Gravity Analysis Regge Bloch Star Edge Origins4 D Seed Edge Contribs T22 Length

A counted list of contributions

In the framework's four-dimensional gravity analysis, a recognition ledger, a discrete record of geometric events, organizes computations by orbit types, labeled t11, t12, t13, t21, t31, and t22. For each type, the analysis defines a list of seed edge contributions, each entry carrying a class index, a weight, and an origin in a four-component wave vector. The declaration seedEdgeContribs_t22_length is a theorem stating that the list for orbit type t22 has exactly 32 entries.

This count is not a numerical approximation or a statistical estimate; it is a definitional equality, verified by the framework's machine-checked library of formal theorems. The proof is immediate from the definition of the list: the theorem states that the length of seedEdgeContribs_t22 equals 32, and the proof is by reflexivity, meaning the definition itself makes the count true. The neighboring orbit types have different counts: t12 has 22 entries, and t13 has 24 entries, each also established by a theorem.

The count serves a structural role in the larger computation. The list feeds into functions that compute phased deficit contributions and mass-squared truncation coefficients for non-t11 orbits. The t22 list, with its 32 entries, participates in these sums alongside contributions from other orbit types, and the total moment across all orbits combines them with weights based on orbit star sizes.

What the theorem does not claim is equally important. It does not assert that the t22 list is complete, that its entries are physically meaningful, or that the computation it feeds is correct. It does not claim that the t22 orbit type has any special status compared to others. It does not even claim that the list is non-empty in any deeper sense; the count is a formal fact about a definition, not a statement about the physical world. The theorem's scope is exactly the length of one list in one file of the framework's library.

In the Recognition Science framework, this theorem is a small but necessary piece of a larger formal structure. It ensures that the computation over t22 contributions is well-defined and that the list has the expected number of entries, a prerequisite for any further reasoning about the sums that use it. The count itself is a bookkeeping fact, but it is a bookkeeping fact that the framework's machine-checked library guarantees, not one taken on faith.

theorem seedEdgeContribs_t22_length :
    seedEdgeContribs_t22.length = 32 := rfl

theorem seedEdgeContribs_t22_length :
    seedEdgeContribs_t22.length = 32 := rfl

What this page does not claim

The theorem does not assert that the t22 list is complete or that its entries are physically meaningful. The theorem does not claim the t22 orbit type has any special status compared to other orbit types. The theorem does not establish that the computation using the t22 list is correct.

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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