Study 12 Quantum Parallel Repetition Shear

Study 12 — Quantum Parallel Repetition Shear

Status: CHARTER SEALED — 2026-08-22
Program: Conjecture Alignment · Shear Studies Index

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For every reader

Quantum parallel repetition asks: if Alice and Bob play a nonlocal game (G) in parallel (n) times, how fast does the winning probability decay? The standard proof uses continuous amplitudes and tensor products in (\mathbb{C}). UUM-8D replaces amplitudes with vQbit primitives and Jordan-bonded entanglement matrices — discrete state transitions with exact rationals.

This study will grade whether integer-bounded parallel repetition bounds match published thresholds — and whether float amplitude models shear the bound.

Corpus: OPEN. Results page will land when the frozen law is derived.

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The forcing and the track

Piece	Instantiation
Forcing	Parallel repetition index (n) (integer rounds)
Clock	Round index (k=1\ldots n)
Track	Bipartite strategy simplex in the integer manifold
Raw archive	Published game tables (CHSH, Magic Square, etc.) with exact rational winning thresholds
Adversary	Float amplitude product model — continuous (\mathbb{C}^{d^n}) tensor
Future events	New games registered before bounds are examined

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UUM-8D integration path

Standard	UUM-8D
Complex amplitude (\alpha\in\mathbb{C})	vQbit ((\tau, \mathrm{phase}, \mathrm{amplitude})) with unit-norm rational
Tensor product Hilbert space	Jordan algebra state on M⁸ = S⁴ × C⁴
Winning probability (float)	Ordinal comparison via cross-multiplication on (\mathbb{Q})
Parallel repetition bound	Discrete collapse turn count at sealed (\chi_{\max})

Reference substrate map: cells/xcode/Sources/InvariantCompiler/QuantumShearMap.swift — transport criterion per algorithm row.

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Success criteria (pre-registration)

1. Integer Jordan-bonded repetition bound (\le) published upper bound for CHSH at (n=1,2,4,8).
2. Float amplitude adversary over- or under-estimates the sealed bound at least once (shear measurable).
3. No Float/Double on the seal path.

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Status

CHARTER SEALED — corpus and frozen law OPEN.

When complete, results will publish as Study-12-Quantum-Parallel-Repetition-Results.md.