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Manuscript I@2 · I.tex · figure · 85631fa7

Stability budgets

Stability and represented measurements › Resource-budgeted record stability · lines 2046–2063

I@2#fig:stability-budget

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(a) Outcome law
nn qubits
whole-register record adds nn
peak 2n≤N2n\le N
record discrepancy ε\varepsilon
diagonal anchoring discrepancy ε\varepsilon
dTV(PψS,BornψS)≤2εd_{\mathrm{TV}}(\mathsf P^S_\psi,\mathsf{Born}^S_\psi)\le 2\varepsilon
(b) Joint continuation law
nn plus kk record qubits
further record test adds n+kn+k
2(n+k)≤N2(n+k)\le N
errors ε+2ε\varepsilon+2\varepsilon

Joint-law error ≤ 3ε. Exact composability; approximate anchoring and records.

(c) Conditional residual
b≥γ>0,ε≤γ/8b\ge\gamma>0,\qquad \varepsilon\le\gamma/8D(u,φ)≤min⁡{1,6ε/γ}D(u,\varphi)\le\min\{1,\sqrt{6\varepsilon/\gamma}\}
Rare branches amplify conditional error.

Registers are counted as stacked resources, not as a performance curve. No approximate theorem is claimed for the first four requirements.

The sufficient stability budget counts record qubits for intermediate whole-register tests. It is not merely the peak of the original source and its first deferral.

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