Gravity Analysis Regge Bloch Star Edge Origins4 D Seed Edge Contrib

Seed edge contributions

In the framework's machine-checked library of formal theorems, SeedEdgeContrib is a plain data structure, a labeled box with three slots. The first slot holds a class index, a number from 0 to 14 that identifies which of fifteen symmetry classes the edge belongs to. The second slot holds a real number called the weight, the strength of the edge's contribution. The third slot holds an origin, a four-component vector that records where in the lattice the edge starts. The structure's own documentation calls it "one seed-frame star edge contribution: class index, weight, origin," and that is exactly what it is: a single, self-contained record.

The structure is not an isolated curiosity. The library defines lists of these contributions for each of the six orbit types that a four-dimensional hinge can take. For example, the list for orbit type t12 has exactly 22 entries, the list for t13 has 24, and the list for t22 has 32; these lengths are proved by computation. Two of the orbit types, t21 and t31, are defined as identical to t12 and t13 respectively, a symmetry the library calls "identity-transport complements." The orbit type t11 is special: its list is empty. The library then builds a function that, given an orbit type, returns the appropriate list, and a separate function that transports an origin by a covering permutation, moving the recorded start point according to the symmetry of the lattice.

These pieces assemble into a larger object called the phased deficit dot with edge origins. This is a sum over all contributions, each evaluated at a transported slot, with the weight multiplied by a plane-wave perturbation that depends on the class and the transported origin. The library proves a key property of this sum: scaling the matrix H by a real number c scales the whole sum by the same c. This linearity result, tagged as a theorem, is the main mathematical content attached to the structure in the pack. A second, parallel construction, the phase-squared sum, feeds into a coefficient used for a mass-squared truncation, but the pack proves no theorem about it; it is defined and left at that.

The library also records a status flag for the whole fold-repair effort. The flag says the tables have landed, meaning the coefficient tables are in place; it says gap-action recovery is false, meaning that mechanism is not flipped on; and it says base0 half-repair is forbidden. These are engineering bookkeeping entries, not physics results. The docstring warns that the fold does not flip gap_action_recovery and that base0 half-repair is forbidden. None of this is a claim about gravity itself; it is a claim about which definitions the library currently contains and which it deliberately excludes.

What SeedEdgeContrib does not claim is as important as what it does. It does not claim that these 22, 24, or 32 contributions are physically correct, that they match any measurement, or that they derive from the framework's core forcing chain. The structure is a definitional choice, a model of how edge contributions might be organized, not a proved statement about the universe. The linearity theorem is real, but it is a fact about the definition, not about gravity. The status flags are likewise facts about the library's current state, not about nature. A reader who wants to know whether this organization of edge origins is the right one, or whether it leads to a working theory of four-dimensional gravity, will not find that answer in this pack; that question remains open.

/-- One seed-frame star edge contribution: class index, weight, origin. -/
structure SeedEdgeContrib where
  cls : Fin 15
  weight : ℝ
  origin : Wave4

theorem seedEdgeContribs_t12_length :
    seedEdgeContribs_t12.length = 22 := rfl

theorem seedEdgeContribs_t13_length :
    seedEdgeContribs_t13.length = 24 := rfl

theorem seedEdgeContribs_t22_length :
    seedEdgeContribs_t22.length = 32 := rfl

theorem phasedDeficitDotEdgeOrigins_smul (c : ℝ) (ty : HingeOrbitType)
    (H : Mat4) (m : Wave4) (s : Fin 24) (t : Fin 10) :
    phasedDeficitDotEdgeOrigins ty (c • H) m s t =
      c * phasedDeficitDotEdgeOrigins ty H m s t := by
  unfold phasedDeficitDotEdgeOrigins edgeContribPhased
  exact list_sum_map_smul_planeWave c H m (orbitCoveringPerm ty s t)
    (hingeBase s t) (seedEdgeContribs ty)

theorem starEdgeOriginsStatus_flags :
    starEdgeOriginsStatus.tablesLanded = true ∧
      starEdgeOriginsStatus.gapActionRecovery = false ∧
        starEdgeOriginsStatus.base0Forbidden = true := by
  decide

What this page does not claim

SeedEdgeContrib does not claim that these edge contributions match any measurement or observation. The structure does not claim to derive from the framework's core forcing chain or from the cost function J. The linearity theorem is a fact about the definition, not a statement about the physics of four-dimensional gravity.

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/ReggeBlochStarEdgeOrigins4D.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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