IndisputableMonolith.Gravity.QuantumChannel.NoClassicalMediator
Module packages the no-classical-mediator claim under T0–T8: any substrate with recognition cyclic-shift matter, binary tensor product, and pure-tensor factorization cannot host a nontrivial density-only gravity channel. Gravity workers on Track 2 cite the certificate and one-statement form. Arguments specialize the upstream amplitude-linear dichotomy to that forced substrate.
claimA $T_0$–$T_8$-consistent substrate has matter side given by the recognition cyclic shift, joint system the binary tensor product, and joint operator factorizing on pure tensors. On every such substrate there is no nontrivial classical mediator: no density-only channel response is nontrivial. Equivalently, the channel is forced to be amplitude-linear.
background
Recognition Science derives physics from the T0–T8 forcing chain (J-uniqueness, $\varphi$ fixed point, eight-tick octave, $D=3$). Gravity Track 2 studies quantum channels on the discrete substrate that chain produces.
Upstream AmplitudeLinearForcedCert (Track 2.C) records the Session 85 dichotomy on Signal8: no nontrivial channel response is simultaneously amplitude-linear and density-only. This module lifts that fact to substrates forced by T0–T8. Concretely, the matter update is the recognition cyclic shift, the joint system is a binary tensor product, and operators factorize on pure tensors.
A classical mediator means a density-only response (occupation, not amplitude phase). The module states that such mediators cannot be nontrivial once the substrate is T0–T8-consistent.
proof idea
Defines a structure packaging cyclic-shift matter, binary tensor product, and pure-tensor factorization. Theorems then prove: no classical mediator under T0–T8; nontrivial density-only responses are impossible; no inhabited T0–T8 substrate admits a nontrivial classical mediator; the channel is forced amplitude-linear. Each claim specializes the upstream AmplitudeLinearForced dichotomy to that substrate. A certificate type bundles the results, with an inhabited instance and a one-statement Track 2.D headline.
why it matters in Recognition Science
Supplies the Track 2.D no-classical-mediator closure that Gravity.MasterTheorem imports into the structural master statement (Track 7.A, conditional form, zero sorry on the load-bearing path). Also imported by BMVFalsifierBand, which frames the entanglement witness and falsifier floor; that panel notes BMV entanglement is predicted by any quantum mediator, so this module’s prohibition on classical mediators sharpens why the channel must be amplitude-linear. Converts the Session 85 single-factor dichotomy into a substrate-level ban on density-only gravity mediators, matching the RS claim that gravity rides the recognition update rather than a classical field.
scope and limits
- Does not derive T0–T8; assumes substrates already consistent with the chain.
- Does not treat continuous spacetime or mediators outside the binary-tensor model.
- Does not claim lab exclusion of classical gravity; only RS-substrate impossibility.
- Does not distinguish among quantum-mediator models (BMV is not a discriminator).
- Does not prove the full Gravity Master Theorem; only the no-classical-mediator ingredient.
used by (2)
depends on (1)
declarations in this module (11)
-
abbrev
T0T8ConsistentSubstrate -
theorem
no_classical_mediator_under_T0T8 -
theorem
nontrivial_density_only_impossible_under_T0T8 -
theorem
no_T0T8_substrate_with_nontrivial_classical_mediator -
theorem
channel_forced_amplitude_linear_under_T0T8 -
theorem
T0T8ConsistentSubstrate_inhabited -
theorem
track2D_headline -
structure
NoClassicalMediatorCert -
def
noClassicalMediatorCert -
theorem
noClassicalMediatorCert_inhabited -
theorem
no_classical_mediator_one_statement