[petalas]

Summary

Replace PR3582's supplied immutable shape scheduler with a compact encoded descriptor and an executed sequential counter controller for one borrowed physical address.

borrowed unary shape descriptor + borrowed Boolean address
  parse fields and scan axis flags on their actual tape
  use 21 delimited binary-counter tapes to generate each data action
  accumulate the exact forward/opposite header on four data tapes
  emit one header; erase private tapes and return all heads

The author-written all-finite-valid-shape proof uses 26 fixed finite-alphabet tapes, O(p) cells and O(p^3) complete transitions under the retained source bands. No program, circuit, slot list or participation table is supplied or retained. Exact capacity is Cdata+22N+86 <= 90(A+ell+1) finite-alphabet cells. Binary symbol encoding and the additional constant finite control are stated separately.

This is one encoded header-producer implication. PR3590 instead changes to an owned address stream and still assumes shape scheduling. Neither supplies the other's contract. No packet consumer, complete layer/root invoice, supplier admission, independent human/formal acceptance, kappa gain or selected-frontier change is claimed.

Evidence

• Before: PR3582 charges data arithmetic/movement but leaves descriptor parsing, counters and scheduling outside its bill. After: this package executes and charges actual descriptor/counter current-cell reads, writes and unit moves alongside the direct data operations. The source already states polynomial exponent computation; the result is a specific encoded implementation and linear tape-space proof.
• All 16,440 addresses in 240 complete small shapes agree with independent named-bit arithmetic and the authenticated canonical circuit. All 480 zero/one controller executions have identical schedules/invoices; four larger examples reach ell=32. Independent access sequences verify every data read/write/move and Boolean bill. Counts are model operations, not CPU timings.
• All 256 four-bit counter pairs, 15 boundary cases and 11 optimized actual CLI fault groups pass. Faults cover arithmetic, retained bits, copy/remainder, erasure, uncharged motion, receipt and changed/missing premises. Host malformed-input admission is outside the physical rejection bill; interruption/failure restoration is unclaimed.
• Registered CPython3.12 normal/optimized science and controls, metadata/pins, exact committed bytes/source history, committed export/check and actual Git-free scientific/control commands passed at the publication commit. Source/export before-and-after hashes and shared runtime identity are preserved.

TMPDIR=/absolute/private/run python3.12 -Werror -B scripts/research_package.py --package research/encoded-twiddle-controller
python3 -B scripts/check_research_commit.py --package research/encoded-twiddle-controller --check-source-history

README, PROOF, RESULT, SOURCES, PREDECESSOR and VERIFY contain the contract, exact evidence, replay and limits. PR3582's actual algorithm/proof predecessor bytes are retained with origin commit/path/blob/SHA256 and credit; scientific replay needs no foreign Git objects or network. Credit remains with Nick Petalas's direct-tape/register predecessors, Douglas Colkitt and the retained transform lineage, Philipp/mightyOil's positional engine and Jose Manuel/jmbarrancoml's packet/phase work.

Merge Danger

Door: two-way

Blast Radius: research

Adds only research/encoded-twiddle-controller and opt-in replay. Frozen inputs and the selected frontier remain unchanged.