Conditional kappa 0.00310184 (+1.39e-6 over updated #5599): compose the shared relay and helper splits

research/p104-relay-split-composition/LITERAL-CHANGES.diff

@@ -0,0 +1,31 @@
+--- PR5599/pricing.py
++++ composition/pricing.py
+@@ -12,8 +12,8 @@
+ from fractions import Fraction as Q
+ import local as L
+
+-KAPPA, TESTED = Q('.00309839'), Q('.0030983905')
+-PREVIOUS = Q('.00308189')
++KAPPA, TESTED = Q('.00310184'), Q('.0031018405')
++PREVIOUS = Q('.00309839')
+
+
+ def encode(x):
+@@ -62,7 +62,7 @@
+             second_p[8*(j+1)] += 208
+     L.need((targets,paid) == (second_t,second_p), 'Independent full invoice')
+     L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks')
+-    L.need(sum(targets.values()) == 13084 and sum(paid.values()) == 66852, 'Complete field and call counts')
++    L.need(sum(targets.values()) == 13048 and sum(paid.values()) == 66690, 'Complete field and call counts')
+     L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus')
+     return targets,paid,counts
+
+@@ -150,7 +150,7 @@
+     L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory')
+     bad=outer_module.ledger(dict(params,bit_saving=Q('.0027')))
+     L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected')
+-    return encode({'kappa':KAPPA,'kappa_decimal':'.00309839','previous_open_pr5580':PREVIOUS,'gain':KAPPA-PREVIOUS,
++    return encode({'kappa':KAPPA,'kappa_decimal':'.00310184','previous_open_pr5599':PREVIOUS,'gain':KAPPA-PREVIOUS,
+                    'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper],
+                    'raw_headroom':[lower-KAPPA,upper-KAPPA],
+                    'raw_ceiling':{'interval':[Q(0),cap],'derivative_upper':derivative_upper},'margin_at_previous':E.display(margin(PREVIOUS)),

research/p104-relay-split-composition/PROOF.md

@@ -0,0 +1,79 @@
+# Exact composition and complete invoice
+
+All three ingredients start from the same pinned PR5580 word. Event indices in
+`construct_parent` refer to that immutable source, not an already edited list.
+
+## The corrected relay and commuting cascade
+
+PR5605 replaces owned738's deliveries into public203 and public148 by the
+earlier public587 relay. Its signal has the form `2P+N`, where
+`N=x587-4x734` consists of arbitrary original inputs. The initial nilpotent
+correction `I-uN` and its explicit inverse cancel the nuisance; 18 coframed
+late ADDs restore the full-frame residuals. The published construction is
+retained and regenerated exactly before composition.
+
+PR5565's commuting cascade changes other scalar contacts and raises helper531's
+productive rank from eight to nine. The retained generator is independently
+regenerated and compared to its published word. Its edits and the relay edits
+occupy disjoint intervals of the original event sequence. The verifier merges
+those literal edits independently of `construct_parent` and compares every
+word field. Disjointness alone is not used to infer correctness: the resulting
+735-input word must also pass complete exact scalar/frame/ownership replay.
+
+## Applying independent helper splits
+
+Use Ali Romman's retained PR5599 split construction. For a prefix matrix P,
+suffix matrix S, and a chosen common intermediate chart, a witness supplies
+row a, column b, and boundary vectors c,d with
+
+`a P = c`, `S b = d`, `a b = c d = 1`.
+
+Both boundary vectors belong to one helper group with the same initial and
+final charts. Explicit ordinary basis operations isolate this one channel at
+the initial boundary and at the cut. The old independent input finishes at
+the cut, while a newly introduced independent input runs the remaining suffix.
+The final basis operations restore the independent endpoint interface. No
+new Gaussian call, COPY or CLEAR is introduced by the split itself.
+
+The original 15 witnesses are ordered. Original numbers 12 and 15 need pivot
+visits to line597 removed by the cascade; those witnesses and their credits
+are omitted. For the remaining 13, all rational vectors, pivots, charts and
+split ranks are identical to the source. Only `cut_after` changes.
+The verifier checks the full equalities above over every current public and
+owned coordinate at each evolving cut, then replays all rows after that split.
+This matters because a split basis can interact with later relay cleanup; the
+old six-row residual description is not blindly transferred to the split word.
+
+The final independently counted inventory is 748 public inputs and 540 helpers,
+with the same eight owned lifetimes and peak one. Every extra input remains an
+independent degree of freedom. A zero-dimensional chart never means a
+zero-valued helper. All 25,502 events and every changed native map are checked.
+
+## Signed bill and pricing
+
+Against PR5599 the local paid and target changes respectively are
+
+`Delta paid = -9H1-H2-2H3-2H4+4H5+H6`,
+
+`Delta target = -2H1-H4+H5-2H8+2H9`.
+
+The unchanged physical caller invokes the local word 18 times. All main banks,
+queries, whole idles, adapters, routing and normalizations remain charged.
+The resulting complete bill has 66,690 paid calls, 13,048 targets and unchanged
+rank surplus 760. In particular, omitted split targets are not still credited.
+
+The retained PR5599 price implementation independently recounts this bill,
+encloses the raw crossing with its primary exact rational interval engine,
+independently checks interval overlap and positive funding at the tested
+endpoint with a second engine, and checks the completion tails, uniform
+compiler and all 58 outer predicates at 0.0031018405. It retains decay 39/40 and compiler
+power 1024. The reported claim is 0.00310184. Its exact raw crossing is
+(0.00310184254783,0.00310184254784); a negative derivative bound on [0,0.0034]
+makes this the ceiling for this invoice under the inherited BIT cap.
+
+The finite certificate and conditional calculation preserve the inherited
+framework assumptions listed in README.md. They do not establish a new
+unconditional multiplication theorem or a universal optimality result.
+
+Prepared for flyingviper with substantial OpenAI Codex assistance and independent
+agents, preserving the predecessor attribution in README.md. Apache-2.0.

research/p104-relay-split-composition/README.md

@@ -0,0 +1,125 @@
+# Conditional kappa 0.00310184 by composing a relay, cascade and helper splits
+
+This package combines the compensated public relay in
+[PR #5605](https://github.com/CrocSwap/integer-mult-bounds/pull/5605), the full
+commuting-contact cascade in
+[PR #5565](https://github.com/CrocSwap/integer-mult-bounds/pull/5565), and 13 of
+the 15 independent helper splits in
+[PR #5599](https://github.com/CrocSwap/integer-mult-bounds/pull/5599).
+The complete conditional endpoint is **kappa 0.00310184**, a gain of
+**0.00000345** over the consumed PR5599 version's 0.00309839.
+During verification, PR5599 advanced to **0.00310045** at
+`09dd0965711ca7eeb169057a420abab1c9052137`, independently composing its splits
+with PR5565. Our endpoint is **0.00000139 higher** than that newer claim.
+Our immutable inputs and historical comparison receipt retain the consumed
+versions explicitly; no source head is silently replaced. The selected
+frontier is unchanged.
+
+The exact raw crossing lies in **(0.00310184254783, 0.00310184254784)**;
+the claim is tested at 0.0031018405. The full bill contains **66,690 paid
+calls** and **13,048 independent productive targets**, with rank surplus 760.
+The local word has **748 arbitrary public inputs, 540 helpers, eight owned
+lifetimes, owned peak one and 25,502 events**, below the retained 26,000 bound.
+All extra independent inputs and ordinary basis operations are charged.
+
+Read [PROOF.md](PROOF.md), [construct.py](construct.py), the exact
+[SPLITS.json](SPLITS.json), [RESULT.json](RESULT.json), and [source pins](SOURCES.json).
+
+## Why the composition is not just adding headline gains
+
+The cascade removes the intermediate line visits needed by original split
+numbers 12 and 15. They are omitted, including their target credits. The
+other 13 retain their exact rational witness vectors; only their event cuts
+move. At every new cut, the verifier recomputes the complete prefix functional
+and suffix direction on the evolving word. It then replays every independent
+input and output before proceeding to the next split.
+
+Relative to PR5599, the local paid change is
+`-9H1-H2-2H3-2H4+4H5+H6`, and the target change is
+`-2H1-H4+H5-2H8+2H9`. Both enter the full invoice 18 times.
+The root crossing and compiler reserve are recomputed from that actual bill.
+No universal optimality or concave-order improvement for every possible
+tariff is claimed. Other combinations were used during discovery; the
+submitted claim concerns this explicit word only.
+
+## Reproduce
+
+Python 3.12 and its standard library suffice:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-relay-split-composition
+```
+
+Both registered modes must print `PASS_P104_RELAY_SPLIT_COMPOSITION_KAPPA_00310184`;
+the launcher must print `PASS_REGISTERED_RESEARCH_PACKAGE`.
+
+The verifier authenticates immutable sources and every payload in the unchanged
+33-file PR5545 closure; independently merges the two retained predecessor
+generators' disjoint source edits; checks all 13 rational split witnesses and
+every intermediate arbitrary-input endpoint; regenerates the entire saved word;
+checks the dense transpose and every signed native map; replays the complete
+physical caller; and checks two exact interval engines, charged tail completion,
+compiler conditions and all 58 outer predicates. Five controls reject a false
+split prefix, missing initial/final basis changes, unearned targets and unpaid
+transport. Compressed outputs are compared by complete decompressed payload.
+
+The retained PR5599 pricing code changes only five declarations: the claimed
+and tested endpoints, comparison endpoint, complete target/call counts, reported
+decimal and predecessor key. [LITERAL-CHANGES.diff](LITERAL-CHANGES.diff) records
+them. In particular, its completion decay 39/40 and compiler logarithm power
+1024 are preserved; the older power 1000 is not reused.
+
+## Limits and ceiling
+
+The five framework assumptions remain: native all-column implementation,
+owned erasure, uniform compiler closure, precision and fixed-tape costs, and
+analytic recovery. The source helper-endpoint contract remains inherited.
+Neither a complete rounded multiplier nor the enormous uniform word is
+materialized. Exact finite replay is not proof-kernel verification or selected
+frontier admission.
+
+The signed moment for this fixed invoice is strictly decreasing on [0,0.0034].
+Its raw funding ceiling is the crossing above, leaving between 2.54783e-9 and
+2.54784e-9 above the claimed endpoint. This is not a ceiling for other words,
+helper bases, inventories or compiler choices.
+
+## Sources, scope and credit
+
+Canonical main base: `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision 7.
+The assigned scalar-to-moment task is refined to a fully charged composition
+of changed public dependencies, contacts and independent target splits.
+
+Pinned sources are Ali Romman's PR5580 at
+`6efa248cf456d6101d757e9d09ba29711d18a13a` and PR5599 at
+`0644592d421b375c221045954fdf13932575ffa8`; Pierre-Loic Doulcet (@hexapode)'s
+PR5565 at `9af814164b9dfc21f19ec737959d67cb71488c95`; and flyingviper's PR5605 at
+`4a57d245ac3918ccc9947a867ece24573605e243`. Retained source files are unchanged.
+Source retention commits make their bytes reachable without unmerged-object
+caches. Exact source paths, Git blobs and SHA256 values are in SOURCES.json.
+
+Further credit follows those sources: Joel Pulikkan/GamingPuzzled for the
+helper-706 and successor handoffs; DreamingOfClouds for free endpoints and
+event-level tools; thu-nmrc for coupled contacts; Ali Romman for the complete
+caller and source closure; Gareth Davidson, David Arias and Cinna Davis for
+P104 word, coalescing and private reuse; Cinna Davis for the controller;
+Jacob Alan Sussman for productive recursion; zxv and Cao Yifan for interval,
+compiler and native machinery; and all retained geometry, BIT and analytic
+notices. The elementary basis identity is credited, not claimed as new.
+
+New composition and verification prepared for flyingviper with substantial
+OpenAI Codex assistance and independent agents. Separate agents derived the
+composition, audited its algebraic hazards and reviewed the source/price checks.
+No independent human review is claimed. Apache-2.0.
+
+## Open next questions
+
+Can a different legal cut recover productive credit after the cascade removes
+the old line contacts? Begin with exact prefix/suffix subspaces at a changed
+common chart, not a root search. A new split must introduce an independent input,
+retain a valid endpoint and fund its added completion/ordinary costs.
+
+Can another dirty relay alter the remaining owned consumers? First establish
+the live-input endpoint identity, then an invertible correction and charged
+cleanup. The simple free zero-frame correction lemma for the original 735-input
+word must not be assumed for newly split successors that start at positive
+frames. See structured questions in [TASK.json](TASK.json).