T7_EightTick_Forced
plain-language theorem explainer
Packages the T7 claim that the recognition period is eight ticks: the named period equals 2^3, and the cycle forced by spatial dimension D=3 is that same period. Cited by the complete T-1..T8 spine, the public substrate certificate, and the T5+T7 canonical Hamiltonian bridge. Pure Prop structure whose fields are definitional identities from DimensionForcing, not a derived forcing proof.
Claim. The eight-tick recognition period equals $2^3$, and the cycle length obtained from spatial dimension $D=3$ by the rule $2^D$ equals that same eight-tick period.
background
This module is the public T-1 through T8 forcing spine. T7 is the eight-tick cadence step: after T5 (unique reciprocal cost $J$) and T6 ($\varphi$ as the self-similar fixed point), the ledger needs a minimal compatible cycle. In the primer this is the eight-tick octave of period $2^3$.
Upstream, eight_tick is the constant natural number 8 (also the fundamental time unit $\tau_0$ scale in recognition thermodynamics). EightTickFromDimension D is defined as $2^D$, so at $D=3$ it is exactly eight. The twin structure in UnifiedForcingChain states the same package: "the minimal ledger-compatible cycle is $2^D$; with $D=3$ this gives 8-tick; 8 is not a free parameter."
The local spine deliberately stops before private operator and measurement layers. T8 (forcing $D=3$) sits one step above and can discharge this record via a bridge theorem.
proof idea
No proof body: claim status is definition, style def_or_abbrev. The structure is a Prop record with two fields that are pure equalities of naturals. Both reduce by unfolding: the period constant is 8, $2^3=8$, and the dimension map at 3 is $2^3$, hence equals the period. Downstream constructors (for example the bridge from T8) fill the fields with the corresponding DimensionForcing lemmas or rfl.
why it matters
T7 is a named landmark of the forcing chain: eight-tick octave, period $2^3$, forced by dimension rather than chosen. This bridge copy is the public spine's handle on that landmark.
It is consumed by CompleteForcingChainT8 and the unified CompleteForcingChain, by the public substrate certificate (honest replacement for a bare nonempty T7 witness), and by the T5+T7 canonical Hamiltonian bridge. That bridge uses the eight-cycle for cost-phase duality, the small-deviation quadratic Hamiltonian, and the DFT-8 eigenvalue structure of the cyclic shift. A local theorem also recovers this record from T8 once $D=3$ is forced.
It does not close the audited T4→T5 comparison-surface gap recorded in the module honesty notes; that gap is orthogonal to the eight-tick package.
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