Conditional κ .003128386 (+2.582e-6 over #6030): owned registers 770, 771 and 772 descend through the frames of helpers 705, 706 and 731, which no longer relay them; helper 732 reads 771 at frame 117

research/p104-root-relay-descent-2/EXPECT.json

@@ -0,0 +1,35 @@
+{
+ "interval": [
+  "312839320327/100000000000000",
+  "39104915041/12500000000000"
+ ],
+ "paid_calls": 66762,
+ "productive_fields": 13444,
+ "rank_mass_surplus": 760,
+ "events": 22818,
+ "inventory": [
+  770,
+  29,
+  31,
+  13
+ ],
+ "paid_delta": {
+  "1": -4,
+  "4": -1,
+  "5": 1,
+  "6": -3,
+  "7": 3
+ },
+ "helper_delta": {},
+ "control_sites": {
+  "add0": 0,
+  "add1": 1
+ },
+ "sign_sites": {
+  "add0": 0,
+  "add1": 1
+ },
+ "base_commit": "721c03822c421b7f7fcbb2598993b947c4d88419",
+ "chain_commit": "05cd36e5af06d7a3790e30ce3f449fa89b853768",
+ "status": "PASS_P104_BASE6030_EDIT_KAPPA_312838600"
+}

research/p104-root-relay-descent-2/PRICING-EDITS.json

@@ -0,0 +1,18 @@
+[
+ [
+  "KAPPA, TESTED = Q('0.00312476680'), Q('0.003124766805')",
+  "KAPPA, TESTED = Q('0.003128386'), Q('0.0031283910')"
+ ],
+ [
+  "PREVIOUS = Q('0.00312418633064')",
+  "PREVIOUS = Q('0.003125804')"
+ ],
+ [
+  "sum(targets.values()) == 13444 and sum(paid.values()) == 66870",
+  "sum(targets.values()) == 13444 and sum(paid.values()) == 66762"
+ ],
+ [
+  "'kappa_decimal':'0.00312476680','previous_pr5811':PREVIOUS",
+  "'kappa_decimal':'0.003128386','previous_pr6030':PREVIOUS"
+ ]
+]

research/p104-root-relay-descent-2/README.md

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+# Conditional kappa 0.003128386: owned registers 770, 771 and 772 descend through the frames of helpers 705, 706 and 731, which no longer relay them; helper 732 reads 771 at frame 117
+
+This package edits the word of [PR #6030](https://github.com/CrocSwap/integer-mult-bounds/pull/6030)
+(DreamingOfClouds, merged on main, conditional kappa 0.003125804) and re-certifies it with the chain PR #6030 used:
+PR #5827's own verifier (aliromman, head `05cd36e5af06d7a3790e30ce3f449fa89b853768`), loaded unmodified apart from the declared pricing literals.
+The complete conditional kappa is **0.003128386**, tested at 0.0031283910; the exact raw crossing lies in
+(0.00312839320327, 0.00312839320328) = (312839320327/100000000000000, 39104915041/12500000000000),
+which is +2.582e-06 above PR #6030's raw crossing (0.00312581155791). The paid bill falls to
+**66762 calls** (PR #6030: 66,834) at an unchanged 13444 productive targets and rank-mass surplus
+760. Public inputs, owned fields, owned lifetimes and peak occupancy (770, 29, 31, 13) are unchanged;
+the word has 22,818 events (PR #6030: 22,803; retained cap 26,000).
+
+## The edit
+
+The edit removes three relays and moves one read. In PR #6030's word, the owned registers 770, 771 and 772 are each loaded at one frame, moved once to a neighbouring frame and cleared there (770: 549 -> 593; 771: 541 -> 594; 772: 529 -> 595). A public helper then reads each of them at the landing frame and carries its content back up through the intermediate frames (helper 705: 593 -> 1047 -> 553 -> 549; helper 706: 594 -> 117 -> 534 -> 541; helper 731: 595 -> 737 -> 520 -> 529), delivering at each frame.
+
+In the edited word the owned registers walk those frames themselves, downwards, and the helpers no longer carry the content:
+- 770 runs 549 -> 553 -> 1047 -> 593; 771 runs 541 -> 534 -> 117 -> 594; 772 runs 529 -> 520 -> 737 -> 595.
+- Helpers 705, 706 and 731 keep a single hop, 3 -> 549, 3 -> 541 and 3 -> 529, to their unchanged final frames.
+- The readers that took their content from the relays now read the owned registers at the same frames. The frame-3 reads that paired against the relays' initial values are re-solved against other registers.
+
+Two further changes keep the occupancy and the values exact:
+- **Owned lifetimes.** To keep peak occupancy at 13, the lifetimes of 770 and 771 are placed after the peak window: their INIT/COPY events move from 13452-13456 and 13463-13465 to 13658-13659 and 13637-13638, and their CLEARs from 13462 and 13471 to 15424 and 15427. Register 772 keeps an early lifetime (INIT/COPY at 13478-13481) and its CLEAR moves from 13482 to 13624. Six readers of frame 595 (helpers 134, 450, 496, 572, 581, 582) take their frame-3 -> 595 hop before the root lands, which moves their MOVE events earlier.
+- **Helper 732.** Helper 732 reads owned register 771 at frame 117, on 771's way down, instead of at frame 594. It therefore goes 3 -> 117 -> 222 -> 127 and drops its stop at 594. Its pre-reads (helpers 569, 575, 576) are placed before the owned peak window.
+
+The INIT, CLEAR, COPY and SCALE events are identical as multisets; 52 ADD events are removed and 71 are added, 17 MOVE events are removed and 13 are added, and the event list grows from 22,803 to 22,818 events.
+
+Boundary charts changed by the edit: none. Paid-profile change vs PR #6030: rank 1: -4, rank 4: -1, rank 5: +1, rank 6: -3, rank 7: +3.
+Credited helper ranks: unchanged.
+Every public input column, every signed native map and the physical caller are re-checked in full (see Verification).
+
+`EDIT.json.gz` is the explicit edit list: boundary changes plus the new event list as copy segments of
+PR #6030's program and literal events. `construct.py` (standard library only) applies it to PR #6030's word, taken from
+`inputs/pr6030-WORD.json.gz` (authenticated against main's `research/p104-helper470-twin-rung-removal/WORD.json.gz`, Git blob and SHA256 in `SOURCES.json`), and regenerates
+the complete decompressed `WORD.json.gz` payload byte for byte (gzip-container bytes may differ by platform; this comparison is
+PR #6030's merged portability repair, kept with its `test_portability.py`):
+
+```sh
+python3.12 -I -B research/p104-root-relay-descent-2/construct.py
+```
+
+## Verification
+
+```sh
+python3.12 -I -O -B research/p104-root-relay-descent-2/test_portability.py
+python3.12 -I -B research/p104-root-relay-descent-2/verify.py
+```
+
+`verify.py` authenticates PR #6030's word and the pinned PR #5827 package (`inputs/pr5827-source.tar`, per-file SHA256 and Git blob;
+byte-identical to the archive in PR #6030's package) and its seven-deep source chain, asserts that the shipped `pricing.py` equals
+PR #5827's `pricing.py` plus the literal edits in `PRICING-EDITS.json` (claim, previous claim = PR #6030's, the paid-call count and two labels),
+regenerates the word, and runs PR #5827's chain unchanged: exact replay and storage inventory, all 799 input columns with a separate
+transpose, every signed native map, 208 main adapters, 1,124 helper normalizers, the exact physical caller, the complete invoice, both
+interval engines, compiler and 54 strict plus 4 functional outer checks, a check that PR #6030's full profile fails at the new claim,
+rejection controls, and the committed `RESULT.json`. `--part build` runs the authentication, regeneration and replay only.
+
+## Conditions inherited
+
+The five framework assumptions retained by the P104 line (native all-column implementation, owned erasure, uniform compiler closure,
+precision and fixed-tape costs, claim accounting) and PR #5827's own checker are inherited unchanged. Author checks are not
+independent human acceptance. The finite local word is materialized; the large uniform word and rounded multiplier are not. No merge,
+closure or selected-frontier change is requested.
+
+## Credits
+
+The base word is PR #6030's (DreamingOfClouds, helper 470's frame-593 rung removal), an edit of PR #5907's word (DreamingOfClouds,
+helper 468's frame-593 rung removal), itself an edit of PR #5827's word. The payload comparison in `construct.py`/`verify.py` and
+`test_portability.py` are the maintainer portability repair merged with PR #6030 (Douglas Colkitt, with OpenAI Codex assistance).
+The verifier chain is Ali Romman's (aliromman, PR #5827, with substantial OpenAI Codex assistance), built on PR #5811
+(Mason Hale), PR #5786 and the earlier lineage back to PR #5565 (Pierre-Loic Doulcet), with all retained source notices in the pinned
+archive. This package contributes only the edit above and its packaging.
+
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+
+## Open next questions
+
+- Does an independent reviewer confirm the edit list, the regenerated word and the full chain? First step: run `construct.py` and
+  `verify.py` as above, then compare the changed itineraries with PR #6030's word.