[woklerx]

PR669 gives the selectable-target hierarchy and a criterion for prescribed triples to reach its minimum. This research note resolves every prescribed triple for the nonempty binary two-port star code: for p >= 3, triangles are impossible, a three-edge path on exactly two original pairs needs 6p-11 deletions, and every other triple needs 6p-12. The p=2 boundary is also exact. No new kappa or physical supplier is claimed.

The self-contained bridge/component proof is accompanied by explicit deletion sets and unit decoders. A partition implementation checks 46,348 triples across p=2..6; a code-disjoint RREF implementation checks 800,002 cut subspaces and 12,128 triples across p=2..5. They agree, including 538 edge-restoration controls.

Reproduce offline with Python 3.10+ and the standard library:

python -B research/prescribed-three-port-decoders/reproduce.py

Expected final marker: PASS_PRESCRIBED_TRIPLE_PACKAGE partition_triples=46348 independent_triples=12128 no_new_kappa. The selected-record check and staged whitespace checks also pass. The unrelated full supplier/generator suite was not run.

Base: 007664306fff84fbb1c9a1b4053b69f439764034. Predecessor: PR669 at 7d526020fc368ce4157cd436995c2f4fcf683318; both were unchanged at submission refresh. Credit to Sam Sung / the-missionary-company, Joel Pulikkan / GamingPuzzled, icekylinx and eumemic. Exact pins, local sprint claim (seed41), overlap scope and validation receipts are in the package. Only this research directory changes; selected frontier and upstream remain untouched.

Source access, helpers, frames, copies, restoration, recursive children and full supplier assembly remain unpriced. This is an observation-model theorem, not a multiplication theorem or an improved paid supplier. Prepared for woklerx with substantial OpenAI Codex assistance, including separate Codex workers for proof review and independent implementation; no independent human review is claimed. Apache-2.0.