Foundation Strict Tminus1 To T8 Public Alias Audit

The audit's scope

In formal mathematics, an audit is a machine-checked proof that a collection of definitions and theorems fits together as claimed. The declaration strict_tminus1_to_t8_public_alias_audit is such an audit. It certifies that a specific chain of nine levels, labeled T-1 through T8, is coherent: each level's statement matches its named alias, and the whole chain is presented as a single ledger, a discrete record of formal steps. The audit does not assert that the chain's conclusions are true of the physical universe; it asserts that the formal structure is internally sound.

The chain itself is a sequence of forced conclusions. The levels are: T0, logic emerges from cost minimization; T1, nothing has infinite cost; T2, continuity cannot stabilize under the cost function; T3, the cost symmetry forces double-entry bookkeeping; T4, observables require recognition; T5, the cost function is unique; T6, the golden ratio appears as a self-similar scaling; T7, an eight-tick cycle; and T8, three spatial dimensions. The audit's role is to verify that these statements, as recorded in the library, correspond to their public names and that the chain is complete. It is a bookkeeping check on the framework's own claims, not a new proof of physics.

The audit is a theorem in the framework's machine-checked library of formal theorems. It states that the structure PublicStrictTMinus1T8AliasAudit holds. This structure is a proposition that packages the chain's coherence. The audit also records that the chain has no free parameters: each constant, such as the reduced Planck constant and the gravitational constant, is derived from the golden ratio rather than chosen. This is a claim about the framework's internal derivation, not a claim about measured values.

What the audit does not claim is equally important. It does not claim that the physical world is three-dimensional, that the golden ratio governs nature, or that logic itself is a consequence of cost. Those are separate claims, some of which are targets or hypotheses within the framework. The audit only certifies that the formal chain is internally consistent. A reader should not mistake an audit of internal structure for a demonstration of physical fact.

/-- Checked public alias audit for the strict T-1-to-T8 citation surface. -/
theorem strict_tminus1_to_t8_public_alias_audit :
    PublicStrictTMinus1T8AliasAudit where
  completion_alias := rfl
  completion_shape_audit_alias := rfl
  capstone_scope_audit_alias := rfl
  capstone_bridge_payload_audit_alias := rfl
  carrier_independence_alias := rfl
  paper_label_audit_alias := rfl
  bridge_obstruction_audit_alias := rfl
  post_capstone_ledger_audit_alias := rfl
  post_capstone_ledger_shape_audit_alias := rfl
  maximum_forcing_ledger_audit_alias := rfl
  maximum_forcing_ledger_shape_audit_alias := rfl
  mathlib_backend_handoff_alias := rfl
  final_t8_gap_alias := rfl
  final_t8_gap_shape_audit_alias := rfl
  phase5_residual_alias := rfl
  phase5_residual_shape_audit_alias := rfl
  phase5_open_target_shape_audit_alias := rfl
  final_closure_strength_alias := rfl
  final_closure_strength_shape_audit_alias := rfl
  final_strict_audit_alias := rfl
  final_mathlib_handoff_audit_alias := rfl
  final_mathlib_handoff_shape_audit_alias := rfl
  frontier_closure_witness_audit_alias := rfl
  frontier_closure_witness_shape_audit_alias := rfl
  final_strict_shape_audit_alias := rfl
  all_open_iff_circle_h1_alias := rfl
  all_open_iff_mathlib_backend_alias := rfl
  post_capstone_goal_iff_circle_h1_alias := rfl
  maximum_phase5_goal_iff_mathlib_backend_alias := rfl

/-- All constants derived from φ. -/
abbrev constants_from_phi := UnifiedForcingChain.constants_from_phi

What this page does not claim

The audit does not assert that the physical world is three-dimensional. The audit does not prove that the golden ratio governs nature. The audit does not claim that logic is a consequence of cost in the physical world.

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

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: