Mazur's rational torsion theorem

Blueprint Summary🔗

Overview
Total entries48completed: 0; deps incomplete: 0; sorries: 0; no proof: 48
Ready now1Entries with an actionable next formalization step.
Fully closed0Local code and prerequisite closure are both complete.
Actionable priorities1Entries ready now and already unlocking downstream work.
Actionable priorities (1)
  • Ready for proof work.
    tag: milestonetag: donetag: integratedtag: mazurstage: proofstatement: ready to formalizedirect uses: 14downstream unlocks: 47proof: ready to formalize
Entry index (48)
Theorems48completed: 0; deps incomplete: 0; sorries: 0; no proof: 48
Informal-only entries48
Theorem / Proposition / Lemma / Corollary Index (48)
By parent groups (5)
Integral X₀(N), its Jacobian and Hecke action, a private Eisenstein witness constructor, and the exact Néron/finite-flat specialization needed at 5. Stage weight: 400 points. (14)
Assemble allowed point orders with height-descent torsion finiteness and finite-abelian shape to prove the full fifteen-group classification, then derive the ncard challenge and audit the release. Stage weight: 50 points. (4)
Canonical coherent cohomology, relative Picard, Jacobian, Abel–Jacobi, Néron prerequisites, and elliptic isogenies, split into startable work packages. Stage weight: 300 points. (13)
Close level 13 and orders 18, 25, 35, and 49; obtain order 11 from the uniform formal-immersion route, reuse the same engine for squarefree level 35, and reduce order 49 directly to the checked X_0(49) cusp classification. Stage weight: 100 points. (8)
A route-neutral degree-one formal-immersion collision at 5, followed by the checked minimal-model additive exclusion, prime-to-five specialization, and ten-point enumeration. Stage weight: 100 points. (8)
Dependency insights
Statement-used entries47Entries reused in statement dependencies.
Tracked parent groups5Grouped health rollups for parents with more than one child entry.
Most used in statements (47)
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 14proof uses: 0direct uses: 14downstream unlocks: 47
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 4proof uses: 0direct uses: 4downstream unlocks: 22
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    statement uses: 3proof uses: 0direct uses: 3downstream unlocks: 23
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    statement uses: 3proof uses: 0direct uses: 3downstream unlocks: 20
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    statement uses: 3proof uses: 0direct uses: 3downstream unlocks: 20
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 3proof uses: 0direct uses: 3downstream unlocks: 16
  • «MT-X0-CUSPS»(Theorem)
    Reverse dependencies recorded in statement dependencies.
    statement uses: 3proof uses: 0direct uses: 3downstream unlocks: 12
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 25
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 24
  • Reverse dependencies recorded in statement dependencies.
    statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 23
  • Show all 37 more statement-used entries
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 14
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 10
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 9
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 6
    • «MT-X11-JOIN»(Theorem)
      Reverse dependencies recorded in statement dependencies.
      statement uses: 2proof uses: 0direct uses: 2downstream unlocks: 5
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 26
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 25
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 22
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 22
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 22
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 21
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 21
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 19
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 18
    • «MT-X0-HECKE»(Theorem)
      Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 17
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 15
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 13
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 12
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 11
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 9
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 8
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 8
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 7
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 7
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 7
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 7
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 4
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 4
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 4
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 4
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 4
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 3
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 3
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 2
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 1
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 1
    • Reverse dependencies recorded in statement dependencies.
      statement uses: 1proof uses: 0direct uses: 1downstream unlocks: 1
Group health (5)
  • Canonical coherent cohomology, relative Picard, Jacobian, Abel–Jacobi, Néron prerequisites, and elliptic isogenies, split into startable work packages. Stage weight: 300 points.shared_geometry
    Grouped view over entries sharing the same parent.
    total: 13closed: 0local-only: 0ready: 0blocked: 13incomplete Lean: 0unlock score: 293
    Next: no ready child currently unlocks downstream work.
  • Integral X₀(N), its Jacobian and Hecke action, a private Eisenstein witness constructor, and the exact Néron/finite-flat specialization needed at 5. Stage weight: 400 points.prime_infrastructure
    Grouped view over entries sharing the same parent.
    total: 14closed: 0local-only: 0ready: 0blocked: 14incomplete Lean: 0unlock score: 190
    Next: no ready child currently unlocks downstream work.
  • A route-neutral degree-one formal-immersion collision at 5, followed by the checked minimal-model additive exclusion, prime-to-five specialization, and ten-point enumeration. Stage weight: 100 points.prime_argument
    Grouped view over entries sharing the same parent.
    total: 8closed: 0local-only: 0ready: 0blocked: 8incomplete Lean: 0unlock score: 59
    Next: no ready child currently unlocks downstream work.
  • Close level 13 and orders 18, 25, 35, and 49; obtain order 11 from the uniform formal-immersion route, reuse the same engine for squarefree level 35, and reduce order 49 directly to the checked X_0(49) cusp classification. Stage weight: 100 points.finite_endpoints
    Grouped view over entries sharing the same parent.
    total: 8closed: 0local-only: 0ready: 0blocked: 8incomplete Lean: 0unlock score: 29
    Next: no ready child currently unlocks downstream work.
  • Assemble allowed point orders with height-descent torsion finiteness and finite-abelian shape to prove the full fifteen-group classification, then derive the ncard challenge and audit the release. Stage weight: 50 points.integration
    Grouped view over entries sharing the same parent.
    total: 4closed: 0local-only: 0ready: 0blocked: 4incomplete Lean: 0unlock score: 6
    Next: no ready child currently unlocks downstream work.
Metadata
Tags in use18Distinct tags currently attached to blueprint entries.
Tag rollups (18)
  • tag: mazur
    entries: 16actionable: 1quick wins: 0linked PRs: 0
  • tag: done
    entries: 10actionable: 1quick wins: 0linked PRs: 0
  • tag: integrated
    entries: 10actionable: 1quick wins: 0linked PRs: 0
  • tag: milestone
    entries: 1actionable: 1quick wins: 0linked PRs: 0
  • tag: blocked
    entries: 30actionable: 0quick wins: 0linked PRs: 0
  • tag: nouns-missing
    entries: 24actionable: 0quick wins: 0linked PRs: 0
  • tag: mixed
    entries: 17actionable: 0quick wins: 0linked PRs: 0
  • tag: proof
    entries: 17actionable: 0quick wins: 0linked PRs: 0
  • tag: infrastructure
    entries: 12actionable: 0quick wins: 0linked PRs: 0
  • tag: tau-ceti
    entries: 12actionable: 0quick wins: 0linked PRs: 0
  • Show all 8 more tags
    • tag: upstream
      entries: 12actionable: 0quick wins: 0linked PRs: 0
    • tag: compiled
      entries: 10actionable: 0quick wins: 0linked PRs: 0
    • tag: integration
      entries: 6actionable: 0quick wins: 0linked PRs: 0
    • tag: paused
      entries: 6actionable: 0quick wins: 0linked PRs: 0
    • tag: statement-only
      entries: 4actionable: 0quick wins: 0linked PRs: 0
    • tag: mathlib
      entries: 3actionable: 0quick wins: 0linked PRs: 0
    • tag: open
      entries: 1actionable: 0quick wins: 0linked PRs: 0
    • tag: research-open
      entries: 1actionable: 0quick wins: 0linked PRs: 0
Metadata audit
Missing owner48
Missing effort48
Missing owner (48)
Missing effort (48)
Structure and coverage
Informal-only48Statements with no associated Lean code yet.
Ready to formalize1Entries with an actionable next formalization step.
Blocked or incomplete47Entries not covered by the highlighted readiness buckets above.
Heaviest prerequisites (47)
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 6statement deps: 6proof deps: 0direct uses: 1downstream unlocks: 3
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 4statement deps: 4proof deps: 0direct uses: 1downstream unlocks: 4
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 4statement deps: 4proof deps: 0direct uses: 2downstream unlocks: 6
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 1downstream unlocks: 2
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 0downstream unlocks: 0
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 1downstream unlocks: 7
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 1downstream unlocks: 9
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 1downstream unlocks: 21
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 2downstream unlocks: 10
  • Prerequisite fan-in measured from the current statement/proof dependency graph.
    total deps: 3statement deps: 3proof deps: 0direct uses: 1downstream unlocks: 18
  • Show all 37 more heaviest-prerequisite entries
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 11
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 15
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 8
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 22
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 3downstream unlocks: 20
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 19
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 3downstream unlocks: 16
    • «MT-X0-HECKE»(Theorem)
      Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 1downstream unlocks: 17
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 2statement deps: 2proof deps: 0direct uses: 4downstream unlocks: 22
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 1
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 3downstream unlocks: 23
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 13
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 12
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 1
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 14
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 9
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 4
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 4
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 3
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 7
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 8
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 7
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 7
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 26
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 25
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 24
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 25
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 22
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 23
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 22
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 21
    • «MT-X0-CUSPS»(Theorem)
      Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 3downstream unlocks: 12
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 3downstream unlocks: 20
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 1
    • «MT-X11-JOIN»(Theorem)
      Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 2downstream unlocks: 5
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 4
    • Prerequisite fan-in measured from the current statement/proof dependency graph.
      total deps: 1statement deps: 1proof deps: 0direct uses: 1downstream unlocks: 4
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