Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk13 E 310013

A verified arithmetic identity

In a machine-checked library of formal theorems, a declaration named e_310013 establishes a precise arithmetic identity: for a particular six-index case, the value of a function called m2Num equals eight times the value of a reference function called explicitZ. The theorem states that m2Num 3 1 3 1 3 3 = 8 * explicitZ 3 1 3 1 3 3, and the proof is by decide, meaning a computer program evaluated both sides and confirmed they are equal. This is not a symbolic derivation or a physical law; it is a verified numerical fact about one specific entry in a table.

The identity belongs to a larger family of theorems in the framework's gravity analysis section, all sharing the same form: m2Num with six indices equals eight times explicitZ with the same indices. The declaration e_310013 is one of many such statements, each covering a different combination of the six index values. The indices themselves range over a small set of digits, and the collection of theorems covers all combinations in this chunk of the computation. The docstring describes this as "m2Num = 8·explicitZ, chunk 13 (256 kernel decides)", indicating that this block of theorems handles a specific portion of the full index space.

What the declaration does not claim is important. It does not assert that the identity holds for all possible index values; it proves it only for the specific case 3 1 3 1 3 3. It does not explain what m2Num or explicitZ represent physically, nor does it derive them from any deeper principle. It does not claim that gravity behaves a certain way, that any measurement matches, or that the framework's broader forcing chain is correct. The theorem is a single checked arithmetic equality, nothing more and nothing less.

In the context of the framework's library, this declaration is a building block. The library accumulates many such verified identities, and together they support larger formal developments. The value of e_310013 lies in its exactness: a computer has confirmed the equality, so the fact is not subject to human arithmetic error. For a reader, the takeaway is that this is a reliable, narrow fact, useful as part of a larger verified structure, but not itself a statement about the physical world.

theorem e_313133 : m2Num 3 1 3 1 3 3 = 8 * explicitZ 3 1 3 1 3 3 := by decide

What this page does not claim

The identity holds only for the specific index combination 3 1 3 1 3 3, not for all cases. The declaration does not state what m2Num or explicitZ mean physically. No claim is made that this identity confirms any physical prediction or measurement.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk13.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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