t7_from_t8
plain-language theorem explainer
Given that spatial dimension is forced to three, the eight-tick ledger cycle follows at once: the minimal compatible period is 2^D evaluated at D=3. Anyone assembling the T0–T8 inevitability spine, or comparing the T6→T7 and T6→T8→T7 routes, cites this. The proof is a two-field structure constructor: the identity 8=2^3 plus the dimension-to-period bridge applied to the T8 hypothesis.
Claim. If spatial dimension is forced ($D=3$ is the unique value compatible with nontrivial linking, eight-tick synchronization, and gap-45), then the eight-tick cycle is forced: the canonical ledger period equals $2^3$, and the period-from-dimension map at $D=3$ recovers that eight-tick value.
background
The Unified Forcing Chain module aims to show every level T-1 through T8 is forced from the Recognition Composition Law plus normalization and calibration, not merely compatible. In that spine, T8 asserts that spatial dimension is not free: $D=3$ is the unique RS-compatible value, forced by nontrivial linking (ledger conservation), by matching the eight-tick period, and by gap-45 synchronization.
T7 asserts the dual surface: the minimal ledger-compatible cycle is $2^D$, and with $D=3$ this is the eight-tick octave. The named period construction is $\Pi:D\mapsto 2^D$; the constant eight_tick is that period at the forced dimension. Upstream, eight_tick_is_2_cubed records the pure arithmetic identity $8=2^3$, while the T8-to-T7 bridge packages the statement that dimension three yields the eight-tick value.
Locally this is the reverse edge of the usual narrative (T7 before T8 in the printed chain): once dimension is forced, the octave is an evaluation, not an extra postulate.
proof idea
Term-mode structure construction with two fields. The first field is filled by the upstream arithmetic lemma that the eight-tick constant equals $2^3$. The second field applies the T8-to-T7 bridge theorem to the given T8 hypothesis and projects its dimension_three_eight_tick component, which states that the period-from-dimension map at $3$ recovers the eight-tick constant. No further case analysis or calculus is required.
why it matters
Closes the T8→T7 leg of the complete inevitability chain. Downstream, the T-1-to-T8 bridge re-exports the same constructor inside complete_forcing_chain_t8, and the physical packaging physical_forcing_chain sits on that spine. It also feeds T6_To_T7_RouteEquivalence, which certifies that the direct canonical-period route T6→T7 and the indirect route T6→T8→T7 produce the same T7 surface.
In primer terms this is the link between T8 ($D=3$) and T7 (eight-tick octave, period $2^3$). The module doc lists T7 as "$2^D$ with $D=3$" and T8 as dimension forced by linking plus gap-45 sync; this theorem is exactly that dependence made formal. It does not invent a new physical constant; it shows the octave is forced once dimension is.
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