module module moderate

`IndisputableMonolith.Foundation.SpinStatistics`

The SpinStatistics module classifies ledger states as fermionic or bosonic according to whether their minimal recognition cycle completes in 4 ticks or the full 8-tick period. Researchers working on discrete derivations of quantum statistics would cite it when linking the eight-tick clock to exchange phases. The module supplies a collection of definitions and short theorems that translate cycle length into rotation and exchange signs.

claimA ledger state is fermionic when its minimal recognition cycle has length 4 ticks (half the 8-tick octave), written $T_4 = 4$ with full period $T_8 = 8$; bosonic states require the full $T_8$.

background

The module rests on the 8-Tick Structure imported from EightTick, which supplies the discrete clock with phases at 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. It also imports JcostCore to access recognition-cost machinery. The local setting is the Recognition Science ledger whose states are classified by the number of ticks needed to close a minimal cycle, directly implementing the DOC_COMMENT definition of fermionic behavior.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core definitions (IsFermionic, IsBosonic, rotationPhase, exchange_sign_fermion, spin_statistics_theorem, pauli_exclusion) that realize T7 (eight-tick octave) inside the Recognition framework and feed the spin-statistics results listed among its siblings. It thereby connects the discrete clock to the algebraic signs required for fermions and bosons.

scope and limits

Does not prove the spin-statistics theorem from the forcing chain.
Does not derive numerical values for particle masses or couplings.
Does not address continuous limits or field-theoretic extensions.
Does not contain experimental observables or falsification criteria.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost.JcostCore module_import
IndisputableMonolith.Foundation.EightTick module_import

declarations in this module (12)

def IsFermionic L32
def IsBosonic L36
def rotationPhase L39
theorem fermion_rotation_phase_neg_one L43
theorem boson_rotation_phase_pos_one L49
theorem exchange_sign_fermion L58
theorem exchange_sign_boson L61
theorem spin_statistics_theorem L75
theorem pauli_exclusion L91
theorem pauli_exclusion_simple L99
theorem cpt_composition L107
theorem spin_statistics_certificate L117