T6_To_T8_Dimension_Bridge
plain-language theorem explainer
Packages the T6→T8 step: given φ forced, the named topological and eight-tick interfaces force unique spatial dimension D=3 and emit the T8 surface. Anyone assembling the complete forcing chain or comparing T6→T7 routes cites this certificate. It is a Prop structure, not a proved theorem; the inhabitant is built elsewhere by wiring DimensionForcing lemmas.
Claim. Given a witness that $\varphi$ is forced (unique positive solution of $r^2=r+1$), a dimension-bridge certificate asserts: (i) that uniqueness is available; (ii) every spatial dimension $D$ supporting nontrivial ledger linking equals $3$; (iii) every $D$ with $2^D=8$ equals $3$; (iv) there is a unique RS-compatible dimension; (v) the T8 surface ($D=3$ forced by linking, eight-tick, and uniqueness) is produced.
background
In the Unified Forcing Chain, T0–T8 are claimed as inevitabilities from the Recognition Composition Law plus normalization and calibration. T6 pins the golden ratio: in a discrete ledger with self-similar cost, the only positive scaling ratio is $\varphi=(1+\sqrt{5})/2$, the unique positive root of $x^2=x+1$.
Spatial dimension is not fixed by scale recursion alone. DimensionForcing treats $D\in\mathbb{N}$ as spatial dimension, sets the eight-tick period to $8$, and isolates two forcing routes: nontrivial topological linking of ledger loops, and the identity $2^D=8$. RS-compatible dimension packages the full compatibility predicate used downstream.
T8 is the surface that $D=3$ is the unique dimension satisfying linking, eight-tick sync, and (in the broader narrative) gap-45 synchronization. This bridge structure makes the extra topological interface an explicit hypothesis bundle rather than an unnamed sibling of T6.
proof idea
No proof body: this is a structure definition (a Prop certificate type). Fields are named interfaces plus an output T8 bundle. The companion theorem t6_to_t8_dimension_bridge_holds builds an inhabitant by copying phi_unique from the T6 hypothesis and assigning DimensionForcing.linking_requires_D3, DimensionForcing.eight_tick_forces_D3, and DimensionForcing.dimension_forced, with the resulting T8 surface filled from those same routes. Treat the structure as the typed contract those lemmas discharge.
why it matters
Closes the documented gap between T6 and T8 in the forcing chain: φ fixes self-similar scale, while D=3 needs ledger linking and the eight-tick ($2^3$) constraint (primer landmarks T6–T8). Downstream, CompleteForcingChain includes this bridge in the full T−1…T8 package; T6_To_T7_RouteEquivalence uses it as the indirect T6→T8→T7 path equated with the direct canonical-period route to T7. Naming the topology interface keeps T8 from appearing as an untracked sibling and makes route equivalence checkable. Does not itself derive linking or $2^D=8$; it only records that those DimensionForcing facts, once supplied, yield T8.
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