Seven locks. Behind each, a prize from the treasury and a certificate printed once. In front of each, a sandbox that holds the checker in full; the answer stays with you, in every form. Classical zero is a label laid over a balance — the table calls that a linguistic deception and plays free of it; these seven are the places where the volume says plainly what it has yet to establish, and pays whoever establishes it.
— the five-dollar tier of the till — seats you at a lock for ninety days, with the sandbox and as many submissions as you care to make. Marks are earned at the tables or bought at the till; the entry is paid by signed note, and the ledger records it from the first.
How a lock opens
Three of the seven are decided by a machine: a finite structure is checked clause by clause in exact rational arithmetic, or a Lean project is built and every target printed with the axioms it rests on. When the check passes, the engine issues a release token — a keyed hash over the lock, your key, and your artifact — and the token, presented at the till, mints the certificate to you and pays the marks. The key that makes the token is the one thing that stays outside the sandbox. The other four are proofs, and proofs are read: the clock starts at submission, the read is under the review terms of this record, and the verdict is published beside the submission. A refutation releases the same prize as a proof. Where a partial result is a result, the lock says so and prices it.
The locks
Exhibit a finite structure, in exact rational arithmetic, that satisfies every axiom of P_base together with the reference clauses, and in which the referent admits.
- The sandbox holds
- axioms/pbase.json — the base theory, clause by clause
axioms/refclauses.json — the reference clauses
axioms/target-L7.json — the admission sentence the model must satisfy
models/model-A.json, models/model-B.json — the two witnessing models of the class-wide theorem, as worked examples of the submission format
verify/fo-eval.js — the checker, runnable offline: node verify/fo-eval.js axioms/... models/... - What releases it
- Automatic. Every axiom true, the target sentence true, the universe finite, every numeric carrier exact.
- The prize
- 12,000 marks · the certificate THE ADMITTING MODEL, a print run of one
Why it is first. It carries the chain that joins the class-wide theorem to the zeta instance. Model B separates the class-wide schema by evading the reference clauses; a model that satisfies them while admitting is the instance-separation itself.
Name a nontrivial finitely axiomatized subclass for which the Selberg-axiom recovery of the trace typing is exact, and decide class-wide Admission over it: submit the axiom set, and either a derivation certificate or a pair of finite models separating Admission from its counter-inscription.
- The sandbox holds
- axioms/pbase.json
axioms/admclass.json, axioms/counteradmclass.json — the schema and its counter-inscription
verify/fo-eval.js
verify/derivation-check.js — checks a Hilbert-style derivation certificate against the submitted axiom set - What releases it
- Automatic for the separating-pair route (both models check). The derivation route releases automatically when the certificate checks and the axiom set is nontrivial by the posted criterion; the nontriviality criterion is printed in the sandbox.
- The prize
- 9,000 marks · the certificate THE FINITE AXIOM SET, a print run of one
Extend the kernel formalization from G_K to the full strict grammar, with the implementation blank eliminated and numeral canonicity machine-checked.
- The sandbox holds
- lean/ — the kernel project as it stands, pinned toolchain
lean/Statement.lean — the theorem list a submission must discharge, as declarations with sorry
verify/lean-check.sh — runs the toolchain, then #print axioms on every target - What releases it
- Automatic. The project builds, every target in Statement.lean is closed, and #print axioms lists only the three allowed.
- The prize
- 15,000 marks · the certificate THE FULL GRAMMAR, CHECKED, a print run of one
Prove the unconditional stiffness wedge: exhibit exact boundary bounds under which Φ > 0 on a right neighborhood of the line, or show no such bounds exist.
- The sandbox holds
- wedge/phi.py — Φ evaluated in exact rationals against the Odlyzko/Platt zero data shipped with it
wedge/known.md — what is known: Lagarias 1999, the explicit zero-free regions, the verification height
wedge/format.md — what a submission contains: the statement, the constants, the proof - What releases it
- A read under the review terms. The clock starts at submission; the referee's verdict is published on the ledger with the submission. A correct partial result — exact constants on a bounded height range — earns a partial release printed in the sandbox.
- The prize
- 15,000 marks · the certificate THE STIFFNESS WEDGE, a print run of one
Partial release: 2,000 marks for exact constants on a stated height range, checked by wedge/phi.py.
Prove or refute that the standard analytic roster represents every exit-locus formation of the completed descent; that is, that C_cov holds for ζ.
- The sandbox holds
- coverage/statement.md — C_cov stated in both registers
coverage/roster.json — the standard analytic roster as the volume fixes it - What releases it
- A read under the review terms. Refutation and proof release the same prize.
- The prize
- 12,000 marks · the certificate THE COVERAGE THEOREM, a print run of one
Determine whether the di-cone sextic's paired critical ratios admit a spectral interpretation under the prime-fused field, and prove or refute the silhouette comparison at all truncations.
- The sandbox holds
- dicone/sextic.py — the sextic, its paired critical ratios, the silhouette at each truncation, in exact arithmetic
dicone/table.csv — the ratios to the truncations the volume computed - What releases it
- A read under the review terms.
- The prize
- 9,000 marks · the certificate THE DI-CONE RATIOS, a print run of one
Give a formation-faithful interpretation of a zero-based foundation into P† and compute its price on the explicit-formula ledger.
- The sandbox holds
- interp/faithfulness.md — what formation-faithful requires, clause by clause
interp/ledger.json — the explicit-formula ledger the price is computed on
verify/faithfulness-check.js — checks the clause-by-clause mapping a submission declares; the price computation is read by the referee - What releases it
- Two stages: the faithfulness check is automatic and gates the read; the price computation is read under the review terms.
- The prize
- 9,000 marks · the certificate THE INTERPRETED FOUNDATION, a print run of one
The ledger
Every entry, submission, verdict and release is appended to /seven/ledger with its hashes —
public from the first entry, readable by anyone, and the only record the engine believes. A released lock stays
on this page with the key that opened it.
Standing
The seven are the volume's own open problems, reproduced from the source of record. The checkers are published in full and run offline; every axiom file names the labelled clause of the volume it transcribes, and a lock opens exactly when its worked example checks against it. Nothing about a lock's standing depends on this site: the statements are the book's, the verifiers are yours to inspect, and the prize is a signed note from a treasury whose census is public.
Write to parkeremmerson@icloud.com with the lock's id for anything the sandbox leaves unclear.