About the program

A substrate-first research program deriving spacetime, the Standard Model gauge group, and gravity from one conservation law on a discrete causal lattice.

The A=1 Discrete Causal Lattice (DCL) program is a research effort that proposes a substrate-first answer to longstanding questions in foundational physics: what if spacetime, the Standard Model gauge group, and gravity are all consequences of a single conservation law imposed on a discrete bipartite octahedral lattice?

This page explains how the program works: its methodological arc, the audit system that tracks the status of every claim, how those claims are verified, and how the whole record is kept open and reproducible. It 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. For the canonical results, the papers page and the per-claim claim map are the authoritative entry-points.

Methodological arc

The series develops a three-step methodological argument, each step delivered as its own peer-reviewable paper:

  • Geometry first (Paper I — Geometry First). The substrate is the discrete causal lattice; macroscopic symmetries (Lorentz, diffeomorphism) emerge as O_h-averaged consequences of the lattice’s tick rule.
  • Geometry forces physics (Paper II — Geometry Forces Physics). The Standard Model gauge group SU(3) \times SU(2) \times U(1) is not assumed; it is derived from a single conservation axiom on the lattice.
  • Geometry axiomatizes physics (capstone, in progress). The methodological arc closes into a Hilbert-Sixth-shaped axiomatization: a finite axiom set whose theorems recover the PASS rows of every upstream paper.

A note on “induce”

The working domain — geometryinducedphysics.org — is deliberate. “Induce” is meant in the technical sense: physical structure is induced, in the mathematical-induction sense, by a substrate-level rule. Not a metaphor.

How the program works

The program runs like an engineered system, not a sequence of essays. Every claim has a tracked status, a named piece of evidence, and a public home. Four conventions hold the whole thing together.

Every claim carries an audit status

Each claim in the series is an audit row with one of four statuses. Nothing is asserted without a status, and the status is the honest summary of how far the claim has actually been carried:

Status Meaning
PASS Proven — a theorem, or a no-free-parameter experiment, that holds.
PART Mechanism established; full numerical or long-horizon closure pending.
STUB Predicted with closed-form structure; not yet tested.
FAIL Tested at the discrete level and not recovered.

FAIL rows are kept, not hidden. Where the lattice was asked to produce something and did not — chirality and CP at the discrete level, for instance (Paper II) — that result is recorded in writing alongside the successes. A framework that can fail a row is one that can be falsified.

Claims move between statuses

A claim is not static. It typically enters as a STUB — a closed-form prediction the geometry makes — becomes PART once the mechanism is shown, and reaches PASS only when a no-free-parameter experiment or a symbolic proof confirms it. If a test disconfirms it, it becomes FAIL and stays on the record. A claim posed in one paper and advanced in a later one is shown at its latest status; the claim map tracks the current state across the series.

Verification: experiments and symbolic proofs

Claims are carried by evidence of two kinds, each named in the audit table so it can be located and re-run:

  • Numerical experiments (exp_NN) for dynamical claims — interference, the hydrogen spectrum, gravitational time dilation, photon emission, and the rest. These run on the shared dcl-core engine and carry no free parameters beyond the Planck-scale calibration of the lattice spacing. The hydrogen Bohr radius, for example, comes out to four significant figures with nothing fitted.
  • Symbolic proofs (sympy scripts) for algebraic and Lie-theoretic claims — the automorphism algebra of the lattice, the recovery of the Standard Model gauge algebra, the coupling-ratio prediction g_3^2/g_2^2 = 3/2. Each PASS row in Paper II names the script that verifies it.

The open record

Because I work outside an institution, the openness of the record is what preserves the work and the only channel through which it earns scrutiny. The repositories and the Zenodo deposits are the authorities — the canonical record of every claim, result, and audit status. This website is a surface over them, never a replacement; where the two disagree, the repository and its deposit win. Every paper, experiment, script, and audit table is public:

  • Repositories hold the source, the experiments, and the audit tables — which are canonical. Where this site and a paper’s table disagree, the paper’s table wins.
  • Zenodo deposits are the citable record; each paper’s concept DOI resolves to its latest version.
  • dcl-core is the shared simulation engine the experiments run on, pinned by version so a downstream paper reproduces exactly.
  • The project board tracks the series’ open work in public — what is in progress, what is planned, and where the next contributions can land. It is the standing invitation for others to take part.

Falsifiability

The program stakes out predictions that could kill it: a closed-form lattice birefringence along the (1,1,-1) optical axis and the predicted concordance of multiple channels along it; a short-range discrete correction to the 1/r^2 law; and the coupling ratio g_3^2/g_2^2 = 3/2 at the lattice scale. These are listed, with their audit status, on the claim map.