Gravity Analysis Regge Bloch Transported All Orbit M2 Eval4 D

The orbital moment check

In Recognition Science, the framework's machine-checked library of formal theorems closes a specific calculation about gravitational orbits. The module examines a quantity called the transported all-orbit m² moment, a weighted average over the possible orbits of a system, evaluated on a particular axis. The central result is that this moment equals -5/2, established by summing integer certificates for each orbit slice. This is a recognition event, a discrete record of a system's state, and the calculation verifies that the framework's model of gravity produces a consistent, finite value.

The module also proves a symmetry property. When the same moment is computed with a distinct-hinge weighting, a fold that treats each hinge of the orbit separately, the value becomes -1/4 for both the plus and cross configurations. The raw all-orbit moment on the cross axis is 0, but the distinct-hinge fold matches the plus result. This agreement is a check that the framework's model is isotropic, meaning it does not prefer one direction over another, at least along the tested axes. The module also proves that a decoy gauge, a test configuration, vanishes under these weights, confirming that the result is not an artifact of the chosen coordinates.

The calculation is not complete. The module explicitly leaves open a question about the axis-aligned ray, a direction along the time axis. On this ray, the plus and cross configurations disagree on the raw moment, and the full two-jet correction, a more complete version of the calculation, does not repair this anisotropy. The framework's library records this as an open target, not a failure, but a place where the model has not yet closed the gap. The module also confirms that the full two-jet calculation does not flip the status of a separate recovery property, preserving that result stable.

What this establishes in plain language is that the framework's model of gravity passes a specific, non-trivial test. The weighted average over orbits is finite and matches a predicted value, and the model is isotropic along the tested directions. The open question on the axis-aligned ray is a known limitation, a place where the model does not yet agree with itself. This is the nature of the framework: it proves what it can, and it names what it cannot.

/-- Named restoration claim: full two-jet makes `axisTTPlus` on `e0Dir`
leave zero.  Status false (plus stays `0` because `A2*K0` vanishes). -/
def Regge4DFullTwoJetRestoresE0PlusVanishing : Prop :=
  m2TransportedAllOrbitMomentDistinctHingeFull axisTTPlus e0Dir ≠ (0 : ℝ)

theorem sum_m2OrbitCertZ22E0_plus :
    (∑ s : Fin 24, ∑ t : Fin 10, m2OrbitCertZ22E0 axisTTPlusCoeffZ s t) =
      (0 : ℤ) := by
  decide

set_option maxRecDepth 12000 in
set_option maxHeartbeats 8000000 in

theorem full_twojet_does_not_flip_gap_action_recovery :
    reggeBlochFullTwoJetM2Eval4DStatus.gapActionRecovery = false :=
  rfl

What this page does not claim

The module does not prove that the model is isotropic in all directions. The module does not derive the value of the fine-structure constant or any other fundamental constant. The module does not claim that the open question on the axis-aligned ray is impossible to resolve.

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/ReggeBlochTransportedAllOrbitM2Eval4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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