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Research: sharp four/five-source dirty-connector boundary (no new kappa) #943

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3,564 changes: 3,564 additions & 0 deletions research/universal-connector-boundary/CERTIFICATE.json
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69 changes: 69 additions & 0 deletions research/universal-connector-boundary/CLAIM.md
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# Local sprint claim

- Track: recursive interfaces. OS-random assignment seed: **52** (`secrets.randbelow(100)`).
- Exact base: `91a2094f2e022930069e8cfdc810a3ea1b81cd09`.
- Start: 2026-10-14 00:26 AEDT; intended finish: 01:11 AEDT (45 minutes).
Final 12 minutes reserved for verification and handoff.
- Object: one arbitrary dirty binary connector, fixed linear source maps B_j
and output maps A_i, with complete additive oracle calls. Determine whether
a single source-toggle schedule with two calls per source can support every
binary row pattern, then price a complete five-source boundary witness.
- Method: subset-difference characterization of paired output readouts;
explicit universal four-source word; exhaustive canonical pairings for five
source labels, with an independently implemented census and literal algebra
replay. Seed 52 selects the four/five-source boundary via 4 + (52 mod 2).
- Deliverable: scoped construction/negative result, exact certificate, full
recursive cost/storage accounting, source pins and mutation controls. No
claim of new kappa or selected-supplier integration.

## Selection and overlap

Three candidates were compared: (1) weighted dirty-echo tree scheduling,
(2) native dyadic query-pair fusion, (3) universal one-connector source paths.
The first is covered by #730/#758/#822; the second by #840. The third changes
#934's finite three-by-three target search into a source-path condition valid
for arbitrarily many output rows, and tests its first failure boundary.
This is not a rerun with a different seed or a claim of priority for dirty
commutators, common-factor fanout or carried connectors.

At assignment, all 724 open PRs were inventoried through #934. Targeted all-state
search covered connector/circle/interlacement/wheel. #889 supplies the direct
fanout predecessor; #934 supplies the exact binary query contract and support
lower bound. #929 concerns grouped rational cyclic inverses, not this binary
source-path condition. The review ledger, selected review/construction and
prior stage-count negative records were inspected; newer research PRs are
outside the ledger's frozen review inventory.

No pinned issue exists (GitHub pinnedIssues query returned an empty list), and
the only open issues are #913 and #650. Therefore this claim is local, as
requested. All delegated work is confined to this source-path boundary.

## Completed result (single claim update)

The universal four-source path is proved by complementary two-bit subspaces.
The two complete five-source censuses agree on all 945 canonical pairings:
maximum 31/32 masks, with no full-coverage ten-call path. Two explicit repairs
attain the exact 74-query minimum for the all-31-nonzero-row batch. One repair
lowers to 182 complete primitive factor calls versus 278 for column stars,
with four borrowed dirty arrays in both cases. No new kappa is claimed.

Result, exact certificate, command and validation:
[review package](https://github.com/RossRichardson/integer-mult-bounds/tree/research/universal-connector-boundary-seed52/research/universal-connector-boundary).
The focused PR is submitted from that branch to CrocSwap/main; no merge is
requested. README.md contains the mathematical statement and complete cost
recurrence; VALIDATION.md records coverage and remaining obligations.

Final submission base is `47481c89fd30a43f8f882eb4b391e89c29273fd0`, refreshed
after main incorporated PR890. Its actual selected certificate/construction/
review were read, and selected-record checks pass. This refresh changes no
contribution files outside this package. PR934's pinned head is unchanged.
The full final queue inventory reached #939, followed by an immediate check
through #941. Concurrent #938's one-source minimizer census is credited and
distinct; #940's Fourier-layout audit and #941's R439 matching improvement do
not overlap. A second pinned-issue query was also empty.

The final verification/handoff phase followed the completed constructions;
normal/optimized checks, standalone relocation, exact regeneration, six
package corruptions, the selected-record gate and its five tests pass. Only
one contribution and one PR are submitted; supplier realization and all-size
analytic obligations remain open.
88 changes: 88 additions & 0 deletions research/universal-connector-boundary/EXPECTED.json
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{
"censuses": [
{
"max_coverage": 16,
"pairings": 105,
"sources": 4
},
{
"max_coverage": 31,
"pairings": 945,
"sources": 5
}
],
"dense": {
"dimensions": [
1,
2,
3
],
"negative_controls_detected": [
"omitted_final_source",
"wrong_output_destination",
"wrong_target_row"
],
"schedules": {
"five_extra_output": {
"basis_states": 222,
"forward_cases": 297,
"inverse_cases": 297,
"map_banks": 3,
"mixed_dirty_states": 75,
"noncommuting_banks": 2,
"nonsymmetric_banks": 2
},
"five_extra_source": {
"basis_states": 222,
"forward_cases": 297,
"inverse_cases": 297,
"map_banks": 3,
"mixed_dirty_states": 75,
"noncommuting_banks": 2,
"nonsymmetric_banks": 2
},
"four_all": {
"basis_states": 120,
"forward_cases": 195,
"inverse_cases": 195,
"map_banks": 3,
"mixed_dirty_states": 75,
"noncommuting_banks": 2,
"nonsymmetric_banks": 2
}
},
"seed": 52
},
"leaf_calls": {
"five_extra_output": 182,
"five_extra_source": 200
},
"pinned_reference_files": 2,
"queries": {
"five_extra_output": 74,
"five_extra_source": 74,
"four_all": 38
},
"root_controls": [
"omitted_final_source",
"readout_crosses_source_toggle",
"unpaid_missing_row_readout",
"wrong_target_pattern",
"underpriced_scratch",
"unpaid_recursive_child",
"aliased_child_ports",
"wrong_factor_order"
],
"scalar_leaf_baseline": 180,
"star_comparators": {
"column_stars": {
"leaf_calls": 278,
"queries": 170
},
"row_stars": {
"leaf_calls": 1950,
"queries": 222
}
},
"unit_lower_bound": 74
}
201 changes: 201 additions & 0 deletions research/universal-connector-boundary/LICENSE
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# Attribution and license

Contribution by **Ross Richardson (@RossRichardson)** with substantial
**OpenAI Codex assistance** in the mathematical argument, implementation,
independent computational checks and writing. New work is Apache-2.0, under
the repository LICENSE. No independent human peer review is asserted.

The direct predecessor is Ross Richardson's PR934,
`f3100aec6ce6a7b061987875d5e9a8b93801ac0b`: carried binary connectors, the exact
query contract, support lower bound and balanced dirty recursive lowering.
Its README and NOTICE are retained byte-for-byte in references/ with Git blob
and SHA256 pins in SOURCES.json. No predecessor executable is imported.
This contribution adds the universal-source-path reduction, the explicit
four-source construction for arbitrary output count, and the complete first
five-source obstruction/repair. It does not claim priority for carried
connectors or dirty commutators.

PR889 at `e2021d1c9e06948528cbc0a8fd7079b671da981d` is the common-factor fanout
predecessor, authored by @shhxera (the pinned PR934 notice uses that handle;
the live GitHub author lookup during this sprint returned @CubeJerry).
Chafik Boukhalfa (@chafreaky), PR628 at
`0768f97d06c623b8211e651543c66135796b62bf`, supplies the dirty-product commutator
lineage. The retained PR934 notice credits additional related work.
PR730/#758/#822 concern tree/connector scratch schedules and #840 native
dyadic query fusion; their mechanisms and costs are not combined here.
PR929 at `85a1d11adbbd7610d269cfeb3e477cf7d457f2eb` groups rational cyclic
inverse factors and has a distinct contract. No claim of a general reversible
circuit optimum or literature priority is made.

Concurrent PR938 by Ross Richardson, inspected at
`df645942469e6a739ec94010a6068c398f4a6c86`, independently counts every minimum
one-source dirty-fanout word. That equality-case evidence and this multi-source
universal-path boundary are distinct; neither consumes the other's code.

The accepted frontier retains Jeremy Kothe, Chafik Boukhalfa, Hao Yan, DreamingOfClouds,
eumemic, Douglas Colkitt and the cumulative community's attribution. Their
selected construction and inherited analytic framework remain unchanged.
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