Gravity Analysis Regge Exact Flat Hessian Symbol4 Daudit Exact Hessian Audit Pac

The audit package

The declaration exact_hessian_audit_package is a formal audit of a specific symbolic computation tool for gravity analysis. It is a theorem in the framework's machine-checked library of formal theorems, meaning its statements have been verified by a computer proof checker. The audit bundles together several checks about a mathematical object called an exact Hessian, which is a matrix of second derivatives used to study how a function curves near a point.

In plain terms, the audit establishes four positive results. First, the Hessian satisfies a symmetry condition called isotropy, meaning it looks the same in all directions. Second, it meets a gauge-zero condition, which is a technical requirement about how the Hessian behaves under coordinate changes. Third, the edges of the Hessian have a certain origin property related to a quantity denoted M2. Fourth, a normalization gate passes, meaning the Hessian is scaled correctly. These four checks are proved true.

The audit also records three negative results. It states that an algebraic M2 table is not present, that a symbol status called srsInhabited is false, and that a gap action recovery is false. These are not failures of the audit; they are honest records that certain symbolic checks have not been completed or do not apply. The audit does not claim that the Hessian is fully understood or that the gravity analysis is complete. It simply certifies which checks pass and which remain open.

The value of this audit is precision. In a field where symbolic computations can be error-prone, a machine-checked record of what is and is not established prevents overclaiming. The audit does not prove that the exact Hessian is physically meaningful or that it leads to a theory of gravity. It only certifies the status of specific symbolic checks. This is a small but important step in building a reliable foundation for further analysis.

theorem exact_hessian_audit_package :
    ExactHessianTTIsotropyTarget ∧
      ExactHessianGaugeZeroTarget ∧
        ExactHessianEdgeOriginsM2Banked ∧
          ExactHessianNormalizationGatePass = true ∧
            ExactHessianAlgebraicM2TablePresent = false ∧
              exactHessianSymbolStatus.srsInhabited = false ∧
                exactHessianSymbolStatus.gapActionRecovery = false :=
  ⟨ExactHessianTTIsotropyTarget_closed, ExactHessianGaugeZeroTarget_algebraic_face,
    ExactHessianEdgeOriginsM2Banked_closed, exactHessianNormalizationGatePass_true,
    rfl, rfl, rfl⟩

theorem exact_hessian_audit_package :
    ExactHessianTTIsotropyTarget ∧
      ExactHessianGaugeZeroTarget ∧
        ExactHessianEdgeOriginsM2Banked ∧
          ExactHessianNormalizationGatePass = true ∧
            ExactHessianAlgebraicM2TablePresent = false ∧
              exactHessianSymbolStatus.srsInhabited = false ∧
                exactHessianSymbolStatus.gapActionRecovery = false :=
  ⟨ExactHessianTTIsotropyTarget_closed, ExactHessianGaugeZeroTarget_algebraic_face,
    ExactHessianEdgeOriginsM2Banked_closed, exactHessianNormalizationGatePass_true,
    rfl, rfl, rfl⟩

What this page does not claim

The audit does not claim the exact Hessian is physically meaningful or that it yields a theory of gravity. The audit does not claim the symbolic checks that remain false are impossible to complete. The audit does not claim the Hessian analysis is complete or that all relevant checks have been performed.

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/ReggeExactFlatHessianSymbol4DAudit.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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