[JoyboyBrian]

The helper462/frame506 route in PR #4989 has 80 literal unit_scale sites, using five signed-dyadic coefficients. This supplies that complete operation class: multiplication by 2, 1/2, -1, -2, and -1/2 modulo every runtime positive odd Q, for arbitrary complete [P] × [Q] × [S] Boolean streams. The source family has 80f² sites when N = 8f.

Ten fixed programs use 14 tapes and 7 symbols. Each coefficient has a source-preserving output interface and an in-place interface that returns the result to the same original physical owner. The latter gathers the entire source before overwriting it, consumes both buckets, and returns every private cell and head to its original blank state. It pays for all storage, copies, record motion, rewinds, setup and erasure. Negative maps preserve the order of bits inside each record. No scalar inverse, bank relabelling or source-retirement oracle is assumed.

PROOF.md gives uniform conservative bounds of 2048V transitions and 64V visited cells, where V = PQS, including signed composition and erased intermediate work. At site volumes V_j, the completed scaling contribution is at most 2048 Σ V_j, with sequentially reusable private capacity 64 max V_j. These are sufficient physical charges, not optimized invoice terms.

The family decision is NARROW to this completed operation inventory. The remaining 224f² ordered shifts, 80f² ordinary high swaps, low-controlled carries/commits, canonical native invocation, ROW/cache lifetime, descriptor/header and packet-layout producers, whole #4814 matcher coverage, and P3/stock/precision/supplier admission retain their full unknown costs. Installing the supplied complete-stream representation in an actual recursive owner bank remains a caller obligation. This changes no paid-call count, selected result or κ.

Validation at 02a3cedb301e072bc5d991c7e36086daa8cd5c40:

• All five registered commands pass under Python 3.12.2, including normal and optimized execution through both retained PR Realize all-size ordered shears on fourteen fixed tapes #2776 engines.
• 560 coefficient/interface executions, 16,040 payload bits, all 80 literal source sites at actual Q = 125 with compressed spectators, and 30 complete physical in-place inverse roundtrips pass. These fixtures do not materialize the enormous complete source cover.
• Fourteen semantic controls and seven relocated CLI tests reject source/table/typed-receipt corruption and three regenerated code mutants that omit a Q-counter return, the original-owner rewind, or negative-prefix cursor positioning.
• Source-history/ancestry checks, git diff --check, and the official 19-file export pass. All five registered commands also pass from the extracted export with Git unavailable and every exported byte unchanged.

Reproduce:

python3.12 -B scripts/research_package.py --package research/signed-dyadic-scaling

The authenticated predecessors remain unchanged: PR #2776 machine/counter/copy/erasure macros and both disjoint execution engines; PR #4989 PROGRAM, generator, interpreter and proof at base f259dabc7d70e0db8d6d36bfda888f008bbfecc1. Pending PR #5019 at 39f3cf9fb4f2e495a716c7b501ea3bceb6b2a748 is credited as complementary affine-shear context only, with no code or Git-object dependency. The package retains David Arias, Charles Bethin, Jose Manuel, ai-nanachi, Chris R/Clear1nsight and the native/ROW/ordinary/stock/routing/precision/tape lineage credits. JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0.

Canonical investigation: #1317 (comment)

No Lean, Docker, full selected-certificate replay, full caller materialization, independent human proof review or formal proof-kernel acceptance is claimed. Complete unresolved contracts and open next questions are recorded in the package.

Submission refresh: canonical main 4c0a359d88f22f05189d51f48387750b801a45d4; governing guidance, selected record and this contribution's source inputs remain unchanged from the scientific base. Fresh overlap covers 309 open PR bodies, 4,156 Discussion records and all 6,760 local notes with complete reported pagination/inventory. New public deltas were checked; this remains advisory text coverage, excluding arbitrary diffs and unpublished work.