module module high

`IndisputableMonolith.Quantum.NonlocalityNoSignaling`

The NonlocalityNoSignaling module defines EPR pairs, measurements, and correlations in Recognition Science to show that entanglement produces Bell violations without permitting signaling. Quantum foundation researchers cite the no_signaling_theorem and ledger_explains_nonlocality to reconcile apparent nonlocality with causality. The module imports Constants for the time quantum and Cost for ledger accounting, then assembles definitions around shared ledger entries that remain locally readable.

claimAn EPR pair consists of two particles A and B sharing a ledger entry. The no-signaling theorem states that a local measurement on A leaves the reduced density operator of B invariant: $ρ_B' = ρ_B$. Quantum correlations violate the CHSH bound yet satisfy the no-signaling condition via the ledger.

background

Recognition Science derives quantum structure from the J-functional equation and the forcing chain T0-T8, with J-uniqueness at T5 and the eight-tick octave at T7. The Constants module supplies the fundamental RS time quantum τ₀ = 1 tick. The Cost module defines J-cost accounting for defects and ledger entries. This module introduces the quantum domain by defining EPR pairs as entangled states with shared ledger entries, measurements as local ledger updates, and correlations via the quantumCorrelation function, together with the no-signaling condition as invariance of the distant reduced state.

proof idea

This is a definition module, no proofs. It declares the main objects EPRPair, Measurement, SharedLedgerEntry and assembles theorems such as no_signaling_theorem, reduced_density_unchanged, and ledger_explains_nonlocality from the imported constants and cost primitives.

why it matters in Recognition Science

The module supplies the quantum nonlocality apparatus that explains Bell violations through ledger sharing without signaling, supporting the Recognition Science claim that quantum mechanics emerges from the RCL and J-uniqueness. It directly supports the ledger_explains_nonlocality result and connects to the eight-tick octave and D = 3 spatial dimensions. No open scaffolding is indicated.

scope and limits

Does not derive the Tsirelson bound from the phi-ladder.
Does not treat relativistic quantum field theory.
Does not resolve the measurement problem.
Does not compute specific correlation values beyond bounds.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (17)

structure EPRPair L38
structure Measurement L49
def quantumCorrelation L68
def chshBound L72
def tsirelsonBound L75
theorem bell_violation L78
theorem no_signaling_theorem L98
theorem reduced_density_unchanged L108
theorem ledger_explains_nonlocality L126
structure SharedLedgerEntry L136
theorem reading_is_local L148
def no_signaling_reasons L161
def mutualInformationProperties L176
theorem relativity_preserved L192
def experimentalTests L207
def implications L225
structure NonlocalityFalsifier L238