no experiment has ever produced a lone quark.

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.

Fixing 14 stale assert_no_sorry guards across 4 files

A Gauge-Invariant Mass Gap for 4D Yang–Mills

A metric space (X, d) in which every Cauchy sequence converges to an element of X is called complete. For any metric space M, it is possible to construct a complete metric space M′ that contains M as a dense subspace; see Complete metric space § Completion.

spectral gap Δ\DeltaΔ—a physical observable with measurable consequences

Calculus of Inductive Constructions

spacetime geometry is an emergent, redundant description of a fundamentally lower-dimensional information-theoretic structure.

definition of kolmogorovComplexity is marked noncomputable, which is not merely a technicality but a reflection of the mathematical content: KKK is provably not computable, and Lean's kernel correctly refuses to extract computational content from a definition that uses Classical.choice and unbounded search via Nat.find

This is the computational content of empiricism — physics is what physics computes.

trapped-ion systems, where preferred pointer states emerge on decoherence timescales matching theoretical predictions.

Stone's theorem is the mathematical reason quantum mechanics works

Mathematical Physics

The most precise prediction in all of science.

it constructs a fixed point — a proposition PPP such that the physical process of verifying PPP is itself an instance of the phenomenon PPP describes.

The deepest It from Bit: spacetime itself emerges from bits.

computational

36 sorry'd defs, 45 downstream poisoned, 1 critical

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

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

interactive diagrams.