v1.0.0 — one equation, textbook-to-research calculation, machine-checked

causal-quantum-gravity v1.0.0 — one equation, textbook-to-research calculation, machine-checked

Tag: v1.0.0 (2026-07-10).

What this is

A calculation tool first, a proof archive second. One graph-Laplacian "mother equation"

M·∂²Φ + D·∂Φ + K·L_R·Φ + ∇V(Φ) = J − η

computes standard physics from high-school level to research level by switching terms on and
off — Newton's laws, projectile and orbital motion (Kepler's third law), harmonic motion, waves on
a string, RC-circuit decay, heat diffusion, exponential/nuclear decay law, quantum dispersion
(Hückel/benzene degeneracy pattern), and, at the research end, a black-hole quasinormal-mode
frequency reproduced to 0.1% (real) / 1.2% (imaginary) of the literature value from a finite
graph with no point at infinity. Every one of the textbook cases has been checked numerically
against the standard formula — same answers, one compact operator instead of a separate
formalism per chapter.

Resource economy, stated at what was actually measured: the whole kernel is
numpy/scipy-on-a-laptop scale — no GPU, no cluster. The installable spine_pde package (v0.1.0,
its own version track) passes its full 43-test suite in seconds; the verification of all Coq
content is one command. Claims of speedups over external solvers are not made here — what is
claimed is architectural economy: one equation, one small dependency footprint, many domains.

What backs it: make verify compiles 69 Coq files / 439 machine-checked theorem
certificates (428 axiom-free over ℚ, 11 on the disclosed +reals tier), every one a live
Print Assumptions check in the build; CI green on every commit. All seed-asymmetry files and
their dependencies are wired into the CI-guarded build (a pre-release review finding caught them
outside it — fixed at the root). This is not a completed continuum quantum-gravity theory and
does not claim to be — continuum GR is [Refused] as a non-readout by design, not left as an
unsolved gap.

Headline results (tier exactly as labeled — do not read past the label)

• Th_coqc, axiom-free over ℚ — QM and SR are the same equation: the quantum
  dispersion relation is exactly (pure ℚ-algebra, no continuum limit) the vanishing condition
  of the same boost-invariant wave operator that governs the relativistic branch. Tier-honest
  reading: a real, non-vacuous ring identity relating two posited constructions (the spine's
  free M,D,K slots; the boost's posited Minkowski signature) under a chosen reparametrization —
  a relabeling of two posits, not a from-the-root derivation that forces them to coincide.
• Th_coqc — two of the spine's three structural terms are now forced, not posited:
  L_R (the unique operator satisfying {symmetric, zero-row-sum, off-diagonal ≤ 0}), and, since
  2026-07-08, D — forced to deg(Wt) − λ·circ(ord) by imposing those same two axioms on the
  whole asymmetric seed R0, proved for arbitrary vertex count by genuine induction
  (InfoSeedArbitraryNForcing.v, InfoSeedCirculationArbitraryN.v). M remains the one posited
  scalar — a settled machine-checked negative (six forcing readings each refuted on explicit
  witnesses), not an unexamined gap.
• Th_coqc — the seed's antisymmetric part is, literally, discrete torsion: the textbook
  definition instantiated at rank 1 (SkewOff(R0) == 2·Torsion), with a genuinely mixed
  (non-decoupled) rank-n torsion proved irreducible to any per-component rescaling
  (InfoSeedTorsionGenuineMixing.v).
• Th_coqc — a complete discrete curvature-tensor chain: Riemann = 2nd finite difference =
  group commutator, both Bianchi identities, pair-symmetry, metric-derived Levi-Civita — all
  division-free over ℚ.
• Th_coqc — the quantum↔classical crossover = the black-hole horizon, derived as one
  internal algebraic discriminant (disc = D²−4MKλ, critical at λ_c = D²/4MK) on the spine
  itself — not an imported Schwarzschild profile.
• Th_coqc — linearized GR (gravitational waves) is genuinely derived from the same root
  box operator (box h = 0 exactly at v=±1, null iff lightspeed, boost-invariant in every
  frame). Full nonlinear GR — the Einstein field equations, Schwarzschild as their solution —
  remains [Refused]/[Open] by design, not derived here.
• finite_diagnostic (explicitly not Th_coqc) — a finite-domain Perfectly-Matched-Layer
  numerical bridge reproduces a literature Schwarzschild quasinormal-mode frequency to
  0.1% (real) / 1.2% (imaginary), from a finite-graph discretization with no point at
  infinity.
• Th_coqc — a decisive falsifiable prediction: a τ_rel floor forced by the bounded L_R
  spectrum (Anderson–Morley-style ceiling).

What this release does NOT claim

• No absolute physical constants — M, D's scale, K, τ_c remain free/posited; nothing
  here predicts a numerical mass, coupling, or Planck-scale value.
• No full nonlinear GR — the Einstein field equations, Schwarzschild-as-a-solution, and
  Friedmann cosmology are [Refused]/[Open] by design, not derived. Only the linearized
  (gravitational-wave) sector is derived.
• No Standard Model content — no gauge groups, no particle content, no masses.
• The QM↔SR identity is a relabeling, not a from-first-principles derivation — it relates two
  posited constructions under a chosen reparametrization; it does not derive relativity or
  quantum mechanics from something prior to both.
• No external peer review yet — internal adversarial self-audits only (documented in
  LOGBOOK.md, including two overclaims the audits themselves caught and corrected: a
  misleadingly-named theorem and an overstated QM/SR "wiring" framing).
• Novelty is partially unaudited against the wider literature — the repo's own honesty
  discipline flags this as open, not resolved.
• The metric-derived full Riemann tensor R^i_jkl in n≥3 and the non-abelian group Bianchi
  identity remain [Open].

Why v1.0.0

This closes out the seed-asymmetry thread (started 2026-07-07/08): the spine's free-parameter
count for {L_R, M, D} dropped from three unrelated posits to two (Wt, λ) plus one relational
constraint (K<M), directionality gained a real geometric reading (torsion) the prior track never
had, and both results generalize to arbitrary vertex count. Combined with the pre-existing
curvature chain, horizon-as-discriminant, and linearized-GR results, this is judged a coherent,
internally-consistent, fully machine-checked snapshot worth tagging as a first stable release —
not a claim that the physics program is complete.

Verification

git clone <repo>
cd causal-quantum-gravity
make verify   # 69 files, 439 certificates, all Print Assumptions checked; QNM diagnostic script runs

One command reproduces every claim above at its stated tier.

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Authorship. Research direction, core ideas, and all substantive claims: Yaoharee Lahtee
(human author, Open Civil Science Initiative). AI tools were used in an assistant role only —
implementation, formal-proof drafting, verification runs, and editorial structuring; tier
assignments and final decisions remain the human author's responsibility.