Gravity Analysis Regge Bloch Star Edge Origins4 D Seed Edge Contribs T12 Length

The t12 seed list

In the Recognition Science framework's gravity analysis, a seed edge contribution is a small record that packs three pieces of data: a class index (a label from a finite set of 15), a real-numbered weight, and an origin, which is a four-component wave vector. The declaration seedEdgeContribs_t12 is a definition: it lists these contribution records for one particular orbit seed, called t12. The theorem seedEdgeContribs_t12_length proves that this list has exactly 22 entries. The proof is by direct computation, and the result is checked by the machine, so the count of 22 is not an estimate or a numerical accident; it is a proved fact about the definition as written.

The list is not an isolated curiosity. It feeds a larger construction: the framework transports each seed contribution's origin by a covering permutation, applies a phase, and sums over the list to build a position-resolved deficit term for the t12 orbit. The length theorem matters because the sum's behavior, and the later proof that the whole expression scales linearly when the matrix is multiplied by a constant, depends on the list being finite and on its exact size. The companion definitions for other orbit seeds have their own counts: t13 has 24 entries, t22 has 32, and t11 contributes none. The t12 count of 22 is one concrete datum in that table.

What the theorem does not claim is just as important. It does not say that the t12 list is complete, that the weights or origins are physically correct, or that the sum over the list produces a number that matches any measurement. It does not assert that the t12 orbit is special or that the count 22 has any meaning beyond being the length of this particular list. The theorem only certifies the arithmetic: the list has 22 entries, and that is all. The status record for the whole fold repair confirms that the tables landed and that a forbidden base0 half-repair is not used, but it does not certify any physics.

The practical upshot is a small but solid brick in a larger wall. Any reader who wants to know whether the t12 seed list has the right shape for the framework's gravity machinery can now rely on a machine-checked count. The length is not a claim about the universe; it is a claim about a definition, and it is exactly as strong as that.

theorem seedEdgeContribs_t12_length :
    seedEdgeContribs_t12.length = 22 := rfl

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

theorem seedEdgeContribs_t13_length :
    seedEdgeContribs_t13.length = 24 := rfl

theorem seedEdgeContribs_t22_length :
    seedEdgeContribs_t22.length = 32 := rfl

def seedEdgeContribs : HingeOrbitType → List SeedEdgeContrib
  | .t11 => []
  | .t12 => seedEdgeContribs_t12
  | .t21 => seedEdgeContribs_t21
  | .t13 => seedEdgeContribs_t13
  | .t31 => seedEdgeContribs_t31
  | .t22 => seedEdgeContribs_t22

What this page does not claim

The t12 seed list is complete or physically correct. The count 22 has any special significance beyond being the list length. The theorem certifies any measurement or physical prediction.

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)

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