Gravity Master Theorem Unconditional Canonical Amplitude Linear Many Body Prop H

The many-body amplitude guarantee

In quantum mechanics, an amplitude is a complex number whose squared magnitude gives the probability of a transition. A linear amplitude means the response to a sum of inputs is the sum of the responses, a property that makes many-body systems tractable. The declaration canonicalAmplitudeLinearManyBodyProp_holds is a machine-checked theorem in the Recognition Science library. It proves, with no unverified assumptions, that three conditions hold together: a single-channel amplitude certificate exists, a many-body version exists, and a specific many-body endpoint is reached. In plain terms, the framework has constructed a formal guarantee that a certain many-body amplitude is linear and forced, meaning it is not a free choice but follows from the framework's axioms.

The theorem is part of a larger master theorem, a central result that assembles five witnesses for quantum gravity. This particular witness supplies the amplitude-linear piece. The proof works by combining three previously established results: the single-channel certificate, the many-body certificate, and the handoff integration endpoint. Each of these is itself a theorem in the library. The declaration does not merely assert the proposition; it provides a formal proof object, so the claim is as strong as the underlying logic allows.

What the theorem does not claim is equally important. The library's own closure status explicitly records that full physical closure is false. Several major targets remain open: the D2 quadrature, general triangulation, tensor train recovery, Lorentzian causal triangulations, boundary terms, and the echo mechanism. The theorem guarantees the amplitude-linear witness exists, but it does not say that this witness is unique, that it matches any experimental measurement, or that the remaining open targets are reachable. It is a structural result inside the framework, not a complete theory of quantum gravity.

For the reader, the practical meaning is this: within Recognition Science, the many-body amplitude linearity is no longer an assumption but a proved consequence. That frees later work to build on it without re-justifying the linearity. But the page also shows the honest boundary: the framework itself flags what remains open. The theorem is a step, not the destination.

theorem canonicalAmplitudeLinearManyBodyProp_holds :
    canonicalAmplitudeLinearManyBodyProp :=
  ⟨QuantumChannel.AmplitudeLinearForced.physicalChannelAmplitudeLinearCert_inhabited,
   QuantumChannel.AmplitudeLinearForced.manyBodyPhysicalChannelAmplitudeLinearCert_inhabited,
   MasterTheoremHandoffIntegration.track2_many_body_endpoint_holds⟩

/-- **Scoped theorem-built quantum-gravity master assembly.**  The five formerly
external master inputs are supplied here by canonical theorem-built witnesses:
D2 physical Regge/EH product-filter convergence plus Schläfli Bianchi,
D3 many-body amplitude-linearity, D4 recognition-tick Page transfer,
D5 PTA observable band, and D5 named strong-field channels.

This is a zero-argument Lean assembly theorem for the current witness route.
It is **not** a claim that the full physical quantum-gravity framework is
closed from primitives.  The D2 route remains scoped to the canonical
product-filter six-tet torus surface, the general triangulation and Lorentzian
causal-simplex problems remain open, and the black-hole echo mechanism is not
yet horizon-consistent.  See `closureStatus_unconditional` below for the
machine-readable physical-scope audit. -/
theorem rs_quantum_gravity_master_unconditional :
    MasterTheorem.RSQuantumGravityMaster
      canonicalRegEHContinuumAndBianchiWitness
      canonicalAmplitudeLinearForcedWitness
      canonicalPageCurveDerivedWitness
      canonicalPTADistinctWitness
      canonicalStrongFieldDistinctWitness :=
  MasterTheorem.rs_quantum_gravity_master_conditional
    canonicalRegEHContinuumAndBianchiWitness
    canonicalAmplitudeLinearForcedWitness
    canonicalPageCurveDerivedWitness
    canonicalPTADistinctWitness
    canonicalStrongFieldDistinctWitness

/-- The current zero-argument master assembly must not be cited as full
physical closure. -/
theorem closureStatus_unconditional_not_full_physical_closure :
    closureStatus_unconditional.theorem_built_witnesses_installed = true ∧
    closureStatus_unconditional.full_physical_closure = false :=
  ⟨rfl, rfl⟩

What this page does not claim

The theorem does not claim that the amplitude witness is unique. The theorem does not claim that the amplitude matches any experimental measurement. The theorem does not claim that the remaining open targets are reachable.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/MasterTheoremUnconditional.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: