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Merge paid jobs in the native word under the rebalanced retirement tree (κ 0.00329700) - #6621
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…ee (kappa 0.00329700) Three compensated edits to the PR6529 native word, under the PR6551 caller: (A) merge the paid hops of one owned register into a single rank-6 job, (B) re-base register 471's addition, (C) re-base the helper-435 input so one rank-9 target becomes rank 8. Complete signed gain over PR6551: 18*(3H1+H3+H5+H8-H4-H6-H9) > 0 for H_r=r^t, 0<t<1. Claim 0.00329700 (+0.00000208 over 0.00329492). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Result
Conditional on the five inherited framework assumptions; the selected frontier is unchanged.
What changes
The PR6551 caller (PR6545 retirement, child trees (7,2,5,4)) is kept as is. The PR6529 native word gets three compensated edits (event numbers in the 18,493-event PR6529 word; the new word has 18,561):
r471 + r525/2 + 2 r704as 18 ADDs in frame 3 at program start; rows 9 and 61 take compensating ADDs in frame 127. Paid jobs of ranks 1, 1, 1, 3 become one job of rank 6.+r174,-r257/2in frame 3 (events 2557, 5664), compensated in frame 676 (events 9677 to 9679), replacing2 r770in frame 593.Per native call: paid {1:-3, 3:-1, 4:+1, 5:-1, 6:+1}, targets {8:+1, 9:-1}. Complete signed invoice gain over PR6551 (18 calls):
For
H_r = r^t,0 < t < 1:(3H1 + H3 - H6) > 0by strict subadditivity, and(H5 - H4) - (H9 - H8) > 0because the derivative strictly decreases. Productive fields stay 13,756, paid jobs fall 67,096 to 67,042, rank-mass surplus stays 760. The shadow register 783 is erased nonzero like 781, under the existingowned_erasureassumption.Verification
Marker
PASS_PAID_JOB_MERGES_KAPPA_00329700. Both modes and the registered hook pass locally. Hosted CI and independent review are pending.Credits
Builds on #6551 (caller, trees, package), #6545 (Gaussian retirement), #6529 (native word), #6453 (compensated native word), #6398 and #6399 (binary suppliers, mixed root), and all retained predecessors; see NOTICE.
Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
🤖 Generated with Claude Code