CompleteForcingChainT8
plain-language theorem explainer
Packages the full public T−1→T8 forcing spine as one record: absolute floor, Boolean logic split, meta-principle, discreteness, ledger, recognition witness, J-uniqueness, φ, D=3, and eight-tick, with every bridge field. Anyone citing the closed foundation chain or the T−2→T8 certificate uses this bundle. It is a pure structure definition; inhabitants are assembled elsewhere from named bridge theorems.
Claim. A complete T−1-to-T8 forcing chain is a record consisting of: an absolute distinguishability floor; a bridge from that floor to Boolean recognition-work logic; forced Boolean logic (zero/positive cost split); a bridge to the cost-form meta-principle; forced meta-principle; a bridge to two-state discreteness; forced discreteness; a bridge to an additive ledger; forced ledger; a bridge to a recognition witness; forced recognition; realization and cost bridges into reciprocal-cost uniqueness; unique $J$; a bridge forcing $\varphi$ from self-similar hierarchy; forced $\varphi$; forced spatial dimension $D=3$; a bridge from dimension to eight-tick cadence; and forced eight-tick period $2^3$.
background
The module is the public theory-only T−1 through T8 forcing spine. It stops before private operator and measurement layers. Landmarks in order: T−1 absolute distinguishability floor; T0 Boolean recognition-work split (consistency costs zero, inconsistency positive); T1 cost-form meta-principle; T2 two-state discreteness of the floor; T3 additive ledger bookkeeping; T4 recognition witness on the discrete floor; T5 uniqueness of the canonical reciprocal cost $J(x)=(x+x^{-1})/2-1$; T6 $\varphi$ from realized self-similar hierarchy; T7 eight-tick cadence; T8 $D=3$ from linking, eight-tick, and gap-sync compatibility.
Upstream, TMinus1_AbsoluteFloor is the closed absolute-floor certificate. TMinus1_To_T0_Bridge supplies the Boolean floor witness and recognition-work interface. T0_Logic_Forced states that logic is the zero/positive split of recognition work. T0_To_T1_Bridge carries T0 into the meta-principle. Later bridges (T1_To_T2, T0_T2_To_T3, and so on) thread those certificates forward. The honesty note on the T4→T5 arrow records that T5 uniqueness is proved from CostUniqueness and law_of_logic_forces_jcost, not from the T−1..T4 floor.
proof idea
No proof body: this is a structure (record type). Each field is a named Prop or bridge structure already defined in this module or in TMinus1ToT1Bridge. Dependent fields take earlier certificates as parameters (for example t0_to_t1 depends on t0; t1_to_t2 on the T−1→T0 bridge and t1; t4_to_t5_cost on the realization bridge). Inhabitation is deferred to complete_forcing_chain_t8, which wires the individual bridge theorems field-by-field.
why it matters
This is the public packaging of the Recognition Science forcing chain T−1 through T8 (primer landmarks T5 J-uniqueness, T6 $\varphi$, T7 eight-tick octave, T8 $D=3$). Downstream, complete_forcing_chain_t8 builds a concrete inhabitant; complete_forcing_chain_t8_nonempty asserts nonemptiness; CompleteForcingChainTMinus2ToT8 extends the spine backward with the T−2 nothing-to-distinction certificate and circle-cohomology linking backend.
The doc-comment is explicit: the structure packages a conditional chain and is not a forcing proof of T5 from T4. T5 consumes nothing substantive from the floor beyond re-exporting an RCL surface; the continuous positive-ratio comparison surface remains an imported hypothesis (SI2/C6). Foundation.RecognitionLedgerFloor is the repair pointer for kernel/cokernel gaps at the floor, but no field of this bridge yet consumes it. Integrating that ledger so the comparison surface is a theorem rather than a hypothesis is an open task.
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