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Research (no κ claim): successor hand-off of productive conduit helpers — new native pattern, verified gadget, pricing, exact screens on #4610 - #5472

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CrocSwap:mainfrom
GamingPuzzled:r18-helper-handoff
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GamingPuzzled wants to merge 2 commits into
CrocSwap:mainfrom
GamingPuzzled:r18-helper-handoff

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@GamingPuzzled

@GamingPuzzled GamingPuzzled commented Oct 25, 2026 •

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New native pattern. A successor helper starts idle at a mid frame F. At F the conduit helper's carried port data is cancelled with co-framed ADDs, the conduit passes to the successor, and consumers above F pre-subtract the successor's input. The paid climbs stay the same, and one rank-(a+b) productive target becomes a + b.

  • Gadget (checked). An exact replay on F2^5 under literal_replay rules, with the interpreter control-matched to the Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 word in both orientations. Targets go from [5] to [3,2] at the same paid profile {1:12, 2:2, 3:1}, and three mutation controls are rejected.
  • Pricing. A 9→4+5 hand-off in each of the 18 locals adds +1.36e-6 to the raw root. A single hand-off would beat U = 0.00302728825 in raw root.
  • Exact screens on Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610. No hand-off point exists. Co-framed cancellation, deferred cancellation and pre-subtraction all find nothing. The only span-feasible points are entrance-pure ones, and their spread inputs are recollected only at the top frame.
  • Requirement for a real gain. A new native word in which helper flags cross port flags at mid frames.

Package: research/helper-handoff-r18. Verify with sh research/helper-handoff-r18/verify.sh, which prints PASS_HELPER_HANDOFF_R18.

Credits: Cao Yifan (#4610), zxv (#4359, literal_replay), Clear1nsight (#5413), #5409, Matarener (#5422/#5426/#5433), aliromman (#5383), #4441/#4470, Aaron Wang (#3039).

AI disclosure: Claude Opus 5.5 (Anthropic) via Claude Code, directed by Joel Pulikkan (GamingPuzzled).

Addendum (follow-up commit f5600651): a local hand-off is gain-neutral once re-flagging is priced. Routing a register through a mid frame costs the same concave g(p,q) as the hand-off gains. An exact screen of all 408 helpers on #4610 (about 1.88M points per orientation) finds 0 net-positive hand-offs, and designed F2^9 blocks are exactly neutral or dominated by a later entrance. The 0.00353 ceiling is gain-only and not achievable locally; a gain needs a new main transform. The package also adds a corrected repricing of the #5270/#5440 p19 line (complex saving 0 once the 4,256 letter Q are charged).

🤖 Generated with Claude Code

…rs — verified gadget, pricing, exact screens on CrocSwap#4610

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
…R19 screen and blocks); p19 corrected repricing (R20)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
@GamingPuzzled

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Follow-up (f5600651): an honest correction to the scope of this mechanism. Between two anchors a register's paid rank mass is fixed, so routing any register through a mid frame F costs g(p,q) = f(p)+f(q)−f(p+q). That is exactly the concave function the hand-off gains.

So the 0.00353 ceiling counts only the gain and is not achievable with local blocks. A hand-off gain needs a new main transform whose port flags pass through the helpers' mid frames with the carried data unchanged. Details are in addendum-r19-neutrality/.

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