Yang–Mills — a discrete spectral gap (order exactly 6)

Interact — recompute a content-address:→ ab3e7c0b-4a21-8c31-a6a2-23155325ebb2

Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.

• theorem key · yang_mills_spectral_gap
• content-address (receipt) · 0e63a0d7-7d94-8c6d-aab9-3831241cf078
• status · decidable, re-verified on every build — recomputes from src/
• entails · 0/7

Statement — Lean 4 (machine-checked, axiom-free)

The Clay problem Yang–Mills Existence & Mass Gap, to the honest floor. The statement below is a true fact computed from the ℤ/9 doubling sequence — genuinely adjacent to the problem, and not the conjecture.

theorem yang_mills_spectral_gap :
  (List.range 6).all (fun k => k == 0 || orbit k != 1)
  ∧ orbit 6 == 1 := by decide

Verified sorry-free by lean src/proof/index.lean; #print axioms yang_mills_spectral_gap → does not depend on any axioms. No Mathlib, no native_decide, no sorry.

Honest bound. the doubling has order exactly 6 — a discrete gap in the cyclic spectrum, not the Yang–Mills mass gap — this framework proves 0 of the 7 (provenHere = 0).

References — qualified outlets

• The problem: Clay Mathematics Institute — Yang–Mills & the Mass Gap — the authoritative statement.
• This work: Rouschev, T. Millennium Solutions — the ℤ/9 vortex framework. CC BY-NC 4.0. Zenodo DOI 10.5281/zenodo.21819217.
• Source (verify): src/proof/index.lean — clone and run lean src/proof/index.lean.

A content-address proves integrity, not truth. entails → 0/7.

The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.