[DreamingOfClouds]

Result

	κ	raw crossing
#6621	0.00329700	0.0032970138574525
This PR	0.00329760	0.0032976213479979
Increment	+0.00000060	+6.075e-7 (+0.0184%)

This result is conditional on the inherited framework assumptions. The selected frontier is unchanged.

What changes

The PR6621 package is kept as is: the PR6551 caller, the PR6545 retirement and child trees (7,2,5,4). The edit is one exact rewrite of the native word.

Public helper register 607 is cut at frame 115. The rest of its life, frames 115 to 127, moves to a new public register 770, and the owned registers shift up by one. Three compensating ADDs go at program start (frame 3) and three at program end (frame 127), into registers 173, 611 and 704. One long helper becomes two shorter ones.

Per native call:

• paid: {2:+1, 4:+1, 6:-1}
• targets: {4:+1, 5:+1, 9:-1}

The complete signed invoice improves by

18 * (H5 + H6 - H2 - H9)

which is positive by concavity of H_r = r^t, 0 < t < 1 (PROOF.md). The new word has 18,577 events.

Declared package-local bounds

These changes are not SPEC. They are verifier literals inherited from earlier packages, and they are changed by exact, counted replacements.

• The public-register inventory bound rises from 770 to 771.
• The owned peak bound rises from 13 to 14.
• The certified tail decay changes from 97/100 to 33/34. The bound stays rigorous: the largest delta is 0.970283 < 33/34, and (33/34)^128 < 1/16 (PROOF.md). The decay does not enter κ.

Verification

python3.12 -I -B research/p104-helper-split-on-retirement-tree/verify.py
python3.12 -I -O -B research/p104-helper-split-on-retirement-tree/verify.py
python3.12 -B scripts/research_package.py --package research/p104-helper-split-on-retirement-tree

The marker is PASS_HELPER_SPLIT_KAPPA_00329760. Both modes and the registered hook pass locally. The package was independently re-audited, including a fresh exact re-price and a native legality check with 0 bad pairs. Hosted CI is pending.

Credits

This builds on:

• Merge paid jobs in the native word under the rebalanced retirement tree (κ 0.00329700) #6621 (native word, package)
• Improve conditional kappa to 0.00329492 with a rebalanced retirement tree #6551 (caller, trees)
• Improve conditional κ to 0.00329394 by retiring an independent Gaussian #6545 (Gaussian retirement)
• Conditional κ = 0.003288299 (+1.285e-6 over #6453): scaled transport fusion #6529 and Conditional κ = 0.003287014 (+1.65e-7 over #6417): a third group-1091 anchor on the clean mixed root #6453 (native words)
• Mixed-query root: conditional κ = 0.00328621476572836015146308 (+4.28455% over #6375) #6398 and Conditional κ = 0.003151787: clean donor-transport merge #6399 (binary suppliers, mixed root)
• all retained predecessors; see NOTICE.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code