Encyclopedia Foundation Foundation Pair Kernel Event Action Ancestry S14 Ledger Normalized Curvature Sig

ARTICLE 4 claims 4 theorems

Foundation Pair Kernel Event Action Ancestry S14 Ledger Normalized Curvature Sig

A machine-checked theorem shows that the simplest bookkeeping events carry a built-in curvature, but the physical meaning of that curvature depends on a choice the theorem does not make.

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The curved attachment

The declaration ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen is a theorem in the framework's machine-checked library of formal theorems. It states that every realized primitive posting pair, the smallest unit of the framework's discrete event record, carries a well-defined curvature and a source, and that these attach to the event in a way that respects a signed symmetry. In plain terms: the simplest possible bookkeeping entry already has a shape, and that shape is not an accident of the entry but a consequence of the framework's forced cost law.

The theorem is a statement about the framework's own objects, not about physics directly. It proves that for any realized posting, there exists a constant curvature, specifically the hyperbolic cosine of 1, and a source, twice the variational source at unit drop, such that the resulting Green field satisfies the attachment condition. The proof is axiom-clean: it uses no additional assumptions beyond the framework's standard postulates, and no unproved steps.

What the theorem does not claim is equally important. It does not claim that this ledger-normalized branch is the one that connects to physical action. The framework proves two mathematically consistent branches: one where the exact-J cost is taken in its native units, and one where it is scaled by the ledger's own unit. The theorem under discussion is about the ledger-normalized branch. The framework explicitly proves that event-to-energy-time attachment alone does not select which branch is physical. The choice of field unit map remains open, and the theorem does not resolve it.

The consequence for a reader is a clear picture of where the framework stands. The curvature is not an input; it is forced by the cost law. But the step from this discrete ledger to a physical energy-time action is a separate, unforced choice. The theorem sharpens the framework's internal structure without overreaching into physics.

THEOREM ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean
ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean:416 
theorem ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen
    {N : ℕ} [NeZero N]
    (hN : 2 ≤ N)
    (event : PostingPair3 N)
    (hevent : event ∈ realizedPrimitivePostingPairs3 N)
    (σ : Equiv.Perm (Fin 3)) :
    ConstantCurvatureSignedPostingAttachment3
      ledgerNormalizedExactJTangentCurvature
      ledgerNormalizedExactJTangentCurvature_pos.le
      ledgerNormalizedOrderedExactJSource event σ
      (constantCurvatureSignedGreenField3
        ledgerNormalizedExactJTangentCurvature
        ledgerNormalizedOrderedExactJSource event) :=
  constantCurvatureSignedPostingAttachment3_realGreen
    hN ledgerNormalizedExactJTangentCurvature
      ledgerNormalizedExactJTangentCurvature_pos
      ledgerNormalizedOrderedExactJSource event hevent σ
THEOREM ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean
ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean:416 
theorem ledgerNormalizedCurvatureSignedPostingAttachment3_realGreen
    {N : ℕ} [NeZero N]
    (hN : 2 ≤ N)
    (event : PostingPair3 N)
    (hevent : event ∈ realizedPrimitivePostingPairs3 N)
    (σ : Equiv.Perm (Fin 3)) :
    ConstantCurvatureSignedPostingAttachment3
      ledgerNormalizedExactJTangentCurvature
      ledgerNormalizedExactJTangentCurvature_pos.le
      ledgerNormalizedOrderedExactJSource event σ
      (constantCurvatureSignedGreenField3
        ledgerNormalizedExactJTangentCurvature
        ledgerNormalizedOrderedExactJSource event) :=
  constantCurvatureSignedPostingAttachment3_realGreen
    hN ledgerNormalizedExactJTangentCurvature
      ledgerNormalizedExactJTangentCurvature_pos
      ledgerNormalizedOrderedExactJSource event hevent σ
THEOREM identityExactJMap_forces_S13_native_package · ledgerScaleExactJMap_forces_dropOne_package · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean
identityExactJMap_forces_S13_native_package · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean:333 
theorem identityExactJMap_forces_S13_native_package
    {N : ℕ} [NeZero N]
    {kinematics : PostingEventKinematics3 N}
    {drop sourceMagnitude : PostingPair3 N → ℝ}
    (hcoherence :
      PrimitivePostingRealizesOneCoherenceEvent3 kinematics)
    (hmap :
      MappedExactJDropRepresentsEventAction3 1 kinematics drop)
    (hsource :
      EventDropSourceIsExactJConjugate3 drop sourceMagnitude)
    {event : PostingPair3 N}
    (hevent : event ∈ realizedPrimitivePostingPairs3 N) :
    drop event = nativeActionCanonicalDrop ∧
      sourceMagnitude event = nativeExactJConjugateSource ∧
      2 * sourceMagnitude event = nativeOrderedExactJSource ∧
      Real.cosh (drop event) = 1 + Constants.hbar := by
  have hdrop :=
    identityExactJMap_selects_nativeActionCanonicalDrop
      hcoherence hmap hevent
  refine ⟨hdrop, ?_, ?_, ?_⟩
  · rw [hsource event hevent, hdrop]
    rfl
  · rw [hsource event hevent, hdrop]
    rfl
  · rw [hdrop]
    exact nativeActionCanonicalDrop_cosh
ledgerScaleExactJMap_forces_dropOne_package · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean:373 
theorem ledgerScaleExactJMap_forces_dropOne_package
    {N : ℕ} [NeZero N]
    {scale : ℝ}
    {kinematics : PostingEventKinematics3 N}
    {drop sourceMagnitude : PostingPair3 N → ℝ}
    (hcoherence :
      PrimitivePostingRealizesOneCoherenceEvent3 kinematics)
    (hscale : PrimitivePostingActionScaleLaw scale)
    (hmap :
      MappedExactJDropRepresentsEventAction3 scale kinematics drop)
    (hsource :
      EventDropSourceIsExactJConjugate3 drop sourceMagnitude)
    {event : PostingPair3 N}
    (hevent : event ∈ realizedPrimitivePostingPairs3 N) :
    drop event = 1 ∧
      sourceMagnitude event = exactJVariationalSource 1 ∧
      2 * sourceMagnitude event =
        ledgerNormalizedOrderedExactJSource ∧
      Real.cosh (drop event) =
        ledgerNormalizedExactJTangentCurvature := by
  have hdrop :=
    ledgerScaleExactJMap_selects_drop_one
      hcoherence hscale hmap hevent
  refine ⟨hdrop, ?_, ?_, ?_⟩
  · rw [hsource event hevent, hdrop]
  · rw [hsource event hevent, hdrop]
    rfl
  · rw [hdrop]
    rfl
THEOREM coherentEventModel_does_not_make_identityLedgerMap · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean
coherentEventModel_does_not_make_identityLedgerMap · IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean:595 
/-- Unit-map countermodel: a coherent-event MODEL is compatible with the
proved failure of the identity ledger conversion. -/
theorem coherentEventModel_does_not_make_identityLedgerMap :
    PrimitivePostingRealizesOneCoherenceEvent3
        (canonicalCoherenceKinematics3 3) ∧
      ¬ PrimitivePostingActionScaleLaw 1 :=
  ⟨canonicalCoherenceKinematics_satisfies_model,
    identityUnitMap_fails_nativeAction⟩

What this page does not claim

The theorem does not claim that the ledger-normalized branch is the physical one. The theorem does not claim that the curvature is a physical observable. The theorem does not claim that the framework derives the fine-structure constant.

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Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/PairKernelEventActionAncestryS14.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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