Foundation Pair Kernel Event Action Ancestry S14 Coherent Event Model Does Not M

The coherent event model

In the Recognition Science framework, a ledger is a discrete record of events, and a recognition is the act of recording one. The theorem coherentEventModel_does_not_make_identityLedgerMap addresses a specific question: when a primitive event carries one unit of coherence energy for one fundamental duration, does the ledger's own bookkeeping automatically match the physical action? The answer is no.

The theorem proves two things together. First, the canonical model of a primitive posting, where each event carries one coherence energy E_coh for one fundamental duration tau0, does satisfy the condition of realizing one coherence event. Second, the primitive posting action scale law fails for the scale factor 1. This means the identity map, which would take a ledger drop of 1 directly to the physical action, is not a valid choice. The two branches that do work are the identity exact-J action units, which select the drop arcosh(1 + hbar), and the ledger-derived scale hbar / Jlog(1), which maps the raw ledger drop 1 to the same physical action.

The declaration does not claim that the coherent event model is impossible, nor that it fails to produce a physical action. It establishes that the attachment of event to energy-time alone does not select the field unit map. The model is consistent; it simply does not force the identity map. The theorem is a precise negative result within the framework's own development, and it is proved with no sorry and no new axioms.

theorem canonicalCoherenceKinematics_satisfies_model
    {N : ℕ} [NeZero N] :
    PrimitivePostingRealizesOneCoherenceEvent3
      (canonicalCoherenceKinematics3 N) := by
  constructor <;> intro event hevent <;> rfl

/-- 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⟩

/-- The unit convention fork is nontrivial: the identity-map native drop and
the ledger-normalized drop are provably distinct. -/
theorem identityDrop_ne_ledgerNormalizedDrop :
    nativeActionCanonicalDrop ≠ 1 :=
  nativeActionCanonicalDrop_ne_ledgerUnit

What this page does not claim

The coherent event model is impossible or inconsistent. The identity map is the only map that fails. The framework derives the fine-structure constant alpha.

Verify this page

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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