IndisputableMonolith.Foundation.SpinStatistics
Foundation module that reads spin-statistics off the eight-tick recognition clock: fermionic ledger states close a minimal cycle in 4 ticks (half-period), bosonic states in 8. It defines rotation phases and exchange signs, then packages the spin-statistics correspondence, Pauli exclusion, CPT composition, and an export certificate. Anyone deriving particle statistics from discrete recognition cycles would cite it. The argument is definitional classification plus direct phase arithmetic on the octave.
claimA ledger state is fermionic when its minimal recognition cycle has length $4$ (half the fundamental $8$-tick period) and bosonic when the cycle has length $8$. Rotation by $2\pi$ multiplies the fermionic amplitude by $-1$ and the bosonic amplitude by $+1$. Exchange of identical fermions (resp. bosons) contributes sign $-1$ (resp. $+1$). Pauli exclusion follows for coincident fermionic modes; a CPT composition identity and an export certificate close the package.
background
Recognition Science takes a discrete eight-tick clock as fundamental (forcing-chain step T7). The imported EightTick module supplies that octave, with phases $0, \pi/4, \pi/2, 3\pi/4, \pi, 5\pi/4, 3\pi/2, 7\pi/4$. Spin and statistics are read from half-period versus full-period closure of recognition cycles on this clock, not from continuous Lorentz representations.
J-cost is imported only as the compatibility surface from JcostCore; the statistics content itself is combinatorial and phase-theoretic. A state is called fermionic when its minimal closed recognition path returns after 4 ticks, and bosonic when it returns after 8. Rotation phase and exchange sign are then forced by that cycle-length parity.
Sibling declarations name the predicates, the phase map, the two rotation-phase lemmas, the two exchange-sign lemmas, the packaged spin-statistics theorem, two forms of Pauli exclusion, a CPT composition identity, and the export certificate.
proof idea
Definitional core plus elementary arithmetic on the eight-tick group. Predicates for fermionic and bosonic states are introduced from minimal cycle length (4 vs 8). A rotation-phase map is defined on that clock; the fermion lemma evaluates it to $-1$ on the half-period, the boson lemma to $+1$ on the full period. Exchange signs are the same $\pm 1$ read under particle swap. The spin-statistics theorem packages the correspondence; Pauli exclusion (and a simplified form) derive non-occupancy of identical fermionic modes from the minus sign; CPT composition and the certificate close the export layer. No deep analytic machinery: direct evaluation on the octave.
why it matters in Recognition Science
Places spin-statistics inside the Recognition foundation rather than as an external QFT axiom. The half-period closure that yields the $-1$ under $2\pi$ rotation is exactly the discrete origin of spin-$1/2$, tied to T7 (eight-tick octave) in the forcing chain. Pauli exclusion and the exchange signs then follow without separate postulate.
Graph-level used_by is empty, so this is presently a leaf foundation module: its natural consumers are particle-classification, measurement, and ledger-occupancy layers that need a fermionic/bosonic split derived from the clock. The certificate declaration is the intended export surface for those higher modules. It does not touch the mass ladder, the alpha band, or D=3 forcing (T8), remaining strictly inside the discrete-clock statistics story.
scope and limits
- Does not derive continuous Lorentz spinors or full relativistic QFT.
- Does not prove uniqueness of the 4-vs-8 split beyond the eight-tick hypothesis.
- Does not treat anyonic or fractional statistics in lower dimensions.
- Does not compute dynamical amplitudes, cross sections, or interactions.
- Does not depend on the mass ladder, alpha band, or D=3 forcing.
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