Repository navigation
Conditional κ = 0.001734846264120199151475 (+0.00176%): hosted remainders as receivers on #3251, complex passes R438 again - #3934
Draft
rohanarun wants to merge 8 commits into
Conversation
…inder donors on PR3148's T740 fill Idle remainders of partially used bins donate axes, under PR1252's commuting rule, to unhosted idle children of the same replica and port (cap 51), followed by PR3184's stars. 391,964 axis moves; complex root 0.00173477055711151316 exceeds the PR589 bit saving, so kappa is bit-capped: +3.238e-6 over PR3184. Independent verifier with eight rejected controls; native admission and outer release with the overlay not rerun. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…RIFY schema, open questions, read-only verifier Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…h PR3190's idle-remainder donors PR3190 pushed the complex root (0.0017347705571115131604951) past the PR589 bit saving. The R438 bit supplier natively replayed on main (0.001734846264120199151475) is above it, so the complex side binds again: +1.3435e-6 over PR3190. Independent re-derivation of both endpoints and the composed kappa; 3 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…e on PR3198 (R438 bit) Adds a third phase of single-axis PR1252-rule moves between unhosted idle children to PR3190's remainder donors and PR3184's stars: 430,164 moves, complex root 0.0017348070217261275520343, still below the R438 bit endpoint. +3.646e-8 over PR3198. Independent verifier re-derives the moves, the complex bracket and the R438 endpoint; 8 controls rejected. Done with help from OpenCode (Space bunny free). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
…34815770385098563484 Idea credit: OpenCode (Space bunny free) - exact search within each replica/port group instead of PR3200's greedy phase 1, scored by the final group cost after phases 2/3. +8.7487e-9 over PR3200; complex binds. PR3200's independent verifier passes (8/8 controls), deterministic build. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
Fixes the registered-package replay check (README.md needs an "## Open next questions" section). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
…pen questions actual_scope/evidence were inherited from PR3200 (greedy phase, 430,164 moves); now describe the exact search and 435,604 moves. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F5n4jqR72j3QDY71gGBVb1
…mainders as receivers on PR3251 After PR3251's exact idle-donor search, idle-remainder axes may also move into the remainder of another partially hosted bin of the same (replica, port) when they commute with its full recipe frame and the PR1252 translations. 437,978 moves; complex root 0.0017348651784727109982331 passes the R438 bit endpoint, so kappa reaches R438 (+0.00176% over PR3251). Independent verifier with nine rejected controls; native admission and outer release not rerun. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy
This was referenced Oct 19, 2026
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Conditional κ =
0.001734846264120199151475 − 10⁻⁴⁶ − 10⁻⁷⁰, +0.00176% over #3251 (0.001734815770385098563484). This takes the whole remaining window to the R438 bit endpoint. Draft: full verification is running.Change
After #3251, 149,514 rank-1 idle remainders remain:
Relaying through an unhosted child was tested and found nothing legal.
New in this PR is a fifth phase: an idle-remainder axis may move into the remainder of another partially hosted bin in the same (replica, port). The axis must commute with that bin's full recipe frame (hosted prefix plus remainder), with all stage X/Y translations and the terminal Y translation, and with both terminal translations. Receivers are capped at 51, and no child both donates and receives.
This adds 2,374 moves, 437,978 in total, mostly merging pairs of rank-1 remainders into rank-2 children. Rank mass is unchanged at
65088·740.Verification
research/rank7-idle-hosted-receivers-r438/verify.pyis #3251's independent verifier, extended for hosted receivers. It re-derives:κ = min(floor₂₄(complex), bit) − …, with the bit side binding.Nine mutation controls are rejected, including a prefix-conflicting hosted receiver.
scripts/research_package.pypasses locally under Python 3.12.Scope
This adds a new hypothesis: hosted remainders may receive axes, extending #3190's hosted-donor hypothesis. No hosted-controller argument is given.
Not rerun yet: the native admission, the overlay-aware controller audit, and the outer release.
The result is conditional on R438 (#1043 is still open) and on the full stack #3251 → #3200 → #3198 → #3190 → #3184 → #3148 → #3133.
Credits: Gonzalo-Mier (#1252), Guéorgui Maissouradze, Jeremy Diviney (#3148), dcharb78 (#3133), Marius-Paul Dumitrean (#2979), Ali Romman (#1043), Sagar Thakrar (#2423), DreamingOfClouds, eumemic, and OpenCode (Space bunny free) for ideas in the stacked predecessors. Prepared by Rohan Arun with Anthropic Claude assistance.
🤖 Generated with Claude Code
https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy