T8_To_T7_EightTick_Bridge
plain-language theorem explainer
Certificate that spatial dimension forcing (T8) yields the eight-tick period (T7): every RS-compatible dimension equals 3, and that dimension carries the identity 2^D = 8. Cited by the complete forcing chain and by the T6→T7 route-equivalence that equates the direct and via-dimension paths. Pure interface structure; the inhabiting theorem fills the three fields from linking-forces-D3.
Claim. A bridge certificate from dimension forcing to the eight-tick law consists of three facts: (i) every RS-compatible spatial dimension $D$ satisfies $D = 3$; (ii) every such $D$ obeys the eight-tick equation $2^D = 8$; (iii) in particular, at $D = 3$ one has $2^3 = 8$.
background
In the Unified Forcing Chain, T0–T8 are claimed as inevitabilities from the Recognition Composition Law plus normalization and calibration. The terminal pair is ordered so that dimension is primary: T8 forces spatial dimension $D = 3$ (Alexander-duality linking and gap-45 sync), while T7 is the eight-tick octave, the fundamental evolution period of length $2^D$.
In DimensionForcing, a spatial dimension is a natural number; eight_tick is the constant 8; EightTickFromDimension D is the period $2^D$ attached to $D$; and RSCompatibleDimension D packages the RS constraints (including linking) that a candidate $D$ must satisfy. Constants elsewhere fix $D := 3$ and identify one octave with eight fundamental ticks $\tau_0$.
The doc-comment states the logical priority explicitly: "Dimension forcing is primary: Alexander-duality linking pins $D = 3$. The eight-tick identity is then a consequence of the dimension, not a premise used to prove the dimension."
proof idea
This declaration is a Prop-valued structure (interface), not a proved theorem. It names the three obligations a T8→T7 bridge must discharge. The inhabiting construction is the sibling theorem t8_to_t7_bridge_holds: given T8_Dimension_Forced, the first field is linking_forces_D3 applied to the linking component of RS-compatibility; the second field reduces the eight-tick equation along that equality; the third is the bare arithmetic identity $2^3 = 8$ at dimension three.
why it matters
Closes the reverse arrow in the forcing chain so T7 is not an independent postulate. Downstream, CompleteForcingChain and CompleteForcingChainT8 include this bridge among the T−1…T8 certificates. T6_To_T7_RouteEquivalence uses it as the via-dimension leg: the direct canonical-period route from φ-forcing (T6) to eight-tick (T7) must match the composite T6→T8→T7 route, and this structure is that composite's T8→T7 step.
Framework landmarks: T8 ($D = 3$) and T7 (eight-tick octave, period $2^3$). The certificate encodes the module's stronger claim that eight-tick is forced by dimension rather than assumed to derive dimension.
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