Mazur's rational torsion theorem

6. 06 — Integration and hardening🔗

Theorem6.1
Group: Pin convergence, stable APIs, final assembly, kernel audit, and exposition. Stage weight: 50 points. (3)
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Theorem 6.2
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uses 1used by 1XL∃∀N

Converge on a shared Mathlib and Tau Ceti pin. Move the imported baseline and every upstream consumer to one exact Lean/Mathlib dependency graph without weakening the kernel, linter, or source-policy gates.

Status: planned.

Canonical deliverables — these names are authoritative for this node:

  • integration (proposed): MazurTheorem.Release.sharedDependencyGraph Pin Mazur and the tested Tau Ceti consumer workspace to one exact Lean, Mathlib, and transitive dependency graph.

  • integration (proposed): MazurTheorem.Release.tauCetiConsumerBuild Build the Tau Ceti contracts as a downstream consumer without weakening either repository's quality gates.

Theorem6.2
Group: Pin convergence, stable APIs, final assembly, kernel audit, and exposition. Stage weight: 50 points. (3)
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Theorem 6.1
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Statement uses 3
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Theorem 2.8
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used by 1XL∃∀N

Integrate finite and prime point-order APIs. Expose one unconditional statement saying that every rational torsion point has one of Mazur's allowed orders.

Status: blocked.

Canonical deliverables — these names are authoritative for this node:

  • theorem (proposed): MazurTorsion.rationalTorsion_orders_mem_cyclicOrders Combine all finite endpoints and the prime-order theorem into an unconditional allowed-order result.

Theorem6.3
Group: Pin convergence, stable APIs, final assembly, kernel audit, and exposition. Stage weight: 50 points. (3)
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Theorem 6.1
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uses 1used by 1XL∃∀N

Kernel-check Mazur's torsion bound. Feed the unconditional point-order theorem to the compiled cardinality reduction and prove that rational torsion has cardinality at most 16.

Status: blocked.

Canonical deliverables — these names are authoritative for this node:

  • theorem (proposed): Challenge.Mazur.torsion_ncard_le Prove the exact Lean Pool challenge statement that the rational torsion set has ncard at most 16.

Theorem6.4
Group: Pin convergence, stable APIs, final assembly, kernel audit, and exposition. Stage weight: 50 points. (3)
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Theorem 6.1
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uses 1used by 0XL∃∀N

Final exposition, provenance, and reproducibility audit. Verify every Blueprint arrow against the actual declaration graph, reproduce the build from the lockfiles, and publish source and axiom reports.

Status: blocked.

Canonical deliverables — these names are authoritative for this node:

  • audit (proposed): MazurTheorem.Release.kernelAndProvenanceAudit Record the final axiom report, exact source pins, declaration provenance, and reproducible build evidence.

  • integration (proposed): MazurTheorem.Release.versoBlueprint Publish a Verso blueprint whose labels and mathematical dependency edges exactly match the canonical programme.