[unpaidmoon]

Change and mathematical scope

Constructive witness for two masks on one word, together with an exhaustive finite census of the realizing pairs of those masks. No new κ, and the selected frontier is unchanged.

The length-42 floor word recorded in PR #7037 misses (3, 5) and (0, 1, 3, 5). The different floor word

350122222224444444000000111111333333555555

with blocks 3, 5, 0, 1, 2^7, 4^7, 0^6, 1^6, 3^6, 5^6, realizes both. On the 903 pairs 0 ≤ s ≤ t ≤ 41, (3, 5) occurs exactly at (0, 2), (0, 30) and (1, 36), and (0, 1, 3, 5) occurs exactly at (0, 4), (0, 11) and (0, 18).

A direct prefix count explains the first of each family. If the first two letters are {3, 5} in either order and the next two are {0, 1} in either order, then q_2 = e_3 + e_5 and q_4 = e_0 + e_1 + e_3 + e_5, so (0, 2) and (0, 4) realize the two masks. The block word is one length-42 completion of the prefix 3501. The four orders are checked. That lemma is not a census of floor words.

The same predicate realizes neither mask on the #7037 witness, and neither mask on the adjacent transposition of positions 1 and 2 of that witness. The transposition check does not list that word's other masks. PR #7037 already records that the transposition has a different non-weight-3 missing set; the difference is not the appearance of these two masks.

This word is not a depth-two block. The other 61 nonzero masks were not classified. The result does not say that a six-source depth-two block exists at characteristic 7, and it does not re-prove the weight-3 bounds of PR #7016 or PR #7032. No supplier, consumer, or selected conditional κ changes. The selected record remains 781451/250000000 from PR #6030.

Evidence class: a proof of the prefix lemma under the stated initial-segment hypothesis, and an exhaustive finite census of these two masks on one named word. The domain is the 903 pairs. The enumeration visits each pair, and the visit count is checked against 42*43/2. A statement about one word is not a census of every floor word.

Task and overlap

Base commit 17469fff78c22941280f04d39dc5a1faee09c840 (upstream main, re-fetched at submission and unchanged). This fork's main is older, so the draft base is the pin branch cursor/upstream-17469fff-pin-5ae9 at that same commit. The diff is only research/six-source-c7-second-floor-masks/.

Task card connector-alphabet-change, priority revision 8. Scope status: changed. The card asks for one new connector operation. This package keeps the alphabet fixed and answers open question 1 of PR #7037. A new operation is not the missing step. The family expansion gate is not invoked.

Overlap checked 2026-11-10. find_overlap.py against open upstream PRs (339, complete pagination) and discussions (7010, complete pagination), with a complete local note inventory at the pinned main (10178 README/TASK records), returns three leads: open #7037, its FINDING comment #1166 (reply in thread), and open #7016. All three pose this question or the witness question #7037 already answered. None evaluates a second floor word for these two masks. The one-pair and two-pair weight-3 arguments of #7016 and #7032 are not repeated. The non-complement walks (10, 14) and (11, 13) are not taken.

Validation

Python 3.12, standard library only, from the repository root:

python3.12 -I -W error -B research/six-source-c7-second-floor-masks/verify.py
python3.12 -I -O -W error -B research/six-source-c7-second-floor-masks/verify.py
python3.12 -B scripts/research_package.py --package research/six-source-c7-second-floor-masks --check-only
python3.12 -B scripts/research_package.py --package research/six-source-c7-second-floor-masks

The replay commands print:

PASS_SIX_SOURCE_C7_SECOND_FLOOR_MASKS pairs=903 (3,5)=3:(0,2),(0,30),(1,36) (0,1,3,5)=3:(0,4),(0,11),(0,18) witness_both=miss transposition_both=miss lemma_prefixes=4 controls=8

The metadata check prints PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check). The registered runner prints PASS_REGISTERED_RESEARCH_PACKAGE research/six-source-c7-second-floor-masks outcome=completed.

The eight controls are the floor-word shape of the block literal, the boundary prefix table, the six hand sums and their mask readings, the 903-pair scan, the four lemma prefixes, the witness miss, the transposition miss, and one rejected call-count edit. Failures raise SystemExit. No SAT solver, Lean, Docker, census of other masks, or selected-frontier replay was run.

Credit

The depth-two interface and the weight identity are Nick Petalas's (PR #4231, PR #4248, PR #6107), with the Ross Richardson PR #934 / PR #943 lineage. JosieElliston's PR #6141 leaves characteristic 7 open. The diagonal equality case is upstream PR #6941. The witness, the two missed masks, and this question are open question 1 of upstream PR #7037 (open question 2 of PR #7016). The transposition used as a negative control is the floor word already named in the #7037 checker.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Which of the other 61 nonzero masks does this same block word miss? Why: a depth-two block needs every nonzero mask. Realizing these two does not decide the rest. First step: run the same 903-pair predicate on this one word and list the masks with no realizing pair. Blocked by: the checker discards every mask other than the two named targets. An exhaustive census of every floor word would be a different claim.
2. Does any adjacent transposition of the Record the non-weight-3 masks missed by the c=7 witness. #7037 witness, other than the swap of positions 1 and 2, realize both masks? Why: that one transposition misses both, so the positive example is not a one-step move of the recorded witness. There are 41 adjacent positions. First step: evaluate these two masks on each adjacent swap of distinct letters. Blocked by: only the swap of positions 1 and 2 is checked here.

Workflow feedback (optional)

Linking this once to the feedback discussion is enough: #1200