Conditional kappa 0.00310299 (+1.15e-6 over #5608): delayed shared P104 preparation

research/p104-delayed-shared-relay/COMPOSITION.md

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+# Composition and ownership accounting
+
+Start from PR5608's authenticated parent construction: the shared587 relay with
+the PR5565 commuting cascade. Apply the source-pinned delayed696 construction
+before splitting. Every735-input endpoint and chart must agree, with exact
+paid change `H4+H7-H5-H6` and unchanged target histogram.
+
+The13 retained PR5608 helper split witnesses keep the same rational vectors,
+pivots, charts and rank declarations. Only event cuts move. PR5599's retained
+split checker recomputes every full prefix functional and suffix direction
+before each application, and all independent endpoints are replayed after each
+split. This is essential: an old endpoint proof alone does not authenticate a
+new intermediate cut.
+
+Next apply the four exact declarations from PR5601. Three scalar contacts move
+to the declared common charts and helper307's endpoint changes from rank5 to4.
+The unique-contact adapter rebuilds only affected public MOVE segments. Full
+replay verifies the paid delta `-2H2+2H3-2H4+H5` and target delta `H4-H5`.
+
+Finally apply Scratch-net's PR5606 preparation to the retained rank-two prefix573.
+At its two actual destination charts, exact current-value identities are
+
+`current573-current572+2current732 = -2 original573`,
+
+`current573-current572-2current710 = -2 original573`.
+
+The verifier derives these identities over all748 source inputs before removing
+the573 coordinate. Preparing that role at zero makes each value reconstructible
+by coframed COPY/ADD operations. Its two H1 transports disappear, and its H2
+productive target is debited. The independent rank-seven successor is retained.
+The573 slot is now an owned role, with explicit initialization, reset and final
+return. It is not simultaneously credited as an independent input.
+
+The resulting interface has747 independent inputs and nine owned roles in756
+slots. There are11 owned lifetimes and peak occupancy two. The exact checker
+validates every field, frame, owned lifetime and final row, including arbitrary
+initial dirty-owned coordinates and every required zero return. Native evaluation
+checks every remaining paid map and source endpoint normalization; the retired
+H2 target and its two external normalizers are then explicitly removed, matching
+PR5606's declared accounting contract.
+
+Relative to PR5608, the complete local changes are
+
+`Delta paid = -2H1-2H2+2H3-H4-H6+H7`,
+
+`Delta targets = -H2+H4-H5`.
+
+The full caller invokes these changes18 times. The complete bill is66,636 paid
+calls and13,030 targets with surplus760. It includes all queries, whole idles,
+main adapters, helper normalization, ordinary scalar work and routes. The
+owned-lifetime count and peak are actual replay outputs, not inherited literals.
+
+The primary exact interval engine encloses the raw crossing, and an independent
+engine checks overlap and positive funding at0.0031029905. Completion, compiler
+and all58 outer predicates are checked with the retained power1024 parameters.
+The claimed conditional endpoint is0.00310299. The inherited theorem assumptions
+and unmaterialized uniform word remain stated in README.md.
+
+Prepared for flyingviper with substantial OpenAI Codex assistance and independent
+agents, retaining the predecessor attribution. Apache-2.0.

research/p104-delayed-shared-relay/MECHANISM.md

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+# Delaying public preparation through a shared component
+
+This construction continues the verified shared587 relay and148 contraction.
+Its source is `contracted-587-relay-WORD.json`, with canonical sorted-key JSON
+SHA256 `95078b95bae0c56927f6daaa4430457cc43862c24a9db3b015bb1366e3381055`.
+The underlying frozen word is PR5580, head
+`6efa248cf456d6101d757e9d09ba29711d18a13a`.
+
+This note proves the new component. The package verifier separately checks the
+composed word, complete native/caller/ordinary bill and analytic predicates.
+
+## The changed preparation
+
+Write `P` for the public133 value copied into owned738. At its final line597,
+public734 contains `x734-P/2`. All `x` variables below are arbitrary original
+inputs; none is assumed zero.
+
+At frame1031, before the relevant producer preparation, let the current public
+values699,701,702,703 be `a,b,c,d`. The original preparation forms
+
+* `696 = x696-a+b+c`;
+* `700 = x700-b-c`, later updated to `700-d`.
+
+The opposite coefficients of `b+c` permit a useful retiming. Public700 retains
+that component after701 and702 have ascended and after `P` has become available.
+Consequently696 need not ascend early just to read701 and702 separately.
+
+After the last original zero-frame read of696, add `x700-x734` to696 while
+all three fields remain at frame3. Delete its original ascent3-to1031 and
+the original three additions from699,701,702. Immediately after734 receives
+the owned value at597, perform
+
+1. `MOVE 696,3,597`; `ADD 696,734,+1`;
+2. `MOVE 696,597,1031`;
+3. `ADD 696,699,-1`; `ADD 696,700,-1`.
+
+The resulting value is exactly the original696 value minus `P/2`:
+
+`x696+x700-x734 + (x734-P/2) - a - (x700-b-c)`.
+
+The changed itinerary uses existing frames. The two new ascent ranks are1
+and4, replacing the original rank5.
+
+## Coupling the two later butterfly inputs
+
+At this point, still before the original `700 -= 703` update, define
+
+`S = current696 + current700 + current699 = Z-P/2`,
+`Z = x696+x700`.
+
+Add `S` into703 using three ordinary ADDs. Then add the same old `S` into700
+using `SCALE 700,2`, `ADD 700,696,+1`, and `ADD 700,699,+1`. The subsequent
+unchanged `700 -= 703` update cancels700's entire added quantity.
+
+Thus the later696/703 butterfly receives perturbations `-P/2` and `Z-P/2`
+in its two inputs. Its sum delivered to159 changes by `Z-P`. Its complementary
+output delivered to222 changes by `-Z`. All other live-input effects cancel.
+
+Delete the remaining owned738 read into159. That read originally added
+`P/2`, later scaled by159's factor `-2`, so deleting it adds `P` to the final159
+value. Combining the deletion with the changed butterfly leaves only
+
+`out159 += Z`, `out222 -= Z`
+
+on outputs whose final frames have dimension below nine.
+
+Four initial common-zero-frame ADDs cancel these nuisance terms: subtract
+both `x696` and `x700` from159, and add both into222. These are distinct
+source and destination coordinates. Exact arbitrary-input replay verifies
+the cancellation; it does not rely on clean helper inputs.
+
+Owned738 now goes directly from591 to597, a rank7 descent. The intermediate
+rank7 frame565 and its scalar contact are removed.
+
+## Full-frame cleanup
+
+Immediately before the original `ADD 133,288,1/2` at full frame127, exactly
+five public rows still differ. Let `L=Z-P/2`. Their errors are
+
+| Role | Error |
+| --- | --- |
+|696|`-P/2`|
+|697|`L`|
+|698|`-L`|
+|700|`L`|
+|703|`L`|
+
+At this cut, the actual current rows satisfy
+
+`133=P`, `696=x696-P/2`, `700=x696+2*x700-P/2`,
+
+so `L=(current696+current700)/2`. All six involved rows are at127. First
+subtract half of each carrier696 and700 from697 and703; add half of each
+to698. Next scale700 by1/2 and subtract696/2, restoring `x700`. Finally add
+133/2 to696, restoring `x696`. These nine operations restore every row
+before the unchanged suffix. Source identities and operation ordering are
+checked over all735 original-input columns.
+
+## Invoice and exact verification
+
+The public preparation replaces `H5` by `H1+H4`. Removing the last owned
+contact replaces `H1+H6` by `H7`. The net paid change relative to the
+shared587 candidate is therefore
+
+`H4 + H7 - H5 - H6`.
+
+For `H_r=r^t`, `0<t<1`, strict concavity gives
+`H7-H6 < H5-H4`, so this change is strictly negative throughout that
+range. This comparison is a transport statement, not by itself a new
+complete multiplication bound.
+
+The source-pinned `delayed.py` implements the component for either the
+published PR5605 word or its commuting-cascade parent. It accepts only their
+exact canonical payload hashes and checks the resulting full payload hash.
+The standalone component has25187 events and adds18 ADDs and two SCALEs,
+with no net MOVE-count change or new register. The full composition is described
+in COMPOSITION.md and verified separately on every independent input.
+
+Prepared for flyingviper with substantial OpenAI Codex assistance and independent
+agent derivations. Retained source lineage and licenses are credited in README.md.
+Apache-2.0.

research/p104-delayed-shared-relay/PRICING-CHANGES.diff

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+--- PR5606/pricing.py
++++ delayed-shared-relay/pricing.py
+@@ -12,8 +12,8 @@
+ from fractions import Fraction as Q
+ import local as L
+
+-KAPPA, TESTED = Q('.00309871'), Q('.0030987101')
+-PREVIOUS = Q('.00309839')
++KAPPA, TESTED = Q('.00310299'), Q('.0031029905')
++PREVIOUS = Q('.00310184')
+
+
+ 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()) == 13066 and sum(paid.values()) == 66816, 'Complete field and call counts')
++    L.need(sum(targets.values()) == 13030 and sum(paid.values()) == 66636, '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':'.00309871','previous_open_pr5599':PREVIOUS,'gain':KAPPA-PREVIOUS,
++    return encode({'kappa':KAPPA,'kappa_decimal':'.00310299','previous_open_pr5608':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-delayed-shared-relay/PRICING-EDITS.json

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+[
+  [
+    "KAPPA, TESTED = Q('.00309871'), Q('.0030987101')",
+    "KAPPA, TESTED = Q('.00310299'), Q('.0031029905')"
+  ],
+  [
+    "PREVIOUS = Q('.00309839')",
+    "PREVIOUS = Q('.00310184')"
+  ],
+  [
+    "sum(targets.values()) == 13066 and sum(paid.values()) == 66816",
+    "sum(targets.values()) == 13030 and sum(paid.values()) == 66636"
+  ],
+  [
+    "'kappa_decimal':'.00309871'",
+    "'kappa_decimal':'.00310299'"
+  ],
+  [
+    "previous_open_pr5599",
+    "previous_open_pr5608"
+  ]
+]

research/p104-delayed-shared-relay/README.md

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+# Conditional kappa 0.00310299 from delayed shared preparation
+
+This construction raises complete conditional kappa from **0.00310184** in
+[PR #5608](https://github.com/CrocSwap/integer-mult-bounds/pull/5608) to
+**0.00310299**, a gain of **0.00000115**. Its new mechanism delays the
+preparation of public helper696 by reusing a complementary component already
+present in helper700. Coupled corrections remove the remaining owned738
+delivery into159. Every retained independent helper input is preserved exactly.
+
+The new mechanism has paid delta `H4+H7-H5-H6`, strictly negative for
+`Hr=r^t`, `0<t<1`. It is composed with the existing 13 independent helper
+splits, Ali Romman's coupled-frame step from
+[PR #5601](https://github.com/CrocSwap/integer-mult-bounds/pull/5601), and
+Scratch-net's prepared split-helper retirement from
+[PR #5606](https://github.com/CrocSwap/integer-mult-bounds/pull/5606).
+Those contributions and their costs are explicit, not attributed to this work.
+
+The exact raw crossing is **(0.00310299359333,0.00310299359334)**; the claim
+is tested at 0.0031029905. The full bill has **66,636 paid calls, 13,030
+independent productive targets and rank surplus760**. The final word has
+**747 independent inputs, 539 helpers, nine owned roles, 11 owned lifetimes,
+peak owned occupancy two and 25,529 events**. Every added ordinary operation,
+owned lifetime, route and target debit enters the complete accounting.
+
+Read [MECHANISM.md](MECHANISM.md) for the new delayed preparation,
+[COMPOSITION.md](COMPOSITION.md) for the full construction, and
+[RESULT.json](RESULT.json) for the exact native/caller/price receipt.
+The selected frontier is unchanged. These are finite exact checks and a
+conditional bound calculation, not independent human or proof-kernel acceptance.
+
+## Reproduce
+
+Python3.12 and the standard library suffice:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-delayed-shared-relay
+```
+
+Normal and optimized modes print `PASS_P104_DELAYED_SHARED_RELAY_KAPPA_00310299`;
+the launcher prints `PASS_REGISTERED_RESEARCH_PACKAGE`. Verification authenticates
+the official 24-file PR5608 export and its nested unchanged33-file framework
+closure before importing code. It reconstructs every stage, checks all13 fresh
+prefix/suffix witnesses and every intermediate independent-input identity,
+checks all756 final rows and transpose columns, all signed native maps, the
+physical caller, complete paid/target bill, two interval engines at the tested
+endpoint, the compiler and58 outer predicates. Five controls reject missing
+owned initialization/return, missing new cleanup, a falsely retained target
+and an uncharged transport. Gzip equality uses complete decompressed payloads.
+
+The checker adaptation from PR5606 changes the explicit interface constants
+750/758/749 to748/756/747, inlines the same exception helper and selects MOVE
+direction by validated ownership. The verifier compares the remaining checker
+body exactly to its pinned source. The retired573 role has no MOVE in the
+submitted word. The [pricing diff](PRICING-CHANGES.diff) retains the source's
+mathematical tests; only endpoint/comparison/count declarations change.
+
+## Limits and ceiling
+
+The five inherited framework assumptions remain: native all-column implementation,
+owned erasure, uniform compiler closure, precision and fixed-tape costs, and
+analytic recovery. The inherited helper-endpoint contract remains. The enormous
+uniform word and complete rounded multiplier are not materialized.
+The prepared-helper step uses the existing owned-erasure contract explicitly;
+it does not count the retired prefix as an independent productive target.
+
+The fixed invoice has a strictly decreasing signed moment on[0,0.0034].
+Its raw funding ceiling is the interval above, leaving between3.59333e-9 and
+3.59334e-9 above the claimed endpoint. This is not an optimum over other words,
+inventories or suppliers. The uniform compiler retains logarithm power1024,
+tail decay39/40 and the full reserve/outer conditions.
+
+## Sources, independent checks and credit
+
+Base: canonical main `5e0052ca0aa3036a3afa8b0438927377c8d97d53`, priority revision7.
+The final upstream refresh reached `d7633ce230196a1d5d061347de7a0fd8be512ed6`;
+the guidance, priority catalogue and selected record were unchanged. That update
+archived predecessor research; archival intake does not change scientific acceptance.
+The assigned scalar-to-moment task is refined to changed public dependencies
+and composition with independently introduced target and ownership changes.
+Source pins and retention history are in[SOURCES.json](SOURCES.json).
+
+PR5608 is pinned at `5ec3b5b3ee4738f896e823c1dfc04e7ff1789ffb`; PR5601 at
+`8f7e870b22885a367b347dc12791da98fd53f83d`; PR5606 at
+`cd7d89345c6c5d2114625e5ce912a52ecd5e1d27`. The PR5608 export retains exact
+PR5580, PR5565, PR5599 and PR5605 source files and their original notices.
+No foreign branch-object cache is required for replay.
+
+Credit Ali Romman for the independent split identity, frame step, source word
+and native/caller/price machinery; Pierre-Loic Doulcet/hexapode for the commuting
+cascade; Scratch-net for prepared573; Joel Pulikkan/GamingPuzzled for successor
+handoffs; DreamingOfClouds for free endpoints and event-level tools; thu-nmrc
+for coupled contacts; Gareth Davidson, David Arias, Cinna Davis, Jacob Alan
+Sussman, zxv, Cao Yifan and all retained geometry, BIT and analytic predecessors.
+The new delayed696 P104 construction, composition and verification were prepared
+for flyingviper with substantial OpenAI Codex assistance. Independent agents
+derived and checked the current-value identities, ordered cleanup, split
+compatibility, prepared ownership and complete invoice. These are separate
+agent calculations, not independent human review. Apache-2.0.
+
+## Open next questions
+
+For another owned delivery, identify complementary early public expressions
+that persist until its signal is available. First derive an exact current-value
+identity and the live-input endpoint effect; only then construct invertible
+nuisance corrections and charge its full itinerary.
+
+A separate opportunity is another prepared split prefix: at each of its paid
+MOVEs, test whether its current row can be reconstructed from already coframed
+public rows modulo that prefix's own independent input. Every reconstruction,
+owned lifetime and retired target must be charged. No further prefix candidate
+is claimed here. Structured next questions are in[TASK.json](TASK.json).