Study 12 Quantum Parallel Repetition Shear

Study 12 — Quantum Parallel Repetition Shear

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

Surface	URL / key	Cited vs sealed
Claim UI	https://affine.earth/language-game/study-12-chance.html	sealed POST
IDE	https://affine.earth/language-game/ide.html#qpr	file template; no auto-POST
Look	https://affine.earth/language-game/#researcher	GET only
Affine story	https://affine.earth/language-game/#story/Study-12-Quantum-Parallel-Repetition-Shear	this charter
Court	POST /language-invariant/game/chance/ingest rounds=3	sealed 27/64 / 27/64 · STUDY12_QPR_PROVEN · float 1.5 → HTTP 400
Humanity	Discrete repetition bounds without a second amplitude law	float adversary 751/1000 is the sealed miss
DFT map	many-electron (\psi), Born amplitudes	Anima approximates a probability in floats. Study 12 replaces (\psi) with (W_n\in\mathbb{Q}).

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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.

LIVE CLAIM — apex chance returns STUDY12_QPR_PROVEN. Named receipt is the court.

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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

LIVE CLAIM — named chance receipt. Not OPEN.

Replacement trio: this page kills the wavefunction · 11 kills continuous density · 13 kills KS potential. Synthesis: Fourier Phantom.

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