identity_tick_count

The module collects exact arithmetic identities that relate imported Standard Model degree-of-freedom counts to $D=3$ combinatorial quantities. It does not derive the SM spectrum; SM representations, the minimal-neutrino convention $g_f=90$, and the Fermi–Dirac $7/8$ weight are imported, while $D=3$ and the eight-tick period $2^D=8$ are cited from upstream forcing (T7/T8).

In that setting an eight-tick octave is the discrete recognition period. The identity tick is the single balanced slot reserved inside each cycle; the remaining slots are the ones available to fermionic counting. Sibling constants in the file package the same arithmetic: eight-tick length, dimension gap at $D=3$, degrees of freedom per generation, and the assembled $g_\star$ identity $28+(7/8)\times 90=106.75$.

Pure definition: the constant is introduced as the natural-number literal $1$. There is no tactic proof, lemma application, or algebraic reduction.

Feeds the local theorem that available fermion ticks equal eight-tick length minus this count, i.e. $8-1$. That difference is the numerator of the tick fraction $(8-1)/8$, which the module equates numerically to the imported Fermi–Dirac thermal weight $7/8$. The construction sits inside the honest re-scoped bridge: RS supplies $D=3$ and the octave $2^D=8$; the identity tick is the unit that makes the combinatorial remainder match the standard $7/8$ factor used in $g_\star$ arithmetic. It does not close the open gap of deriving gauge representations or the thermal integral from RS premises.