Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04 E 100000

A kernel check of one million

The declaration e_100000 is a single entry in a large, machine-checked ledger of arithmetic facts. Each entry, including e_100000, records a specific numerical identity: that a quantity called m2Num, evaluated at a particular six-digit coordinate, equals eight times a quantity called explicitZ at the same coordinate. The proof of each identity is a direct computation, checked by the computer's kernel, not a hand-written argument. The declaration's name encodes its position in the sequence; e_100000 is the hundred-thousandth such check in this chunk of the library.

These identities are part of a broader verification of an equation in gravity analysis, the Regge exact midpoint M2 TT identity in four dimensions. The library is a machine-checked collection of formal theorems, and this chunk verifies that a certain numerical relationship holds across a grid of points. The relationship itself is simple to state: at each coordinate, the value of m2Num is exactly eight times the value of explicitZ. The declaration e_100000 confirms this holds at one specific coordinate, just as its neighbors confirm it at their coordinates.

What e_100000 does not claim is any physical interpretation of the numbers. It does not say what m2Num or explicitZ represent in the gravity theory, nor does it assert that the identity has any consequence for the physics. The declaration is purely a computational check, a single verified line in a long list. It establishes that the arithmetic is correct at that point, nothing more.

The value of such a declaration is cumulative. Individually, each check is trivial. Together, a million of them form a solid foundation for the larger theorem they support. The framework's library proves the identity at each coordinate by direct computation, and e_100000 is one of those proofs, a verified brick in a wall of arithmetic certainty.

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

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

What this page does not claim

The declaration does not assign any physical meaning to m2Num or explicitZ. The declaration does not assert that the identity has any consequence for the physics. The declaration does not prove the entire gravity identity, only the arithmetic at one coordinate.

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

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