t75c_bridge_holds
plain-language theorem explainer
Given that the eight-tick ledger cycle is forced (period $2^3$), the recognition substrate is one-acyclic at every dimension, which is the predicate the codimension route needs. Anyone wiring the T7.5 bridge stack between eight-tick forcing and the $D=3$ linking argument would cite this. The proof is a one-field structure constructor that installs the trivial substrate one-acyclicity fact.
Claim. Assume the eight-tick cycle is forced: the minimal ledger-compatible period equals $2^3$ from spatial dimension three. Then for every dimension $D$ the recognition substrate is one-acyclic in the sense required by the codimension route.
background
The Unified Forcing Chain module derives T0 through T8 as forced steps from the Recognition Composition Law together with normalization and calibration. T7 states that the minimal ledger-compatible cycle is $2^D$; with spatial dimension three this is the eight-tick octave, not a free parameter.
T7.5 sits between T7 and T8. The T7.5c bridge records a single substrate fact: for every dimension $D$, the substrate satisfies the one-acyclic predicate. That predicate is exactly what the codimension route consumes when linking arguments later force $D=3$ (T8).
Upstream, the substrate package already supplies a uniform one-acyclicity witness at every $D$. Dimension constants elsewhere in the stack fix $D=3$, but this bridge itself is parametric in dimension and only packages the acyclicity hypothesis under a T7 assumption.
proof idea
Term-mode structure constructor, not a tactic script. Under the hypothesis that eight-tick forcing holds, the sole field of the T7.5c bridge (existence of one-acyclicity for every dimension) is filled by the substrate axiom that one-acyclicity is trivial. No rewriting, case split, or dimension specialization is needed.
why it matters
Fills the T7.5c slot in the complete inevitability chain: once the eight-tick octave is forced, the substrate must already carry one-acyclicity so the codimension and linking route to $D=3$ (T8) can fire. In the module's stronger claim, every level from the absolute floor through T8 is forced from cost; this bridge is the thin interface that hands T7's eight-tick package to the acyclicity hypothesis of that route. Framework landmarks touched: T7 (eight-tick, period $2^3$) and the approach to T8 ($D=3$). The dependency graph currently lists no downstream consumers, so the declaration functions as a chain-internal connector rather than a widely reused lemma.
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