T8_To_CanonicalDimension_Bridge
plain-language theorem explainer
Bridge certificate that turns T8 (spatial dimension forced) into the canonical D=3 interface used downstream: physical dimension equals 3, RS-compatibility is equivalent to equality with 3, the period at that dimension is 8, and linking, eight-tick, and spinor routes each force D=3. CompleteForcingChain and the companion holds theorem cite it. Pure Prop structure packaging already-forced facts; no new derivation.
Claim. Given a T8 certificate that spatial dimension is forced, the bridge asserts: the canonical physical dimension equals $3$ and is RS-compatible; $D=3$ is RS-compatible; every RS-compatible dimension equals $3$; the period at the physical dimension is $8$; the eight-tick construction at $3$ recovers the canonical eight-tick; nontrivial linking, eight-tick equality, and RS spinor structure each force $D=3$; and there exists a unique RS-compatible dimension.
background
In the Unified Forcing Chain, T0–T8 are claimed as inevitabilities from the Recognition Composition Law plus normalization and calibration. T8 is the dimension step: spatial dimension is not a free parameter. The T8 certificate already records that nontrivial linking forces $D=3$, that matching the eight-tick forces $D=3$, and that a unique RS-compatible dimension exists.
RS-compatible dimension packages the geometric and ledger constraints needed for recognition dynamics (linking for conservation, $2^D$ matching the eight-tick octave, gap synchronization). The canonical physical dimension is the named constant used by constants and alpha modules ($D:=3$). Period-from-dimension is the hypercube vertex count $2^D$; at $D=3$ this is the eight-tick period of the forcing chain (T7).
This bridge does not re-prove T8. It re-exports T8 into the canonical naming used by CompleteForcingChain: explicit $D_{\mathrm{physical}}=3$, bidirectional compatibility, period identity, and the independent forcing routes (Alexander linking, eight-tick, spinor).
proof idea
Definitional Prop structure, not a proved theorem. Fields are named hypotheses a T8 instance is expected to supply once discharged. The companion theorem t8_to_canonical_dimension_bridge_holds builds an inhabitant by rfl on $D_{\mathrm{physical}}=3$, then cites DimensionForcing lemmas: physical and $D=3$ compatibility, uniqueness (dimension_unique) for the forward implication, period and eight-tick identities, and the three forcing routes already present on T8 (linking, eight-tick, spinor), plus the legacy $\exists!$ uniqueness. A Subsingleton instance makes any two certificates definitionally equal.
why it matters
Closes the T8 slot in the Complete Inevitability Chain: after T7 forces the eight-tick octave via $2^D$, T8 forces $D=3$ so the octave is not optional. Downstream, CompleteForcingChain includes this bridge so the full T-1 through T8 stack can name the physical dimension explicitly rather than only existentially.
Framework landmark: primer T8 ($D=3$ spatial dimensions) and T7 (eight-tick, period $2^3$). The four routes (linking/Alexander duality, eight-tick $2^D=8$, gap-sync as in T8's doc, spinor structure) are the independent geometric reasons RS refuses other dimensions. Constants modules already hardcode $D:=3$; this bridge is the foundation-side certificate that that constant is forced, not assumed.
No open scaffold here: claim status is definition. The real work lives in DimensionForcing and in proving T8 itself.
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