IndisputableMonolith.Foundation.SpinStatistics
The SpinStatistics module defines fermionic and bosonic ledger states by their minimal recognition cycle lengths inside the 8-tick clock. Fermionic states finish cycles after 4 ticks while bosonic states require the full period. Discrete quantum theorists cite these predicates when deriving exchange signs and Pauli exclusion from recognition costs. The module supplies the supporting definitions and lemmas that feed the spin-statistics theorem.
claimA ledger state $s$ is fermionic when its minimal recognition cycle has length 4 ticks, i.e., half the fundamental 8-tick period of the discrete clock.
background
The module sits in the Foundation domain and imports the 8-tick structure whose phases run 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. It also draws cost functions from JcostCore to measure cycle completion. The supplied definition states that a ledger state is fermionic (spin-1/2) precisely when its minimal recognition cycle completes in 4 ticks.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The predicates and lemmas supply the discrete foundation for the spin_statistics_theorem and pauli_exclusion results among its siblings. They convert the eight-tick octave into concrete spin-statistics relations, advancing the T7 step of the forcing chain.
scope and limits
- Does not prove the spin-statistics theorem itself.
- Does not connect cycle lengths to continuous rotation groups.
- Does not address higher spin values beyond 1/2 and 0.
depends on (2)
declarations in this module (12)
-
def
IsFermionic -
def
IsBosonic -
def
rotationPhase -
theorem
fermion_rotation_phase_neg_one -
theorem
boson_rotation_phase_pos_one -
theorem
exchange_sign_fermion -
theorem
exchange_sign_boson -
theorem
spin_statistics_theorem -
theorem
pauli_exclusion -
theorem
pauli_exclusion_simple -
theorem
cpt_composition -
theorem
spin_statistics_certificate