Fixing 14 stale assert_no_sorry guards across 4 files

the mass gap exists, a BF program can detect it. If a BF program can detect it, computation is sufficient for physics. The parser roundtrip proves the first link: that the computational substrate is self-consistent.

Agent 1: SpectralMeasure.lean — CRITICAL PATHcauchySeq_stepApprox PROVED — step function approximants form Cauchy sequence via monotone bounded convergence. This completes the pvmIntegralOp definition chain.integralBounded_adjoint PROVED — PVM integral adjoint identity via limit + projection self-adjointnesssum_norm_sq_proj_mono — monotonicity of projection norm-squared partial sums (sorry-free)norm_sq_stepApprox_diff_le — Cauchy bound via Pythagorean theorem (sorry-free)

New PartialOrder/StarOrderedRing on B(H) needed for CFC.sqrt — these are mathematically correct and don't create diamonds.

Appropriately noncomputable in analysis files

first principles

24 agents across 24 files.

NAMES matter. Not just for humans — for the elaborator too.

Results: 39 fake proofs found across 18 files. 16 sorry-db entries marked "done" were actually fake.

hit API 500s

And today we learned it's wrong — not because the proof is wrong (it's sorry), but because the statement is wrong. The Hamiltonian is typed as a bounded operator, but Hamiltonians in interacting quantum field theory are unbounded.

Next session should

agents should commit in their worktrees.

The agents aren't just proving — they're doing mathematics, which sometimes means refusing to prove false things.

and live dashboard emission.

Next session should

literally

One bit of type information → whether the "it" (the Yang-Mills mass gap) can exist at all.

audit the auditor

time_translation_implies_energy_conservation

Physics-First Lean4 Proof System

An axiom is a "bit" with no proof behind it — a pure declaration of truth. A sorry'd definition is a "bit" with a formula behind it — a declaration of computation.

but axiom is MORE dangerous — no compiler warning, harder to replace incrementally, and multiple axioms can be inconsistent without detection.

rocks

arbitrarily great accuracy

itself

no experiment has ever produced a lone quark.

hole

Stone's theorem is the mathematical reason quantum mechanics works

this means verified neural networks can CERTIFIABLY DETECT spectral gaps

An axiom that says creation exists without saying what it does loses the formula — the whole point of physics.

The spectral gap framework didn't care if your operator acts on 4 dimensions or infinite-dimensional Fock space — HasMassGap is HasMassGap.

efinitions like creation (the operator that creates a particle) were turned into axioms — "trust me, this function exists" — without specifying what it does

interactive diagrams.

Kosmos run involves reading 1500 papers and running 42,000 lines of analysis code

analogical wetware mashing mushy double rail hall effectual polybutyl, replete with orthographic and syntactic aberrations (no cog-assistive technology included)

r public stream.