amplitude_linear_forced_canonical_prop

In RS gravity, Tracks 2.C/2.D force the gravitational channel response on eight-tick ledger signals (the T7 octave) to be amplitude-linear rather than a classical density readout. Amplitude-linearity means the response agrees with some $\mathbb{C}$-linear map, so coherent superpositions of ledger states are preserved. Density-only responses are invariant under unit-modulus phase multiplications: the structural footprint of a CPTP-classical readout from $|\psi\rangle\langle\psi|$.

This module ships a structural witness for the master-theorem hypothesis AmplitudeLinearForcedUnconditional, using the canonical recognition-coupled factorization (Session 88): an explicit factor-product witness with cyclic shift on both factors and the recognition update on the matter side. Status is structural (zero sorry, zero RS-internal axiom), not fully unconditional; the factor-product hypothesis remains.

Upstream, IsAmplitudeLinear and IsDensityOnly name the two structural predicates. The canonical recognition-coupled object supplies the concrete factorization whose channel response is tested.

Definition, not a theorem. The body is the conjunction of two clauses on the channel response $R_C$ of the canonical recognition-coupled factorization: (i) $R_C$ is amplitude-linear, and (ii) if $R_C$ is density-only then $R_C$ is identically zero on every eight-tick signal. No tactics or lemmas fire; the Prop simply wires the two named predicates to the canonical witness field.

Sibling theorem amplitude_linear_forced_canonical_prop_holds discharges this Prop by applying track2C_headline to the canonical coupling. That holding result feeds amplitudeLinearForcedUnconditionalWitness, which inhabits the master-theorem hypothesis input AmplitudeLinearForcedUnconditional from Gravity.MasterTheorem (Session 97).

In the framework this is the structural content of Tracks 2.C + 2.D under the named factor-product hypothesis: channel forced amplitude-linear, density-only collapse to zero. The eight-tick signal space is the T7 octave (period $2^3$). Fully unconditional closure, retiring the factor-product hypothesis from a stricter substrate axiom or eliminating it on the joint-operator side, remains future work. The anti-retreat principle is met by pinning the witness to the Session 88 canonical factorization with its named FactorizableJointSubstrate hypothesis.