Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Daudit M2 Tt Identity Audit

The audit package

In formal mathematics, a proof is only as trustworthy as the steps it takes for granted. The declaration m2_tt_identity_audit_package is a compact certificate: it states two facts at once. First, a table used in the calculation has exactly 1,208 entries. Second, a particular theorem about a gravity-related identity, called exact_midpoint_m2_tt_identity, is marked as proved. The declaration bundles these two statements into a single package that other proofs can refer to.

The table's size matters because of how the proof was checked. The identity involves a large calculation over many cases. The framework's machine-checked library of formal theorems verified each entry of the table individually, using a slow but certain method. It then lifted those verified entries into the main theorem. This avoids a shortcut called native_decide, which can be fast but is harder to audit. By using the slower method, every step is visible to the proof checker.

The main theorem itself, exactMidpointBlochM2_eq_neg_eighth_frobenius_tt, is what the audit establishes as sorry-free. In formal proof systems, a "sorry" is an admitted gap, a place where the author says "trust me." This theorem has none. The audit confirms that the proof relies only on the standard axioms of the underlying logic: propositional extensionality, choice, and quotient soundness. No special axioms were added to make the calculation work.

What the audit does not claim is just as important. It does not say the identity is physically true in gravity. It only says the formal proof is logically complete. The identity might still be wrong in its assumptions, or the model might not match reality. The audit also does not claim the 1,208-entry table is correct by itself; it certifies that each entry was checked, not that the table was derived from a simpler formula. Finally, it does not claim the theorem is useful or meaningful, only that it is proved.

The practical consequence is a higher standard of trust. When a calculation is too large to inspect by eye, a certificate like this lets a reader know exactly what was checked and how. It turns a vague "the computation was verified" into a precise statement: 1,208 entries, each kernel-checked, no shortcuts, clean axioms. That is what the audit package establishes.

theorem m2_tt_identity_audit_package :
    couplingTable.size = 1208 ∧
      ExactMidpointM2TTIdentityProved = true :=
  ⟨couplingTable_size, exactMidpointM2TTIdentityProved_true⟩

theorem m2_tt_identity_audit_package :
    couplingTable.size = 1208 ∧
      ExactMidpointM2TTIdentityProved = true :=
  ⟨couplingTable_size, exactMidpointM2TTIdentityProved_true⟩

theorem m2_tt_identity_audit_package :
    couplingTable.size = 1208 ∧
      ExactMidpointM2TTIdentityProved = true :=
  ⟨couplingTable_size, exactMidpointM2TTIdentityProved_true⟩

What this page does not claim

The audit does not claim the identity is physically true in gravity; it only claims the formal proof is logically complete. The audit does not claim the 1,208-entry table is derived from a simpler formula; it only certifies that each entry was individually checked. The audit does not claim the theorem is useful or meaningful, only that it is proved.

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/Gravity/Analysis/ReggeExactMidpointM2TTIdentity4DAudit.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

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