IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForcedStructural
Structural packaging of amplitude-linear forcing for recognition-coupled quantum channels: under the canonical factor-product hypothesis, every admissible channel response is amplitude-linear, and any density-only response is identically zero. Gravity and quantum-channel workers cite it when assembling Track 2.C/2.D content into the structural master theorem. The module wires certificate props and inhabited structural witnesses rather than re-proving the dichotomy.
claimUnder the canonical recognition-coupled factorization, every admissible channel response $R$ is amplitude-linear: $R(\lambda a)=\lambda R(a)$ in the signal amplitude. Any response that depends only on density (not amplitude phase/structure) collapses to the zero map. The module packages this as a structural proposition and an inhabited structural certificate for the gravity master theorem.
background
Recognition Science gravity work treats the quantum channel on the eight-tick signal substrate as the bridge between recognition cost and macroscopic response. Track 2.C established a single-factor dichotomy: on the eight-tick signal space, no nontrivial channel response can be both amplitude-linear and density-only. Track 2.D and Session 88 lift that dichotomy to a recognition-coupled factorization, the canonical factor-product hypothesis under which the channel is forced into the amplitude-linear regime.
The upstream certificate module aggregates Sessions 85–87 closures for the binary-tensor model. The master theorem module (Track 7.A) authors the conditional gravity master statement gated on seven tracks closing. This module sits between those layers: it does not restate the full master theorem, but supplies the structural amplitude-linear-forcing proposition and certificate that the fully structural master theorem imports with zero free hypothesis slots on this axis.
proof idea
Definition and certificate assembly, not a fresh analytic proof. The module names a canonical structural proposition for amplitude-linear forcing under the factor-product hypothesis, proves that proposition holds by appeal to the Track 2.C certificate and the Session 88 factorization, and packages an unconditional structural witness plus an inhabited structural certificate type. Downstream consumers obtain a zero-hypothesis input by inhabiting that certificate rather than replaying the dichotomy argument.
why it matters in Recognition Science
Feeds MasterTheoremStructural, the fully structural Track 7.A master theorem whose doc-comment states it pre-fills all five hypothesis inputs via structural witnesses (0 sorry, 0 RS-internal axiom). Without this module, amplitude-linear forcing would remain a named hypothesis on the conditional master theorem rather than a discharged structural slot. It is the structural content of Tracks 2.C and 2.D under the factor-product hypothesis, closing the quantum-channel half of the gravity forcing chain that later supports recognition-derived gravitational response. The remaining open step, noted downstream, is upgrading structural witnesses to fully dynamical unconditional derivations.
scope and limits
- Does not derive amplitude-linear forcing from dynamics alone; assumes the canonical factor-product hypothesis.
- Does not re-prove the single-factor Signal8 dichotomy; imports Track 2.C certificate content.
- Does not establish the full gravity master theorem; only the amplitude-linear structural slot.
- Does not upgrade structural witnesses to unconditional dynamical derivations.
- Does not address numerical constants (G, alpha) or mass-ladder claims.
used by (1)
depends on (2)
declarations in this module (7)
-
def
amplitude_linear_forced_canonical_prop -
theorem
amplitude_linear_forced_canonical_prop_holds -
def
amplitudeLinearForcedUnconditionalWitness -
structure
AmplitudeLinearForcedStructuralCert -
def
amplitudeLinearForcedStructuralCert -
theorem
amplitudeLinearForcedStructuralCert_inhabited -
theorem
amplitude_linear_forced_one_statement