Gravity Analysis Regge Exact Midpoint M2 Ttidentity4 Dm2 Num Chunk04 E 100012

The chunk's arithmetic

The declaration e_100012 is one entry in a large table of arithmetic identities. The table concerns a function called m2Num, which takes six numbers as input, and another function called explicitZ. The identity states that for the input (1, 0, 0, 0, 1, 2), the value of m2Num equals eight times the value of explicitZ. The proof is a direct computation: the line reads "by decide", meaning the machine checked the equality by evaluating both sides.

This is part of a chunk labeled "chunk 4" in a broader file about something called the Regge exact midpoint M2 TT identity in four dimensions. The chunk contains 256 such identities, each verified the same way. The docstring describes the chunk as "256 kernel decides," which is a plain way of saying the machine checked all 256 entries by calculation rather than by a longer proof. The declaration e_100012 is one of those 256 checks.

In Recognition Science, this table is part of a larger framework that derives physical structure from a ledger of recognition events. The framework's library is a machine-checked collection of formal theorems. This particular declaration does not itself prove any physical law. It is a computational building block: a verified numerical fact that other, larger theorems may rely on.

The declaration makes no claim about what m2Num or explicitZ mean physically. It does not say that the identity holds for all inputs, only for the specific six numbers listed. It does not derive the Regge exact midpoint identity from first principles. It does not state that gravity works this way. It only establishes that for this one input, the two functions agree up to a factor of eight, and the machine checked it.

The practical consequence is that a reader can trust this one line of the table without rechecking the arithmetic. The machine did the work. The table as a whole, with its 256 entries, provides a verified numerical foundation for whatever larger structure the framework builds on top of it. For a single entry, that is the whole story: a checked number, ready to be used.

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

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 prove any physical law about gravity. The identity is checked for one specific input, not for all inputs. The declaration does not derive the Regge exact midpoint identity from first principles.

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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