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structure definition def or abbrev high

SuperstringCert

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SuperstringCert is a structure that packages three equalities linking the seven extra dimensions of superstring theory to the flip variants of the three-dimensional cube in Recognition Science. A researcher comparing critical dimensions across frameworks would cite it to record that 10 minus 3 equals both the compactification count and 2 cubed minus 1. The declaration is a bare structure definition with no computational content or proof obligations.

claimA structure whose fields assert that the number of extra dimensions equals 7, that this number equals $2^D-1$ where $D$ is the spatial dimension, and that $7=2^3-1$.

background

Recognition Science fixes the spatial dimension at three via the eight-tick octave (T8). The module defines rsDimension as this constant 3 and extraDimensions as the difference between the superstring critical dimension and rsDimension. The local setting notes that superstring theory requires ten dimensions while RS enforces three, so the seven compactified dimensions coincide with the seven flip variants of the three-cube.

proof idea

The declaration is a structure definition that directly encodes the three required equalities extra_dim, flip_variant_match, and seven_flip with no tactics or lemmas applied.

why it matters in Recognition Science

This structure supplies the certificate instantiated by superstringCert, which witnesses the RS-superstring dimensional match. It records the observation that 10-3=7=2^3-1, connecting the T8 derivation of D=3 to the Recognition Composition Law and the eight-tick octave. It touches the open question of how compactified dimensions interface with the phi-ladder mass formula.

scope and limits

formal statement (Lean)

  37structure SuperstringCert where
  38  extra_dim : extraDimensions = 7
  39  flip_variant_match : extraDimensions = 2 ^ rsDimension - 1
  40  seven_flip : (7 : ℕ) = 2 ^ 3 - 1
  41

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (4)

Lean names referenced from this declaration's body.