Foundation Public Strict Tminus1 T8 Alias Audit

The audit's scope

In formal mathematics, an alias is a second name for the same object. The declaration PublicStrictTMinus1T8AliasAudit is a machine-checked certificate, a proof that the public names for the framework's foundational chain all point to the same underlying theorems and definitions. It establishes that the strict audit-first surface, called StrictTMinus1ToT8, is consistently exposed through its public aliases, and that the label map connecting written names to formal declarations agrees with the actual library structure.

The audit covers the chain from T-1 to T8. In the framework's own numbering, T0 is logic emerging from cost minimization, T1 is the claim that nothing has infinite cost, T2 is discreteness, T3 is the ledger, T4 is recognition, T5 is the unique cost function J, T6 is the golden ratio φ, T7 is the eight-tick cycle with 2^3, and T8 is three spatial dimensions. The audit does not prove any of these theorems anew. It verifies that the public names for these results, the abbreviations and structures that users import, are faithful aliases of the underlying formal statements. It also checks the scope: which parts are forced, which are conditional, and which remain open frontier entries.

The audit's value is in what it prevents. A large formal library can drift, where a public name no longer matches the theorem it claims to export, or where a reference points to a declaration that has changed meaning. This certificate closes that gap by machine-checking the alias map. It is a hygiene certificate for the library's public interface, not a new mathematical result.

What the audit does not claim is equally important. It does not assert that the physical recognition-to-linking bridge for three dimensions is complete; that bridge remains an open target. It does not claim that all frontier goals are closed, only that the open ones are correctly recorded. And it does not claim to have proved the Riemann Hypothesis or any other external conjecture; the framework's statements about such topics are equivalences, not proofs. The audit is about naming and scope, not about extending the chain of forced results.

/-- 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

/-- 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

/-- Exact scope of the strict theorem kernel. -/
abbrev strict_tminus1_to_t8_scope :=
  StrictTMinus1ToT8.strict_kernel_iff

What this page does not claim

The audit does not prove the Riemann Hypothesis or any other external conjecture. The audit does not close the physical recognition-to-linking bridge for three dimensions. The audit does not introduce new mathematical theorems beyond the existing chain.

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: