Manuscript Em03-G@1 · Em03-G-v1.tex · section · 0bb3a8a3

Complete records and statistics

Coherence witnesses, moments, and local observable access › Complete records and statistics · lines 1755–1786

Suppose final local readout has a separately justified complete-law allowance $e_{read, s}$ , including all declared failure records with fixed scores in $[0, 1]$ . For each preparation, a sufficient observable allowance is

e_{s} = e_{loc, s} + e_{read, s},

capped at one. Any independently justified coefficient or source error is added at its own comparison interface.

For independent attempted trials, with fresh preparations and fixed parameters, define

u_{s} = \frac{lo g ( 4/ β _{conf} )}{2 n _{s}}, 0 < β_{conf} < 1.

Then with probability at least $1 - β_{conf}$ ,

∣ p_{+} - p_{-} ∣ \geq Δ_{X} (l) - e_{+} - e_{-} - u_{+} - u_{-} .

The proof is the exponential-moment bound $Pr (∣ p - p ∣ > u) \leq 2 e^{- 2 n u^{2}}$ for independent scores in $[0, 1]$ , followed by a union bound. Every failure is scored, not removed.

These statistical and observable allowances are not inserted into a coherent-recovery diamond-distance ledger.

Displayed formulas in this passage

unlabeled · line 1761
$e_{s} = e_{loc, s} + e_{read, s},$
unlabeled · line 1769
$u_{s} = \frac{lo g ( 4/ β _{conf} )}{2 n _{s}}, 0 < β_{conf} < 1.$
unlabeled · line 1774
$∣ p_{+} - p_{-} ∣ \geq Δ_{X} (l) - e_{+} - e_{-} - u_{+} - u_{-} .$