Circulation rigidity of discretely self-similar blow-up for the Navier–Stokes equations.

A research program on one of the open corners of the Navier–Stokes regularity problem — built, checked, and error-corrected under a two-agent adversarial protocol with a human router.

ν⟨M_w − M_a⟩ = −⟨(Γ_x/2)Ȳ⟩ − ν⟨R⟩ − ⟨I⟩

the kill identity · the paper's central display — a mean-form ledger a balanced-firing blow-up cannot close

Papers

Circulation Rigidity of Discretely Self-Similar Blow-up for the Navier–Stokes Equations

preprint — final preparation

Backward discretely self-similar blow-up at Leray exponents, in the two-plane mirror-symmetry class of antiparallel vortex configurations. Circulation is dimensionless at Leray scaling, so the solution's two circulation books are exactly periodic in similarity time — while an exact viscous accounting identity on the contact line governs their transfer. The paper proves a constancy lemma, a rigidity theorem (one unbalanced window, in either direction, excludes blow-up), a trichotomy of the surviving scenarios, and a conditional exclusion of the balanced-firing case through the kill identity — with every hypothesis stated in full and the open work named on the theorem's face.

Posting imminent; the full draft, verified reference list, and verification-script index will appear here.

The Decorrelation Protocol: Adversarial Two-Agent Verification in AI-Assisted Mathematics

companion piece — in preparation

How the paper above was actually made: two AI agents with separated registries, a human router as the only channel between them, two-gate ratification of every load-bearing claim, pre-registered falsifiers, cold-runnable verification scripts, and a public self-strike ledger. Its central exhibit is uncomfortable and true: the protocol repeatedly caught its own authors — including in the reference list.

The Method

Two-gate ratification. Nothing load-bearing stands on one agent's word: derived by one, independently cold-run and hand-checked by the other.
Pre-registered falsifiers. Expectations are sealed before computation and graded in place; a failed prediction is recorded as WRONG in the script output, never reworded.
Agreement is not evidence. Two models agreeing on narrative is treated as noise; only the mechanism layer — scripts, exact anchors, ground truth — decorrelates.
The error ledger is the product. Every self-strike is kept, named, and published. In the paper's final week the protocol caught six errors, five of them the same disease, two of them in the reference list — all before shipping.

A note on claims. The main theorem is conditional, and says so in its first sentence. Nothing here claims a resolution of the Navier–Stokes problem. What is claimed — an exact accounting identity, a rigidity theorem, and a conditional exclusion with its hypotheses priced — is stated with the open work on its face, and every computable claim ships with a script you can run.