Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk03 E 030003

A single checked identity

The declaration theorem e_030003 is a single, verified statement inside a larger formal proof about gravity. It says that for one particular set of six input numbers, the value of a function called m2Num equals eight times the value of a function called explicitZ. The proof is a direct computation: the computer checks the arithmetic and confirms the equality holds.

This is not a new physical law or a discovery about the universe. It is a bookkeeping step, a check that two different ways of calculating the same quantity agree for this one case. The numbers in the name, such as 0 3 3 3 3 3, are the specific inputs to the functions. The declaration is part of a series of similar checks, each covering a different combination of inputs, building confidence that a larger identity is true.

The statement is proved by the decide tactic, which means the computer evaluates both sides and verifies they are equal. This is a mechanical confirmation, not an argument from general principles. The declaration does not explain what m2Num or explicitZ represent physically, nor does it derive the larger identity they are part of. It only certifies that this one numerical case is correct.

In Recognition Science, this kind of check is one small brick in a wall. The framework's library of formal theorems builds results from many such verified steps. This particular declaration, however, stands alone as a fact about two functions, not as a statement about the framework's core ideas like the cost function or the golden ratio. Its value is local: it confirms a piece of arithmetic in a specific calculation.

What the declaration does not claim is as important as what it does. It does not claim that the equality holds for all inputs, only for the one listed. It does not claim that m2Num and explicitZ are the same function. It does not claim any physical interpretation for the numbers or the functions. It is a precise, narrow, and fully verified statement, and its power comes from that precision.

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

theorem e_033333 : m2Num 0 3 3 3 3 3 = 8 * explicitZ 0 3 3 3 3 3 := by decide

What this page does not claim

The equality holds for all possible inputs, only for the specific six numbers listed. The functions m2Num and explicitZ are the same function or have the same meaning. The declaration provides any physical interpretation for the numbers or functions 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/ReggeExactMidpointM2TTIdentity4DM2NumChunk03.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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