Hodge — the algebraic span equals the units

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 · hodge_span_is_the_units
• content-address (receipt) · 9e90f78b-225d-8c1a-809c-753ccec81926
• status · decidable, re-verified on every build — recomputes from src/
• entails · 0/7

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

The Clay problem Hodge Conjecture, 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 hodge_span_is_the_units :
  (List.range 9).all (fun d => span.contains d == isUnit d)
  ∧ (List.range 9).all (fun d => isUnit d || ! span.contains d) := by decide

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

Honest bound. the doubling span (algebraic generation from 2) is exactly the units, non-units outside — generation/containment, not rational (p,p) ⇒ algebraic — this framework proves 0 of the 7 (provenHere = 0).

References — qualified outlets

• The problem: Clay Mathematics Institute — Hodge Conjecture — 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.