Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk00

A machine-checked ledger entry

This entry is a small piece of a large machine-checked library of formal theorems. Its name describes its place: it concerns gravity analysis, uses a midpoint rule in a Regge-style discretization, and handles the m2 quantity in four dimensions. The chunk00 part means it is the first of several batches of statements, each batch covering a fixed set of index combinations.

The core object is m2Num, a function of six indices. Each index takes one of four values, so there are 4^6 = 4096 possible combinations. The entry proves, for each combination in this first batch, that m2Num equals 8 times a reference value called explicitZ. For example, one theorem states m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3. The proof is by decide, meaning the kernel checks the equality by direct computation rather than by a long chain of symbolic steps.

In plain language, the entry establishes a scaling relation: the m2 quantity at each point is exactly eight times the corresponding reference value. The factor 8 is not an approximation or a fitted constant; it is proved exactly for every index combination in this chunk. The theorems are tagged THEOREM, so they carry no axioms beyond the three standard ones of the ambient type theory.

This is a verification artifact, not a physical derivation. It confirms that a specific numerical identity holds throughout a discrete grid, which is the kind of check that gives confidence in a larger computational framework. The reader should take away that the library contains exact, machine-checked statements about this gravity quantity, and that the factor 8 is not a numerical accident but a proved equality.

theorem e_003333 : m2Num 0 0 3 3 3 3 = 8 * explicitZ 0 0 3 3 3 3 := by decide

What this page does not claim

This module does not derive the m2 quantity from first principles; it verifies a scaling relation. The factor 8 is proved for this chunk, not for all 4096 combinations at once. No claim is made about the physical meaning of explicitZ beyond its role as a reference value.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk00.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: