IndisputableMonolith.CrossDomain.TwoCubeUniversality
This module defines 2³-structure as the property that a type has cardinality exactly 8 and collects cross-domain instances of it. Researchers unifying discrete models in Recognition Science would cite it when invoking the eight-tick octave. The module supplies the shared definition plus equicardinality lemmas for DFT, Q3, Pauli, and tick-phase objects.
claimA type $T$ has $2^3$-structure if and only if $|T|=8$.
background
Recognition Science derives three spatial dimensions from the eight-tick octave (period $2^3$) in the forcing chain. The module introduces the predicate HasTwoCubeCount whose body is the statement that a finite type has cardinality 8. Sibling declarations then verify this predicate for DFTMode, Q3Vertex, PauliElement, and TickPhase.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the common 2³-structure interface used by the four domain-specific lemmas that establish equicardinality. It thereby supports the T7 step that forces the eight-tick period and the subsequent derivation of D=3.
scope and limits
- Does not derive the 2³-structure from the J-cost functional equation.
- Does not address continuous or infinite types.
- Does not connect cardinality 8 to the phi-ladder mass formula.
- Does not prove universality beyond the four listed domains.
declarations in this module (18)
-
def
HasTwoCubeCount -
inductive
DFTMode -
inductive
Q3Vertex -
inductive
PauliElement -
inductive
TickPhase -
theorem
dft_has_2cube -
theorem
q3_has_2cube -
theorem
pauli_has_2cube -
theorem
tick_has_2cube -
theorem
two_cube_equicardinal -
theorem
two_cube_pair_64 -
theorem
two_cube_powerset_256 -
theorem
dft_q3_equicardinal -
theorem
pauli_tick_equicardinal -
theorem
dft_q3_product -
theorem
sixtyfour_identities -
structure
TwoCubeUniversalityCert -
def
twoCubeUniversalityCert