[GamingPuzzled]

Summary

This PR claims a complete conditional κ of .00308181, tested at .0030818105. The exact raw crossing lies in
(.00308181851522, .00308181851523). That is +3.94e-7 over the raw crossing of #5561, .0030814243 (claim line
.00308142).

The package is research/p104-priced-handoff/. It applies one priced successor hand-off to the headline word of
#5561.

Mechanism

This is the successor hand-off of #5472, with one co-framed partner.

• Last read. Helper 706 (initial dim 0, final dim 9) is last read at event 15443. From then on its row is
  706 + D, and no other register holds its symbol.
• The partner. Main register 173 sits at frame 559 (dim 8) from event 13089 to event 17248, and row(173) = 2D
  is constant there.
• The hand-off. 706 climbs 549→559, cancels D at 559 (ADD 706 += -1/2*173) and ends there. Before, it climbed
  549→127 (dim 9) and cancelled there. The successor would be a rank-1 spectator with no data (moment-neutral, like
  Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553's Variant A), so it is omitted.
• What the word looks like. It has the same 25,140 events and the same scalar events (one ADD moved and
  relabelled), with 735 public inputs. The only other change is final[706], which goes from 127 to 559.
• Per call. Helper credit 9 → 8 and paid climb 2 → 1. Surplus 760, fields 12,814 and paid calls 66,852 are all
  unchanged. Net concave gain: g(8,1) − g(1,1) = +0.005365 at each of the 18 calls.

Exhaustive screen

The screen covers all 527 helpers, every event and every mid frame. Tools are in tools/, with outputs.

• Free hand-offs (Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553's form). 0 on P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561. The control on Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551's word finds exactly Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553's two.
• Frame-independent windows. There are no mid-life pure windows, so free hand-offs reduce to endpoint retimes,
  which P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 already absorbs.
• Co-framed span at existing frames. 0.
• Priced holder lifts. 589,992 points. 81 are span-feasible, all net < 0, because the helper's own new stop
  costs as much as the split gains (R19 neutrality).
• Priced span closure and single partner, any nested F. Exactly 1 net-positive hand-off, the one
  implemented here.
• Not screened. 2,832 points with owned-scratch holders (stated in the README).

Conditional on

The same as #5561:

• (a) the five framework assumptions of Conditional κ = 0.00304057 (+1.3281765e-5 over #5413) #5544/Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545/Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551;
• (b) Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551 and P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561, neither independently reproduced;
• (c) free helper final frames. Audit #5561 free helper endpoints against the #5550 P104 endpoint contract (no new κ) #5567 argues these are the P104 local.py contract.

No independent human or proof-kernel acceptance is claimed. The selected record is unchanged.

Verification

• python3.12 -B scripts/research_package.py --package research/p104-priced-handoff gives
  PASS_REGISTERED_RESEARCH_PACKAGE (about 3.5 min, stdlib). It checks:
  • input pins, and byte-exact regeneration by handoff.py from P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561's word;
  • the edit inventory;
  • the exact hand-off condition in rational arithmetic;
  • the unmodified Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545 local.py replay, transposed columns and native maps;
  • the physical caller;
  • P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561's pricing.py with only the claim line and label changed (LITERAL-CHANGES.diff);
  • both moment engines;
  • all 54 strict + 4 functional outer checks;
  • the exact crossing;
  • four mutation controls, all rejected: no stop, wrong coefficient, final not lowered, and the hand-off placed
    before the last read.
• Second check, run outside the package. The Independently verify the P104 forward caller and target bindings (no new κ) #5550 checker, patched as in Audit #5561 free helper endpoints against the #5550 P104 endpoint contract (no new κ) #5567, gives
  PASS_SCOPED_CALLER_AND_TARGET_BINDING on this word and invoice (66,852 / 12,814, all 10 controls reject).

Credits

• DreamingOfClouds: P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 (base word, free endpoints) and Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 (free hand-offs on Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551).
• thu-nmrc: Improve complete conditional κ to 0.00304153 via coupled P104 contacts #5551.
• aliromman: Conditional κ = 0.00304057 (+1.3281765e-5 over #5413) #5544/Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545 (P104 word line).
• Lineage: Compose P104 private descent reuse with coalesced frames #2305/Construct complete P104 forward word and conditional hosting invoice #2152/Record P104 private descent fanout reuse construction #2219.
• zxv: Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359 paradigm and Research: the productive-helper path (#4440 lineage) can't pass κ ≈ .00304 without cheaper helpers #5554.
• Cao Yifan: Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 native semantics.
• Clear1nsight: Independently verify the P104 forward caller and target bindings (no new κ) #5550 checker.
• Matarener: Audit #5561 free helper endpoints against the #5550 P104 endpoint contract (no new κ) #5567 contract audit.
• GamingPuzzled: Research (no κ claim): successor hand-off of productive conduit helpers — new native pattern, verified gadget, pricing, exact screens on #4610 #5472 successor hand-off.

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

🤖 Generated with Claude Code

Stacked on #5561 (this branch includes #5561's commits; the new material is research/p104-priced-handoff/).

[Matarener]

Independent reproduction of this PR on head af9f091ac (base main 5e0052ca0), for Matarener:

• verify.py: PASS P104_PRICED_HANDOFF (Python 3.12, 3 min 31 s); research_package.py: PASS_REGISTERED_RESEARCH_PACKAGE.
• Own exact replay of WORD.json.gz and inputs/pr5561-WORD.json.gz (no source imports; span nesting, common charts, all 743 endpoint rows, owned lifetimes): both pass. The only endpoint change is helper 706, (dim 0 → 9) becoming (0 → 8). The local paid delta is +H1 − H2, the helper target delta is +H8 − H9, and the invoice differs from PR5561's by exactly 18 times that (paid 1: +18, 2: −18; targets 8: +18, 9: −18).
• PR5550 checker, patched as in Audit #5561 free helper endpoints against the #5550 P104 endpoint contract (no new κ) #5567: PASS_SCOPED_CALLER_AND_TARGET_BINDING, 66,852 / 12,814, 274 anchors, 10/10 controls, 124,232,680 ordinary passes. This matches the README.
• No new MOVE map (549→559 already occurs in PR5561's word). The one new helper endpoint pair (frame 3 → 559, rank 8) passes the PR5548 dense all-column check with absolute phase and support 2^8.
• Separate decimal interval engine (80 digits, 1e-70 padding): .00308142, .00308181, .0030818105 and .00308181851522 are positive; .00308181851523 and .00308182 are negative. This equals the stated raw interval.

Conditions unchanged: PR5551 (independent audit in #5572) and PR5561 admission, and the framework premises.

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[Matarener]

Follow-up on the hand-off screen, for Matarener: an exact version of tools/lift21.py.

• Closure search. Greedy closure is replaced by a search over partner subsets: every zero-cost co-framed partner plus subsets of up to 6 positive-cost partners, pruned at cost ≥ gain.
• Generic frames. The extended (span-fail) branch also tries a generic hand-off frame F of each admissible dimension. Every member then pays its split.

The pricing model, point enumeration and filters are unchanged from yours.

Headline word of PR5561, and this PR's word. Both ran to completion at depth 6. On PR5561 the only net > 0 point is 706/173 at F = 559, net +0.0053649 per call. The generic-F version of the same point reaches the same net with partners [121, 173]. This PR's word has no net > 0 point. So 706/173 is the unique priced hand-off of this family on both words; the greedy closure missed nothing there.

PR5561 starts-only word, depth 4. Three further net > 0 points appear in addition to 706/173. Each lowers a dim-9 helper final to dim 8 at frame 245, with two partners:

helper @ event	partners
587 @ 16530	[436, 734]
451 @ 16551	[228, 732]
450 @ 16554	[230, 732]

Each has net +0.0010977 (gain 0.0096321, cost 0.0085343). These are priced only; no word was constructed. Since the starts-only branch is below the headline word, they are unlikely to move the frontier.

Depth 6 on the starts-only and PR5551 words did not finish (the subset search explodes) and was stopped. Code and logs can be shared on request.

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