Gravity Analysis Regge Bloch Star Edge Origins M2 Eval4 D

A fold repair

In the Recognition Science framework, gravity is not a force between masses but a pattern in a discrete ledger, a record of recognition events. The module named ReggeBlochStarEdgeOriginsM2Eval4D is a repair to one small part of that picture. It concerns the edges of a structure called a Bloch star, a local configuration of points and hinges in a four-dimensional space. The question was whether a certain quantity, the second moment of the edge origins, could be forced to a specific value or whether it could vary depending on the configuration.

The module proves that for the two main axis directions, the plus and cross modes, this moment is exactly -1/4. The proof works by breaking the problem into integer certificates: a list of 22 contributions for one mode, 24 for another, and 32 for a third, each with a weight and an origin. The library's machine-checked theorems confirm these lists sum to the right values, and the result holds for all 240 possible orbit slices (24 positions times 10 hinge types).

The repair also eliminates two false candidates. A pure gauge configuration, a setup that looks like it might produce a different value but is actually a symmetry artifact, is shown to yield zero. A decoy gauge, another tempting but incorrect configuration, is also killed. The module explicitly does not change a separate result called gap_action_recovery, and it forbids two other approaches, base0 and covering-perm chase, as invalid paths.

In plain language, the module closes a specific hole in the framework's account of gravity. It shows that the edge origins of a Bloch star contribute a fixed, forced amount, -1/4, and that this is not an accident of a particular choice but a structural fact. The integer certificates make the proof checkable by direct computation, and the Python oracle script provides an independent check. The result is a small but necessary step in the larger project of showing that the framework's geometry is fully determined, not arbitrary.

theorem M2EdgeOriginsPlusSymbolDirEval_holds : M2EdgeOriginsPlusSymbolDirEval :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins_axisTTPlus_symbolDir

theorem M2EdgeOriginsCrossSymbolDirEval_holds : M2EdgeOriginsCrossSymbolDirEval :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins_axisTTCross_symbolDir

def M2EdgeOriginsCounterexM1100E2Eval : Prop :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins gaugeM1100E2 symbolDir = (0 : ℝ)

theorem M2EdgeOriginsDecoyGaugeEval_holds : M2EdgeOriginsDecoyGaugeEval :=
  m2AllOrbitMomentDistinctHingeEdgeOrigins_decoyGauge_symbolDir

What this page does not claim

This module does not derive the value of the gravitational constant or any other physical constant. It does not prove that gravity in the framework is fully equivalent to general relativity. It does not establish the physical bridge from recognition events to space-time geometry.

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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