Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk05 E 110000

The chunk's arithmetic

In numerical analysis, a large computation is often split into many small, independent checks. The declaration e_110000 is one such check. It belongs to a family of 256 statements, each asserting that two different expressions for the same quantity are equal. The expressions are written with six indices, each index taking a value from 0 to 3, which gives 4^6 = 4096 possible combinations. The chunk covers a block of 256 of those combinations, and every one of them is verified by direct computation.

The equality itself has a simple shape. One side, called m2Num, is a number that arises in a gravity calculation at a midpoint. The other side, called explicitZ, is a reference value. The theorem states that m2Num equals eight times explicitZ for each combination of indices. For example, the declaration e_113333 states that m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3. The proof is a single word: decide. That means the computer evaluates both sides and confirms they match, with no symbolic reasoning and no axioms beyond the standard ones.

What this establishes is narrow but precise. It confirms that for these 256 index combinations, the midpoint calculation m2Num produces exactly the value that explicitZ predicts, scaled by a factor of eight. The factor eight is not derived from a deeper principle in this chunk; it is part of the statement being checked. The declaration does not explain why the factor is eight, does not derive the formula for m2Num from first principles, and does not connect this chunk to the broader forcing chain that the Recognition Science framework uses to derive constants like the golden ratio or the number of spatial dimensions.

In Recognition Science, this chunk is a brick in a larger wall. The framework's library of formal theorems builds physical structure from a single cost function, and this gravity analysis is one application of that machinery. But the chunk itself is only arithmetic verification. It proves that a specific computation matches a specific reference value. It does not prove that gravity works this way, that the midpoint method is physically correct, or that the factor eight has any physical meaning. Those claims would require additional theorems that connect this arithmetic to the framework's physical postulates, and those theorems are not in this chunk.

The practical value is in the verification. When a large calculation is split into thousands of small checks, each one being machine-verified means the whole assembly can be trusted at the level of its weakest link. This chunk removes 256 possible sources of error. It does not remove the need for the surrounding theory, but it does mean that anyone relying on this part of the calculation can do so with confidence that the arithmetic is correct.

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

theorem e_113333 : m2Num 1 1 3 3 3 3 = 8 * explicitZ 1 1 3 3 3 3 := by decide

What this page does not claim

This chunk does not prove that the factor eight has physical meaning. This chunk does not derive the formula for m2Num from the framework's cost function. This chunk does not establish that the midpoint method is physically correct for gravity.

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/ReggeExactMidpointM2TTIdentity4DM2NumChunk05.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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