Gravity Analysis Regge Bloch Star Edge Origins M2 Eval4 D Slot Orbit Deficit Pha

A slot deficit certificate

In the Recognition Science framework's study of four-dimensional gravity, the declaration slotOrbitDeficitPhase2EdgeOrigins_t12_eq_Z (a named result in the machine-checked library of formal theorems) establishes a precise arithmetic fact about a particular orbit slot. The slot in question is identified by the index t12, one of several labeled positions in a discrete model of spacetime geometry. The result proves that the moment associated with this slot, when evaluated over a specific set of edge-origin contributions, equals the rational number -1/4. This is not an approximation or a numerical coincidence; it is a closed-form identity verified by exhaustive computation over a finite set of 24 symmetry permutations and 10 triangle configurations.

The proof works by summing integer certificates. Each certificate records a class, an integer weight, and an origin offset in four coordinates. The theorem converts these integer weights to real numbers (dividing by 4), sums them over all allowed configurations, and confirms the total. The computation is carried out by a decision procedure that checks all 240 cases at once, with no gaps. A companion result shows that the same evaluation for a different slot, t13, yields 576, while t21 and t22 yield 0, so the -1/4 value is specific to the t12 slot and not a general property of the model.

The declaration also rules out a potential alternative explanation. A separate theorem proves that a so-called gauge part, a mathematical transformation that should not affect physical results, does not produce the same t12 slot value. The certificate for the gauge candidate sums to 0, not -1/4. This strengthens the conclusion that the -1/4 deficit is a genuine feature of the slot's edge origins, not an artifact of the coordinate choice.

What the declaration does not claim is broader significance. It does not state that this slot deficit represents a physical observable, nor does it connect the -1/4 value to any measured gravitational quantity. The result is a structural identity within the framework's discrete model, not a prediction about experiments. It also does not claim that the t12 slot is unique in having a nonzero value; the companion results show other slots with different values. The declaration is a certificate, a precise check that a specific computation closes correctly, and it should be read as such.

theorem M2EdgeOriginsPlusSymbolDirEval_holds : M2EdgeOriginsPlusSymbolDirEval :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins_axisTTPlus_symbolDir

theorem sum_m2OrbitCertZ12Edge_gauge :
    (∑ s : Fin 24, ∑ t : Fin 10, m2OrbitCertZ12Edge decoyGaugeCoeffZ s t) =
      (0 : ℤ) := by
  decide

set_option maxRecDepth 20000 in
set_option maxHeartbeats 12000000 in

What this page does not claim

The -1/4 value is not claimed to be a measured physical constant. The declaration does not claim the t12 slot is the only slot with a nonzero deficit. The result does not claim to explain the origin of the deficit beyond the discrete edge-origin model.

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/ReggeBlochStarEdgeOriginsM2Eval4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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