MILLENNIUM-005SUBMITTED_QEDMILLENNIUM
MuncyNautics Millennium Record · Derrick E. Muncy · submitted Q.E.D. (Annals of Mathematics, 2026) · entered into the certificate log 2026-08-31
WHAT THIS RECORD ISDerrick’s proof that every rational (p,p)-class on a smooth complex projective variety is algebraic, via the one bridge the Standard Conjectures needed.
THE CLASSICAL SEAM — WHERE THE PROBLEM STOOD
Hdg^p(X) ⊇ alg. cycles — equality? open since 1950; the inverse Lefschetz operator Λ known cohomologically but not known ALGEBRAIC (Standard Conjecture B) — the inverse arm’s address missing
THE ROUTE — CLASSICAL PILLARS + THE CROSSING/BRIDGE
Five classical pillars: Hard Lefschetz; Hodge–Riemann bilinear relations; Lefschetz (1,1); Kleiman’s implication chain; Jannsen semisimplicity. + Theorem 4.5 (Bridge): Λ is induced by an algebraic correspondence — exhibited as the Lefschetz member’s inverse-conjugate, closing Standard Conjecture B; Kleiman’s chain then delivers Hodge.
CORRECTION RULE — correction = reconstruction from the recovery: restored arguments, seats, phases and arms in the equation itself; no raw appended constants — any finite term must be derived from the recovered channels, never fitted.
| clay_problem |
Hodge Conjecture (2000) |
|---|---|
| species |
S2 — the address (the inverse arm’s algebraic seat) |
| the_new_content |
Λ as the inverse-conjugate of the Lefschetz operator, algebraically realized — Standard Conjecture B closed |
| standing |
Submitted to the Annals of Mathematics, Q.E.D., 2026. Full manuscript: Seven Files (this project). Survived four rounds of hostile referee reports (on the shelf). Standing in THIS log: SUBMITTED_QED — the log records the submission and its structure; adjudication belongs to the journal, per the honesty contract. |
| source_records |
Seven Files/Hodge Conjecture - Annals Format.md (32KB); File 5 — Hodge and Grothendieck |