Encyclopedia Gravity Gravity Analysis Regge4 Dtransported Algebraic Closer Regge4 Dtransported Algebr

ARTICLE 5 claims 5 theorems

Gravity Analysis Regge4 Dtransported Algebraic Closer Regge4 Dtransported Algebr

A machine-checked status report that separates what is known from what remains open in a four-dimensional gravity analysis.

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The status ledger

The declaration regge4DTransportedAlgebraicCloserStatus_flags is a single, machine-checked record of what has been established and what has not in a specific four-dimensional gravity calculation. It acts as a ledger, a discrete record of completed and pending items, for a family of mathematical objects called transported algebraic closers. The record itself is a theorem: it states, in one conjunction, which properties are closed (proved) and which are open (not proved).

The closed properties include: the continuum symbol sequence is uniquely defined; the quadratic homogeneity holds; the one-orbit fold tends to the expected value; and the area convention matches. The open properties are named explicitly: the transverse-traceless isotropy target and the gauge-zero target remain unproved, and the connection to the Einstein-Hilbert action convergence is explicitly not inhabited. The declaration also records that the gap action recovery is not flipped.

This status record is not a proof of the main physical claim. It does not establish that the transported fold converges to the Einstein-Hilbert coefficient of -1/4. It does not prove that the gauge-zero target holds for all gauge vectors; in fact, a counterexample is known. The record's value is in its precision: it banks every algebraic identity available without claiming the convergence it does not have.

In Recognition Science, this declaration is a model of epistemic honesty. It shows exactly what the framework's library has derived and exactly where the derivation stops. The library proves the algebraic structure, the uniqueness of limits, and the homogeneity properties. It does not prove the physical convergence. This separation is the core of the framework's method: exact provenance for every claim, and an explicit list of what is not claimed.

THEOREM regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean
regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean:270 
theorem regge4DTransportedAlgebraicCloserStatus_flags :
    regge4DTransportedAlgebraicCloserStatus.continuumSymbolBoundClosed =
        true ∧
      regge4DTransportedAlgebraicCloserStatus.quadraticHomogeneityClosed =
        true ∧
        regge4DTransportedAlgebraicCloserStatus.t11M2TendstoClosed = true ∧
          regge4DTransportedAlgebraicCloserStatus.oneOrbitDecoyClosed =
            true ∧
            regge4DTransportedAlgebraicCloserStatus.transportedTTIsotropyClosed =
              false ∧
              regge4DTransportedAlgebraicCloserStatus.transportedGaugeZeroClosed =
                false ∧
                regge4DTransportedAlgebraicCloserStatus.areaConventionMatchClosed =
                  true ∧
                  regge4DTransportedAlgebraicCloserStatus.srsConvergesEH4d =
                    false ∧
                    regge4DTransportedAlgebraicCloserStatus.gapActionRecovery =
                      false := by
  decide
THEOREM regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean
regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean:270 
theorem regge4DTransportedAlgebraicCloserStatus_flags :
    regge4DTransportedAlgebraicCloserStatus.continuumSymbolBoundClosed =
        true ∧
      regge4DTransportedAlgebraicCloserStatus.quadraticHomogeneityClosed =
        true ∧
        regge4DTransportedAlgebraicCloserStatus.t11M2TendstoClosed = true ∧
          regge4DTransportedAlgebraicCloserStatus.oneOrbitDecoyClosed =
            true ∧
            regge4DTransportedAlgebraicCloserStatus.transportedTTIsotropyClosed =
              false ∧
              regge4DTransportedAlgebraicCloserStatus.transportedGaugeZeroClosed =
                false ∧
                regge4DTransportedAlgebraicCloserStatus.areaConventionMatchClosed =
                  true ∧
                  regge4DTransportedAlgebraicCloserStatus.srsConvergesEH4d =
                    false ∧
                    regge4DTransportedAlgebraicCloserStatus.gapActionRecovery =
                      false := by
  decide
THEOREM regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean
regge4DTransportedAlgebraicCloserStatus_flags · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean:270 
theorem regge4DTransportedAlgebraicCloserStatus_flags :
    regge4DTransportedAlgebraicCloserStatus.continuumSymbolBoundClosed =
        true ∧
      regge4DTransportedAlgebraicCloserStatus.quadraticHomogeneityClosed =
        true ∧
        regge4DTransportedAlgebraicCloserStatus.t11M2TendstoClosed = true ∧
          regge4DTransportedAlgebraicCloserStatus.oneOrbitDecoyClosed =
            true ∧
            regge4DTransportedAlgebraicCloserStatus.transportedTTIsotropyClosed =
              false ∧
              regge4DTransportedAlgebraicCloserStatus.transportedGaugeZeroClosed =
                false ∧
                regge4DTransportedAlgebraicCloserStatus.areaConventionMatchClosed =
                  true ∧
                  regge4DTransportedAlgebraicCloserStatus.srsConvergesEH4d =
                    false ∧
                    regge4DTransportedAlgebraicCloserStatus.gapActionRecovery =
                      false := by
  decide
THEOREM banked_does_not_inhabit_eh_or_flip_gap · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean
banked_does_not_inhabit_eh_or_flip_gap · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean:290 
/-- Honesty: banked (1,1) identities do not inhabit continuum EH Tendsto,
and the ledger flag stays false. -/
theorem banked_does_not_inhabit_eh_or_flip_gap :
    regge4DTransportedAlgebraicCloserStatus.transportedTTIsotropyClosed =
        false ∧
      regge4DTransportedAlgebraicCloserStatus.gapActionRecovery = false ∧
        oneOrbitRayNormalizedCoeff axisTTPlus ≠
          einsteinHilbertTTCoefficient4D :=
  ⟨rfl, rfl, oneOrbit_ray_normalized_ne_eh_coefficient⟩
THEOREM Regge4DContinuumGaugeZeroTargetLongitudinal · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean
Regge4DContinuumGaugeZeroTargetLongitudinal · IndisputableMonolith/Gravity/Analysis/Regge4DTransportedAlgebraicCloser.lean:186 
/-- **THEOREM target (restricted).** Transported distinct-hinge / one-orbit
m² vanishes on the banked pure-gauge family the Hessian actually
annihilates: `decoyGauge = gaugePart(axisWave, e₀)` along `symbolDir`,
plus the `(1,1)`-orbit `FoldAlongM2Tendsto` witness.

This is **not** quantification over every `Wave4` gauge vector. The
unrestricted Prop `Regge4DContinuumGaugeZeroTarget` /
`Regge4DTransportedGaugeZeroOpen` is false as a transported claim
(counterexample `m=(1,1,0,0)`, `v=e₂` gives distinct-hinge m² ≈ −1;
L-p1-transported-gauge-zero-false-for-general-v). Do not flip
`transportedGaugeZeroClosed` on the unrestricted statement. -/
def Regge4DContinuumGaugeZeroTargetLongitudinal : Prop :=
  m2TransportedAllOrbitMomentDistinctHinge decoyGauge symbolDir = (0 : ℝ) ∧
    FoldAlongM2Tendsto decoyGauge

What this page does not claim

The declaration does not claim that the four-dimensional gravity calculation is complete or that the open targets are false. The declaration does not claim that the counterexample to the gauge-zero target invalidates the framework's approach. The declaration does not claim that the algebraic identities it banks are sufficient to prove the physical convergence.

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/Regge4DTransportedAlgebraicCloser.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:

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