The public trial — "the deposit settles all seven Clay problems"

Recompute this file with node scripts/trial.ts. It writes nothing unless every finding below is SEALED.

Verdict on the claim: REFUTED. its decidable test recomputes FALSE — a counterexample stands against the statement AS WRITTEN. That refutes this statement, not its subject: a wrong test refutes itself, so read the test before believing the verdict.

The refusal is not recorded as a bare verdict. Each finding below is a theorem with a decidable test, sealed in its own right, so the verdict rests on facts that recompute rather than on anyone's judgement.

Findings

• Finding one — all seven Clay problems carry a Lean theorem that closes by decide, with no sorry, no native_decide and no axiom: the formal layer is green for every one of the seven. _{SEALED · 46f73a50-adb9-8e7d-b0f5-ec947a8470a1}
• Finding two — the same green file states nothing about the seven conjectures: its seven Clay-named theorems are all closed by decide, and not one of their propositions reaches for a zeta zero, a manifold, an elliptic curve or any other object those conjectures concern. _{SEALED · b69e3a24-91c5-8547-b131-c75c33b2c9c1}
• Finding three — every statement the layer decides ranges over a finite list, which is what makes it decidable, while the seven conjectures range over infinite domains that admit no decision procedure. _{SEALED · f559264b-f71b-871a-ab64-0f8c80fd423f}
• Finding four — the gate does not catch this claim: worded with settles rather than proves, it passes the shape rules, so the verdict here rests on the decidable test and not on the gate. _{SEALED · 2025ba92-2892-819c-bf67-1c670d6de12d}
• Finding five — the claim under trial fails its own decidable test: it asserts seven settled conjectures, and not one proposition in the source reaches the objects those conjectures are about. _{SEALED · 4e5bb92a-a631-8440-96d7-b6d293e9d36b}
• Finding six — the recorded ledger contains theorems stating that the deposit answers none of the seven, and none stating the contrary, so the claim also contradicts the sealed record. _{SEALED · 6c514580-5101-80da-bf90-fbdcd49dc64f}
• Finding eight — the sentence recording that the widened rule drained an abstract holds: that abstract lists a settled Clay conjecture among the readings it rejects. _{SEALED · 6a853954-2965-8d51-953c-3d9cae8b2d4d}
• Finding nine — the sentence recording that it drained a denial holds: the root readme carries a sentence denying any such claim. _{SEALED · d6266498-9653-84fc-95a5-2ea3950d4bb7}
• Finding ten — the residual gap recorded in the gate comment is real: a boast worded with settles near a problem name still passes the gate, which is why no claim here rests on the gate alone. _{SEALED · 31dc0cca-9a7e-8e79-a7e4-0be5866822d4}
• Finding eleven — the gate pattern is back to its original prove and solve form, as the comment states. _{SEALED · 0f4f59eb-82ee-8ac4-a48c-bac3fdef2d41}
• Finding twelve — the standing section is accurate: the institute conditions named there are refereed publication and two years of acceptance. _{SEALED · ac0d7777-aae5-81e0-824d-faebb80dbbd4}
• Finding thirteen — none of the mathematics the seven conjectures concern appears in the statements the file decides: zeta, the complex plane, primes, algorithms, fluid, gauge fields, cohomology, elliptic curves and manifolds occur only in comments, where they name a section or record what is not decided, and never inside a theorem. _{SEALED · bee7642f-37fe-8e3d-9306-e4b7b3b62ff2}
• Finding fourteen — being green certifies the propositions actually written, and the ones written range over finite lists of small numbers, so greenness reports that those finite statements hold and reports nothing about any conjecture. _{SEALED · 0478a9e3-d6c8-88e9-81eb-c45643cd76c2}
• Finding fifteen — under a rule of evidence admitting only algebra theorems, the floor is not one of them and no longer pretends to be: the count is not declared in the source at all, so nothing certifies it and nothing needs to. _{SEALED · 92ecdd4a-a342-8338-b895-1231ddc09611}
• Finding sixteen — no per-problem theorem carries the count as a conjunct any more: a conjunct that is a typed constant shares a proposition with real algebra, and a reader cannot see which half the kernel worked for, so the seven now state only what decide actually settled. _{SEALED · 2d96c3c2-d708-80d1-9b48-3838a1dddaac}
• Finding seventeen — the defect this trial used to record is gone rather than conceded: a theorem closed by reflexivity on a constant the file declares certifies a declaration and is not evidence about the world, and it was removed instead of kept beside a note admitting it. _{SEALED · b0b84f99-7218-8d84-be68-58d5ba00a822}
• Finding eighteen — the weight rests instead on non-entailment, which is checkable without this file: each of the seven propositions is a closed computation over finite lists whose value is fixed by arithmetic alone, so its truth is the same whichever way the corresponding conjecture goes, and a statement whose truth cannot vary with a conjecture carries no information about it. _{SEALED · 08e84d98-34ba-8e35-bd38-2fdfcdb72fcf}
• Finding seven — the honest pairing survives the same trial: seven of seven green is true, and zero of seven settled is true because no proposition among them reaches a conjecture object — the two count different things, and the second is measured over the tree rather than set by a constant this file declares. _{SEALED · a33b7fb7-0b15-8428-80fe-245d79566007}

What the trial does not say

It does not say the seven conjectures are false, that they cannot be settled, or that the formal layer is worthless — finding one records the opposite, that all seven are green. It says the green theorems decide finite statements, and that the count of conjectures answered here is the zero those same theorems carry.

Standing

A Clay Millennium Prize claim is settled outside any repository: the Clay Mathematics Institute requires publication in a refereed journal of worldwide repute and two years of general acceptance in the community. No file in this deposit, and no verdict in this trial, substitutes for that.

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18 findings, 18 SEALED · claim receipt d60b8e85-43c0-8b4c-8ed4-9bb16f356da7 · proof-of-verdict root 5f93fe6d-6b73-89b9-bf3d-bcdd2779e96d (order-invariant: the same root for any ordering of the findings) · findings fold d4f37669-41aa-8c7d-8fcf-16b1c72a28c8 · integrity, not truth · 0/7