Conditional kappa 0.00310440 (+1.41e-6 over #5612): compose the paid helper boundary

research/p104-delayed-basis/PRICING-CHANGES.diff

@@ -0,0 +1,31 @@
+--- PR5612/pricing.py
++++ pricing.py
+@@ -12,8 +12,8 @@
+ from fractions import Fraction as Q
+ import local as L
+
+-KAPPA, TESTED = Q('.00310299'), Q('.0031029905')
+-PREVIOUS = Q('.00310184')
++KAPPA, TESTED = Q('.00310440'), Q('.0031044005')
++PREVIOUS = Q('.00310299')
+
+
+ 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()) == 13030 and sum(paid.values()) == 66636, 'Complete field and call counts')
++    L.need(sum(targets.values()) == 13030 and sum(paid.values()) == 66618, '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':'.00310299','previous_open_pr5608':PREVIOUS,'gain':KAPPA-PREVIOUS,
++    return encode({'kappa':KAPPA,'kappa_decimal':'.00310440','previous_open_pr5612':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-basis/PRICING-EDITS.json

@@ -0,0 +1,22 @@
+[
+  [
+    "KAPPA, TESTED = Q('.00310299'), Q('.0031029905')",
+    "KAPPA, TESTED = Q('.00310440'), Q('.0031044005')"
+  ],
+  [
+    "PREVIOUS = Q('.00310184')",
+    "PREVIOUS = Q('.00310299')"
+  ],
+  [
+    "sum(paid.values()) == 66636",
+    "sum(paid.values()) == 66618"
+  ],
+  [
+    "'kappa_decimal':'.00310299'",
+    "'kappa_decimal':'.00310440'"
+  ],
+  [
+    "previous_open_pr5608",
+    "previous_open_pr5612"
+  ]
+]

research/p104-delayed-basis/PROOF.md

@@ -0,0 +1,44 @@
+# Helper341 boundary composition
+
+This composes Ali Romman's PR5602 identity, pinned at
+`6c224aa720203c4f4615e6538d8038a275387db8`, with the published delayed/prepared
+word. The source canonical SHA256 is
+`df44a24231edd04954ebf066b1efb311441e5d9d48b64d03e555cbea087b25c6`.
+This is a checked composition, not a new basis identity.
+
+Immediately after the source's last read of341, event11285,
+`ADD346,341,+1` at frame240, exact rational replay gives
+
+`current341 - 2*current337 = x341 - 2*x93 - 2*x339 + 2*x351`.
+
+Both current rows are at240. Initially93,339,341,351 are all at frame3.
+Precompose the word with the three ordinary ADDs implementing
+
+`x341 <- x341 + 2*x93 + 2*x339 - 2*x351`.
+
+The update is invertible and does not change its source coordinates.
+The original endpoint column of input341 is the unit helper341 column, so
+this precomposition changes no other final output. After the last341 read,
+subtract twice337 from341. The displayed relation now gives exactly the
+original independent input `x341`.
+
+There are no later reads of341. Its remaining eight destination operations,
+including its rank5 ascent240-to127, can therefore be removed, and its final
+frame declared240. All other operations remain unchanged. No new input,
+temporary, owned lifetime, or zeroing operation is introduced.
+
+The exact paid change is `-H5`. Helper341's productive target changes from
+rank9 to rank4, giving target change `H4-H9`. Thus the signed funding gain
+is `H4+H5-H9`, strictly positive for `H_r=r^t`, `0<t<1`. The target debit is
+essential; counting only the removed paid transport would overstate the gain.
+
+The separate independent agent calculation checked all756 original
+input columns, all756 endpoint rows, every common frame and ownership
+transition, and the unchanged INIT/CLEAR/COPY sequence. It confirms747
+independent inputs,11 owned lifetimes, and peak2. Candidate canonical SHA256:
+`22aa2b59ed2900dbd7ed6060586422cc6e72927cf7045727b68ec1b0b24b4209`.
+The package verify.py separately checks native, caller, ordinary-cost and compiler obligations and records the full result in RESULT.json.
+
+Independent audit prepared for flyingviper with substantial OpenAI Codex
+assistance. Retain Ali Romman's PR5602 attribution and the composed sources'
+notices. Apache-2.0.

research/p104-delayed-basis/README.md

@@ -0,0 +1,96 @@
+# Conditional kappa 0.00310440 by composing a paid boundary change
+
+This composes Ali Romman's helper341 boundary identity from [PR #5602](https://github.com/CrocSwap/integer-mult-bounds/pull/5602)
+with the delayed/prepared construction in [PR #5612](https://github.com/CrocSwap/integer-mult-bounds/pull/5612).
+The complete conditional endpoint increases from **0.00310299 to 0.00310440**,
+a gain of **0.00000141**. The basis identity is credited to its author;
+this contribution verifies that it survives the intervening shared relays,
+changed contacts, independent splits and owned preparation.
+
+Three initial coframed ADDs and one final coframed correction replace eight
+operations on helper341. Its last rank5 transport disappears, and its
+productive target changes from rank9 to rank4. The local funding gain is
+`H4+H5-H9`, where `Hr=r^(1-kappa)`. The complete gain is18 times that expression.
+The target debit is included; the removed transport alone is not the gain.
+
+The exact raw crossing is **(0.00310440547057,0.00310440547058)**, tested at
+0.0031044005. The full invoice has **66,618 paid calls,13,030 productive
+targets and rank surplus760**. The word has25,525 events,747 independent
+inputs,539 helpers,nine owned roles,11 owned lifetimes and peak occupancy two.
+No independent input or owned lifetime is added. Every retained input is
+preserved exactly, and every owned role returns zero.
+
+Read [PROOF.md](PROOF.md), [the pinned witness](WITNESS.json), [the small constructor](construct.py)
+and [the complete receipt](RESULT.json). The specialized constructor must agree
+exactly with the unchanged published PR5602 constructor on this new source.
+Only the causal cut index changes, from11151 to11285; the boundary covectors,
+helper identity and chart remain exactly the same.
+
+## Reproduce
+
+Python3.12 and its standard library suffice:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-delayed-basis
+```
+
+Both registered modes print `PASS_P104_DELAYED_BASIS_KAPPA_00310440`.
+The launcher prints `PASS_REGISTERED_RESEARCH_PACKAGE`. Replay authenticates the
+official24-file PR5612 export, its retained PR5608 export and33-file framework;
+checks the exact published witness, two complete constructions, all756 endpoint
+rows and dense transpose columns, every signed native map, the full physical
+caller, complete invoice and ordinary charges, two interval engines at the
+tested endpoint, the compiler and58 outer predicates. Five controls reject
+missing input correction, missing cut correction, missing owned initialization,
+old target credit and an unpaid transport. Complete decompressed candidate
+payloads are compared; compressed source archives remain byte-pinned.
+
+The inherited prepared checker is reused unchanged and checked against its
+retained source adaptation. [PRICING-EDITS.json](PRICING-EDITS.json) and
+[PRICING-CHANGES.diff](PRICING-CHANGES.diff) declare the only five price changes:
+endpoint, comparator, paid count, output decimal and comparator label.
+The original mathematical inequalities and compiler reserves remain unchanged.
+
+## Scope and ceiling
+
+The five inherited framework assumptions remain: native all-column realization,
+owned erasure, uniform compiler closure, precision and fixed-tape costs, and
+analytic recovery. The helper-endpoint contract remains. The enormous uniform
+word and complete rounded multiplier are not materialized. No independent
+human or proof-kernel acceptance is claimed, and the selected record is unchanged.
+
+The signed moment is strictly decreasing on[0,0.0034]. The fixed-invoice raw
+ceiling is the interval above, leaving5.47057e-9 to5.47058e-9 above the claimed
+endpoint. This is not an optimum over other constructions. Logarithm power1024,
+tail decay39/40 and the complete outer/ordinary conditions are retained.
+
+## Sources and independent checks
+
+Base: canonical main `d7633ce230196a1d5d061347de7a0fd8be512ed6`, priority revision7.
+PR5612 is pinned at `faa9f6dbe6b8cc4a996d3edeca71823056453e1a`;
+PR5602 at `6c224aa720203c4f4615e6538d8038a275387db8`. Exact archives,
+source files, hashes and original notices are retained through[SOURCES.json](SOURCES.json).
+Replay requires no foreign Git objects, network or local workspace files.
+
+Two independent agents checked the compatibility: one derived the causal
+witness and compared complete histograms; another implemented separate exact
+scalar/frame/ownership replay over all756 original columns and checked the
+ordered basis updates. This is agent verification, not independent human review.
+
+Credit Ali Romman for PR5602's identity and constructor, independent splits,
+frame changes and native/caller/price machinery; Scratch-net for prepared573;
+Pierre-Loic Doulcet/hexapode for commuting contacts; flyingviper for shared and
+delayed relays; Joel Pulikkan/GamingPuzzled, DreamingOfClouds, thu-nmrc,
+Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan
+and all retained geometry, BIT and analytic contributors. This composition
+and verification were prepared for flyingviper with substantial OpenAI Codex
+assistance and independent agents. Apache-2.0.
+
+## Open next questions
+
+Can a changed independent split cut make another published boundary identity
+compatible without losing more target credit than it saves? First derive a
+current-value relation after the helper's last source read; preserve its full
+arbitrary-input boundary basis and debit every changed productive rank.
+The other five PR5602 witnesses are not claimed compatible here. Structured
+questions and the assignment refinement are in[TASK.json](TASK.json).