[unpaidmoon]

Change and mathematical scope

Scoped partial obstruction. No new κ and no selected-frontier change. Selected κ stays 781451/250000000.

In the restored binary singleton model, 28 <= f(8) <= 32 is unchanged. For a closed eight-source word of length 30:

• Every admissible multiplicity vector has a coordinate of multiplicity 2. There are 1016 labeled vectors in {2,4,6}^8 summing to 30, in four shapes.
• If the open sojourn of that coordinate uses at most two other sources, the word is not universal. The layer-0 projection would need at least 32 points and has at most 29 slots.
• If the open sojourn uses exactly three other sources, the layer-0 projection has at least 17 points. Equality at 16 would be a vectorial bent map F_2^4 → F_2^3. The census finds 896 bent Boolean functions on four bits and no 3-dimensional bent family.
• No prefix set of size 30 contained in a direct sum of two 4-dimensional subspaces covers F_2^8. Prefix sets contain 0, and every covering subset of such a union that contains 0 has at least 31 points.

An explicit legal word of length 30 has coverage 255 and misses only mask 131. Its three multiplicity-2 sojourns have ranks 6, 4 and 7, so the near-miss is outside the excluded region. This is not a proof that coverage 256 is impossible. Length 28 is not treated. The length-32 Gray concatenation remains a universal upper example.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a.

Session r109, item 2 of the handoff-first list. The item is discussion #1166 comment 19377982 (Nick Petalas): the length-30 eight-source singleton search failure, with the coordinate-split next step. The claim on that comment is released.

Card connector-alphabet-change, priority revision 8. Scope status: changed. The card asks for one new connector operation. This package stays in the published singleton alphabet. The card's scope-change trigger is keeping the alphabet and only increasing the source count. The length-30 gap can change the connector query bill without a new call.

Ordered eligible list used for selection:

1. Three signed added frames at seven calls (comments 19377832 updating 19377345).
2. This package. Eight-source singleton connector at length 30 (comment 19377982).
3. Six-source depth-two block at c = 7 (comment 19384981).
4. Complex helpers (p104-side-correction, coverage-law-change).
5. BIT (bit-helper-contract).
6. New decoders and interfaces.
7. Supplier audit (supplier-boundary-audit).
8. All-size audit (uniform-transfer-audit).
9. Verification tooling (replay-runtime).
10. bit-new-register-model.

Nearest work:

• Research: exact seven-source singleton minimum f(7) = 24 #3058 leaves the eight-source question open and proves f(7)=24, cited and not replayed.
• Prove an eight-source singleton floor of 28 calls (no new κ) #5234 / research/eight-source-singleton-floor proves 28 <= f(8) <= 32 and the length-28 multiplicity shape. This package does not revisit length 28 or the 538-query batch bound.
• Research: projection matching obstruction for eight-source singleton lifts (partial result) #5430 / research/eight-source-lift-obstruction excludes one fixed 24-step projection. The sojourn split is a different question and does not reuse that matching obstruction.
• Research: six-source universal dirty-connector boundary, f(6)=16 (no new kappa) #1185 supplies the length-32 Gray upper bound, checked here as a positive control.
• Comment 19377982 reports an unpublished anneal with best score 255 and no exclusion. This package does not replay that search. It proves the low-rank and 4+4 restrictions and checks one explicit coverage-255 word.
• Open-PR search on 2026-11-09 found no length-30 eight-source sojourn PR. Overlap cache: open PRs fetched 2026-11-09T13:44:12Z (883 records, complete pagination); discussions fetched 2026-11-09T13:45:19Z (6926 records). Local head inventory at 7c49fe32 was complete. Fork cursor/* branches were listed before push; none was this topic. Closed PRs are covered only through local notes and the ledger, not a full closed-PR body search.

Validation

CPython 3.12, standard library, from the repository root:

python3 -B research/length30-singleton-sojourn/verify.py
python3 -O -B research/length30-singleton-sojourn/verify.py
python3 -B scripts/research_package.py --package research/length30-singleton-sojourn
python3 -B scripts/check_research_commit.py --package research/length30-singleton-sojourn --check-source-history
python3 -B scripts/research_selected_baseline.py

Observed:

• PASS_LENGTH30_SINGLETON_SOJOURN counts=1016 bent=896 gray=32 witness_coverage=255
• PASS_REGISTERED_RESEARCH_PACKAGE research/length30-singleton-sojourn outcome=partial
• PASS_RESEARCH_COMMIT_BYTES at c1cf726df3a06e50ef655ae91e8c8aac942b19a7, source pin 7c49fe32c55de02c2c873655c804b16e4c3fef0a
• PASS_RESEARCH_BASELINE_BINDINGS_ONLY (bindings only, not a scientific replay)

The bent census enumerates all 2^16 truth tables. The 4+4 check covers the coordinate union and one sheared union: every 30-point subset that keeps zero fails, and deleting zero covers but is not a prefix set. A swapped first pair on the witness is a failure control. f(7)=24 was not replayed. No SAT search of the remaining rank-at-least-3 words, no Lean, no Docker, and no frontier6030-verify.

Credit

Ross Richardson, #943, for the singleton model and prefix criterion. Douglas Colkitt, #1185, for the length-32 construction. conorholds, #3058, for f(7)=24 and the eight-source question. Nick Petalas, #5234 and discussion comment 19377982, for the deletion floor and the length-30 handoff, including the layer-split next step. Nicholas Stone, #5430, for the fixed-projection lift obstruction that this split does not reuse.

Prepared by unpaidmoon with substantial Cursor Grok assistance. New work is Apache-2.0. Independent human and proof-kernel review are unclaimed.

Open next questions

1. Does a universal length-30 word exist when every multiplicity-2 sojourn uses at least three other sources, and at least 17 layer-0 projections if it uses three? A yes answer lowers the upper bound on f(8) from 32 to 30. The recorded witness shows coverage 255 is attainable, so there is no one-mask counting contradiction yet. First step: fix one multiplicity-2 source and search the two seven-source arcs whose layers meet the sumset split.
2. Does a universal length-28 word with multiplicities (4,4,4,4,4,4,2,2) exist? That is the sharpness question of Prove an eight-source singleton floor of 28 calls (no new κ) #5234 and is not decided here.

Workflow feedback

The coordinate split suggested in comment 19377982 separates a short coset obstruction from the remaining word search. No further session report.