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IndisputableMonolith.Gravity.QuantumChannel.NoClassicalMediator

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Module ruling out a classical (density-only) gravitational mediator on any substrate consistent with the T0–T8 forcing chain. It defines the T0–T8-consistent binary-tensor substrate and packages the no-classical-mediator certificate. Gravity master-theorem and BMV-band authors cite it. The argument lifts the Signal8 amplitude-linear versus density-only dichotomy to that substrate class.

claimOn any substrate consistent with the T0–T8 chain (matter update $=$ recognition cyclic shift, joint space $=$ binary tensor product, joint operator factorizing on pure tensors), no nontrivial channel response is both amplitude-linear and density-only. Hence a classical mediator is impossible under T0–T8.

background

Recognition Science forces physics from the T0–T8 chain: unique cost $J(x)=(x+x^{-1})/2-1$, self-similar fixed point $\varphi$, eight-tick octave (period $2^3$), and $D=3$. Gravity Track 2 studies quantum channels on the eight-tick signal space.

Upstream Track 2.C (AmplitudeLinearForcedCert) closes the single-factor dichotomy: on Signal8, no nontrivial channel response is simultaneously amplitude-linear and density-only. Density-only response is the mathematical stand-in for a classical mediator.

This module fixes the joint setting that inherits that dichotomy: matter side is the recognition update (cyclic shift), joint substrate is the binary tensor product, and the joint operator factorizes on pure tensors. That package is the T0–T8-consistent substrate used below.

proof idea

Definition layer introduces the T0–T8-consistent substrate (cyclic-shift matter, binary tensor product, pure-tensor factorization) and shows it is inhabited. Theorems then specialize the upstream amplitude-linear forced dichotomy to that class: nontrivial density-only response is impossible, so no classical mediator exists under T0–T8. A one-statement form and a NoClassicalMediatorCert bundle the result for downstream import. Headline lemmas restate the same exclusion for Track 2.D consumers.

why it matters in Recognition Science

Closes the classical-mediator exclusion half of Gravity Track 2 so later tracks can assume a quantum (amplitude-linear) channel. Imported by Gravity.MasterTheorem (Track 7.A structural master statement) and by BMVFalsifierBand (entanglement-witness floor). Sits downstream of the Session 85–87 amplitude-linear forced certificate; without this lift, the master theorem could not cite a T0–T8-native ban on classical mediators. Does not itself discriminate RS from other quantum-mediator models (BMV panel framing).

scope and limits

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (11)