Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04

The numerical check

In numerical analysis, a Regge approach breaks a continuous gravitational field into discrete pieces, much as a polygon approximates a circle. The calculation here concerns a specific midpoint rule, a standard method for estimating an integral by sampling at the middle of each interval. The question is whether a large table of numbers, produced by one route, agrees exactly with a second route that uses a closed-form expression.

The module named in the title is one chunk of that verification. Its job is narrow and mechanical: it checks a set of entries, each indexed by six digits, and proves that the value from the first route equals eight times the value from the second. For example, the theorem e_103333 states that m2Num 1 0 3 3 3 3 equals 8 * explicitZ 1 0 3 3 3 3. The proof for each entry is by decide, meaning the computer evaluates both sides and confirms they are identical.

This is not a derivation of new physics. It is a bookkeeping audit. The library, a machine-checked collection of formal theorems, verifies that the numerical core of a larger gravity calculation is internally consistent. Each theorem in this chunk, from e_103333 down to e_103122, is a single line confirming one equality. The value of the exercise is trust: when a later theorem relies on this table, it rests on checked arithmetic rather than on an unexamined computation.

In Recognition Science, this kind of audit matters because the framework builds physical structure from a small set of forced conditions. A slip in a numerical table would propagate through later results. Chunk 4 covers a specific block of indices, and the docstring notes it is the 256 kernel decides, meaning this portion settles 256 such equalities. The plain-language outcome is simple: for this block, the two ways of computing agree exactly, with no rounding and no approximation.

The consequence is that the larger gravity analysis can proceed on solid footing. A reader who wants to check the work can do so entry by entry. The module does not claim to prove anything about gravity itself; it proves that a particular numerical implementation matches its own closed-form reference. That is a modest but necessary step before any physical claim built on top of it.

theorem e_103333 : m2Num 1 0 3 3 3 3 = 8 * explicitZ 1 0 3 3 3 3 := by decide

theorem e_103332 : m2Num 1 0 3 3 3 2 = 8 * explicitZ 1 0 3 3 3 2 := by decide

theorem e_103331 : m2Num 1 0 3 3 3 1 = 8 * explicitZ 1 0 3 3 3 1 := by decide

theorem e_103330 : m2Num 1 0 3 3 3 0 = 8 * explicitZ 1 0 3 3 3 0 := by decide

What this page does not claim

This module does not derive any physical law or gravitational effect. This chunk does not prove the full identity for all indices, only the block it covers. The equality is numerical, not a statement about the meaning of the quantities involved.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk04.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: