Manuscript En02-D@4 · En02-D-v4.tex · section · e19ec871

Joint dashboard and evidence boundaries

Joint dashboard and evidence boundaries · lines 1271–1313

For each realized circuit and horizon, the supplement is designed to record

π_{t}, S (C_{t}), S (D_{\leq t}), S (D_{\leq t} F_{\leq t}), δ_{dec} (t),

the exact finite energy expectations, unrestricted recovery estimates, complete A–D channels, and resource histories.

The predeclared closed-core spreading diagnostic is

C_{n} (U) = \frac{1}{n ( n - 1 )} i \neq = j \sum \frac{1}{4 2 ^{n}} tr ([U^{†} X_{i} U, Z_{j}]^{†} [U^{†} X_{i} U, Z_{j}]), n \geq 2.

Set $C_{0} = C_{1} = 0$ . The dashboard uses $\sum_{n} π_{t - 1} (n) C_{n} (U_{t, n})$ . This is an opportunity-local closed-core diagnostic, not a cumulative open-system OTOC or recovery certificate.

Opportunity, actual emitted count, and accumulated internal layers are distinct clocks. Recording the distribution of emitted counts does not grant the decoder access to hidden counts. Replotting against their mean is not conditioning on a physical emission-count trajectory.

Ensemble summaries must average per-realization quantities. Entropy or recovery of an averaged channel is a different object.

status. No dashboard values for the new entangling study are supplied. No conclusion about depth, memory improvement, or recovery coincidence is prewritten. The analytical transport table is the only results table above.

Displayed formulas in this passage

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$π_{t}, S (C_{t}), S (D_{\leq t}), S (D_{\leq t} F_{\leq t}), δ_{dec} (t),$
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$C_{n} (U) = \frac{1}{n ( n - 1 )} i \neq = j \sum \frac{1}{4 2 ^{n}} tr ([U^{†} X_{i} U, Z_{j}]^{†} [U^{†} X_{i} U, Z_{j}]), n \geq 2.$