[unpaidmoon]

Change and mathematical scope

One fixed seven-tape inventory carries two rounds of the typed actual-width physical H. Previous-output reset blanks the root and consumer tapes between rounds, so the live cell count stays one round's footprint

F = 6 M r (w + W)

instead of two retained one-shot inventories (2F).

On the predecessor's two-record witness (ell = 2, flags = (False,), k = 1, p = 4), that footprint is 624 cells. The layout has one height, so the two rounds are two admissible presentations of h = 0. Each presentation matches a fresh one-shot tensor and the one-round bill of 768 reads, 1200 writes, 3890 moves and 620 gates. Each output-tape reset writes 96 bits and moves 190 cells.

On flags = (True,), the smallest ell=2 layout with two heights, the same contract carries h = 1 then h = 0 in 1248 cells. The selected bits are (1,) and (0,).

This is a scoped stock certificate. It is not a scalar saving, a paid-profile improvement, or a change to the selected frontier κ = 781451/250000000. Both outputs are not live together. Rounds with different selected-bit counts do not fit this exact-length inventory. The PR #3617 diagonal is not attached. The five selected framework assumptions remain.

Task and overlap

Base commit: 626e936ce4d61f2584316914fc71baf96940c512 (canonical CrocSwap/integer-mult-bounds main). Priority revision 8. Selected record SHA-256 9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa.

Task card: uniform-transfer-audit. Scope status: changed. The card asks for one of the five selected assumptions at its caller. The first structured open handoff in discussion #1166 is comment 19016699, whose typed actual-width return is already on main (research/typed-actual-width-physical-h, upstream #4123 and #4127). This package takes that handoff's remaining stock question, which is open question 1 of that package. A fixed footprint is the stock term a later caller would pay for two rounds of this return. It does not move the selected main_transform outer row.

Nearest work:

• Clear1nsight, PR research: match actual-width twiddle layout and validate diagonal caller #3623, and the one-round machine in research/typed-actual-width-physical-h: the tapes, tensor and toward-zero return used here. This package does not re-prove that return.
• unpaidmoon, upstream Add a typed one-round actual-width H and rounded return. #4123 / research/typed-actual-width-h: the other one-round answer to the same handoff. Its first open question is the same stock gap.
• No open upstream PR and no package on this main constructs the shared inventory. Fork branches cursor/typed-actual-width-h-e442 and cursor/typed-actual-width-physical-h-003b are the delivered one-round results, not this schedule.

The executable dependency is research/typed-actual-width-physical-h/physical_h.py, pinned in SOURCES.json and checked by SHA-256 before the schedule runs.

Validation

CPython 3.12.3, standard library, from the repository root:

python3 -B research/two-round-cube-stock/verify.py
python3 -B -O research/two-round-cube-stock/verify.py
python3 -B scripts/research_package.py --package research/two-round-cube-stock --check-only
python3 -B scripts/research_package.py --package research/two-round-cube-stock

Both direct runs and the registered package check printed PASS_TWO_ROUND_CUBE_STOCK. Metadata check printed PASS_PACKAGE_METADATA_AND_PINS. python3 -B scripts/research_selected_baseline.py printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY.

Failure controls: the predecessor object rejects a second run with one-shot physical H; a numerator 17 at p = 4 still raises unit disk; an eighth tape or a wrong length raises inside the redirect; the reset bill is checked against n writes and 2(n-1) moves.

Not run: make frontier6030-verify, Lean, Docker, a production ell, and the PR #3617 diagonal. Finite agreement with the one-shot machine is not a proof for layouts whose g changes.

Credit

The matched layout, one-round machine, tensor and toward-zero return are Clear1nsight's PR #3623, incorporating Sagar Thakrar's PR #3617 diagonal contract and the PR #3493 / #3593 / #3599 / #3611 sources credited there. The one-round tape bill is unpaidmoon's research/typed-actual-width-physical-h. The handoff is #1166 (comment).

Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel acceptance is claimed. Apache-2.0.

Open next questions

1. Can one inventory carry rounds whose selected-bit counts differ? ell = 3, flags = (True, False), k = 1 has g = 1 followed by g = 2. The exact-length redirect rejects the shorter round. First step: pad the g = 2 scratch and butterfly tapes so the g = 1 round uses a checked prefix. Blocker: this allocator requires each requested length to equal the inventory length.
2. What stock is required when the caller keeps both round outputs? Reset is what keeps the live count at F instead of 2F. First step: add a second root/consumer pair and compare it with F.
3. Can one reset output sit under PR Execute complete encoded twiddle diagonal passes on fixed tapes #3617's framed diagonal without a fresh stage object? That remains the predecessor's second question. First step: feed one rounded consumer packet into the unchanged diagonal consumer and price the framing.