[1337isnot1337]

Result

This follow-up proves the exact minimum frame cost for every valid readout-boundary assignment in the fixed two-projection connector model in research/two-projection-connector-seed51a5.

For the fixed source word B0 B1 B0 B1 B2 B3 B4 B2 B4 B3, with source 3 using direction (1,1), the other sources using (1,0), paired readouts using projections (1,0) or (1,1), and only the two paid row-shear generators:

• The exhaustive domain contains 4,194,304 sets of boundary/projection demands.
• Exactly 848 demand sets cover all 31 nonzero masks.
• The exact minimum frame-XOR histogram is 10:38, 12:248, 14:386, 16:176.
• Therefore every assignment in this fixed model costs at least 10 full-row XORs. The predecessor's 10-XOR schedule attains the bound.

PROOF.md reduces paired readouts to same-projection prefix differences and proves the six-frame shortest-transition DP is exact. verify.py independently enumerates the full demand-set domain, validates all 31 predecessor readout pairs, prices the retained frame schedule, and rejects a corrupted mask-pair control.

Scope

This is a finite optimum for the one pinned source word, direction assignment, two projections, paired-readout contract, and two shear generators. It does not bound other source words or connector models. It does not price the row XORs against multiplication children, place the second dirty row in the selected supplier, or change kappa. The predecessor's local 180-child versus 182-child comparison remains a separate cost vector until a supplier-supported row-XOR/storage tariff is supplied.

Reproduction

Commands pass locally under Python 3.14.8:

python3 -I -O -B research/two-projection-boundary-optimum/verify.py
python3 -I -O -B research/two-projection-connector-seed51a5/verify.py
python3 -I -O -B research/universal-connector-boundary/verify.py
python3 scripts/research_package.py --package research/two-projection-boundary-optimum --check-only

The repository's full package runner is pinned to Python 3.12. Python 3.12 is not installed in this environment, so I ran the same three replay commands directly with Python 3.14.8 and ran the package metadata/source-pin check separately.

Context

Base: 463113d675af7410ac91d53a4fed51ec6494eb9a (canonical main remained unchanged at submission). The final overlap refresh covered 361 open PRs and 2,159 discussion/comment/reply records. No open PR or exact-term discussion matched the all-boundary follow-up; the old #1167 claim is the predecessor construction, while #2221 and #2262 concern different connector models. Details and timestamps are in OVERLAP.json.

The predecessor construction retains its source credit in its own NOTICE.md; this PR credits that work and adds only the all-boundary lower bound and checker.