Gravity Analysis Regge Bloch Star Edge Origins4 D Seed Edge Contribs T13 Length

The t13 seed list

The declaration seedEdgeContribs_t13_length is a theorem in the framework's machine-checked library of formal theorems. It proves that the list named seedEdgeContribs_t13 has exactly 24 entries. Each entry is a small record: a class index, a weight, and a position offset called an origin. These entries are the starting contributions attached to the edges of a star-shaped configuration in one orbit type, labeled t13, within a four-dimensional model of gravity.

The theorem itself is a simple counting statement, proved by direct computation. It does not derive any physical law, and it does not claim that the number 24 has any special significance. It is a bookkeeping fact: the list contains 24 items, no more and no less. The surrounding code shows that this list feeds into larger sums that compute quantities like the deficit phase and the m² truncation coefficient for non-t11 orbits. The theorem guarantees that when the code sums over the t13 list, it sums over exactly 24 terms.

In the broader framework, this kind of exact count matters for reproducibility. The code transports origins by covering permutations, phases the contributions, and sums them into slot coefficients. A wrong length would silently change the sums. The theorem pins the length down as a formal fact, so the rest of the construction can rely on it. The docstring notes that this is a "fold repair" for a typed blocker: the list now carries lattice origins explicitly, and the covering permutations transport both class index and origin into the deficit phase.

What the theorem does not claim is equally clear. It does not say that the t13 orbit is the most important one, or that 24 is a preferred number in the framework. It does not establish any property of the physical model, such as stability or consistency. It only counts the entries in one list. The status flags in the same file record that the tables have landed, that gap action recovery is off, and that base0 half-repair is forbidden, but those flags are separate definitions, not consequences of this theorem.

theorem seedEdgeContribs_t13_length :
    seedEdgeContribs_t13.length = 24 := rfl

theorem seedEdgeContribs_t13_length :
    seedEdgeContribs_t13.length = 24 := rfl

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

What this page does not claim

The theorem does not assign any physical meaning to the number 24. The theorem does not prove any property of the gravity model beyond the list length. The status flags about gap action recovery are not consequences of this theorem.

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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