Zenodo. Individual papers are also featured in independently curated communities: Geometric Foundations of Quantum Theory and Gravity (both papers) and Quantum Gravity Research (Open Source) (Paper I).

Published

Paper I — Geometry First

The substrate-priority paper. Establishes the discrete bipartite octahedral lattice as the ontological substrate and recovers Lorentz invariance as an O_h-averaged consequence of the tick rule. v2.0 is a corrective re-version recording Paper IV’s single-domain no-go: the three-diagonal single-domain vacuum’s phenomenological viability is withdrawn, while \mathcal{A}=1 conservation is not — see the claim map.

Paper II — Geometry Forces Physics

Characterises the Standard Model gauge group SU(3) \times SU(2) \times U(1) as the factor-product projection of the lattice’s 71-dimensional automorphism algebra — containment holds, exact equality does not. Predicts the coupling ratio g_3^2/g_2^2 = 3/2 at the lattice scale and leaves the universal gauge-coupling prefactor c open; its closure is the centerpiece of the planned discrete-probability paper. v2.0 records that the derivation’s single-domain substrate is superseded by Paper IV; the algebraic results are unaffected and the coupling ratio is open, not withdrawn.

Paper IV — Optical-Axis Anisotropy: Birefringence Cancellation and a Single-Domain No-Go

The series’ falsifiability instrument. On the (1,1,-1) optical axis, vacuum birefringence is forbidden by the adjugate closure Q_B=\operatorname{adj}(P) — a passed null that also excludes the dimension-5 birefringent rivals. The forward-testable dispersion channel then delivers a no-go: the single-domain three-diagonal vacuum’s induced-photon common-mode speed anisotropy is order-unity and dimension-four, excluded by cavity / Michelson–Morley bounds, and the matter sector is excluded too. Both trace to the omitted fourth cube body diagonal \mathbf{V}_4. \mathcal{A}=1 conservation is not falsified; the escape (an O_h-restoring four-orientation vacuum) is open.

dcl-core — Python engine

The simulation engine that underlies the experiment scripts in the paper repositories. Ships two engines under one import: dcl_core.core is a verbatim port of Paper I’s continuous-amplitude implementation; dcl_core.core3d is an integer-token reimplementation that enforces A=1 by exact integer arithmetic — a session is a budget of N probability tokens with \sum_x N(x) = N exactly, fractional bits carried by a Bresenham-style residual accumulator, CPU (NumPy) and GPU (CuPy) backends. The two engines let discrete A=1 be tested head-to-head against continuous probability (the δp_min question). v0.3.0 adds a U(1) Peierls gauge field with vacuum response, and quarantines every physical-unit conversion (seconds, hertz, joules, metres) behind a single calibration boundary — the counting engine holds zero hard-coded physical constants.

In progress

Paper III — Tidal Ionization and the Quantum Roche Limit

A third ionization channel (gradient detuning) alongside the standard thermal (Saha) and pressure (Pauli) channels, implying an atomic ISCO. Two candidate observational channels (21 cm HI inner-edge morphology near compact objects; Fe K\alpha line-profile inner edge in accretion disks) are noted; their measurability is not yet established.

dcl-generator-zoo — Catalog of the 71-dim per-site automorphism algebra

A standalone catalog paper / artifact for the lattice’s automorphism algebra; consumed by Paper II’s gauge derivation and the planned proton-internals paper.

Planned

The following subprojects are in the framework’s forward-looking design but not yet drafted:

  • Discrete-probability paper — empirical companion to dcl_core.core3d v1.0; the centerpiece showcase closes Paper II’s open gauge-coupling prefactor.
  • dcl-formalism package + paper — a sympy-extending formalism package (axioms / theorems / continuum-limit primitives) and companion paper. Designed to support the Hilbert-Sixth capstone.
  • Hilbert-Sixth axiomatization — Geometry Axiomatizes Physics. The methodological capstone tying Papers I → II → III → discrete-probability → dcl-formalism into a single axiomatic treatment.
  • Proton internals — a future paper that consumes Paper II’s SU(3) machinery and the generator-zoo catalog.