Scheduled region orders on balanced frames: conditional κ = 5.2111890493145e-5

[maxime-fleury]

Dependency

This branch is composed on top of the open #82 head (3410b94), so its diff against main includes that PR's content, exactly as #82 itself composes the pinned PR76/PR79 archive. The candidate added by this PR is the fourteen files under research/envelope-scheduled/ plus .github/workflows/envelope-scheduled.yml.

What this composes

The pinned envelope-balanced witness fixes one region order per axis through
balanced_split_graph.configuration(h)['schedule'] (cover-core at h23,
reverse-node at h25). This candidate keeps every other setting — groups
[1,1,2], anchors, half-plane versus row coarse sums, future-compatible
completion, 0 versus 3 carry-exchange passes, exact next-use profile costs, the
coordinate-conjugated oracle pricing at h25, the PR74 scalar-envelope
reordering, and the pinned coordinate orders order-23.json / order-25.json
— and changes only the region order: node-asc at h23, width-node at h25.

Result

Quantity	Pinned witness	This candidate
kappa (1e-18 grid)	5.2032798885190e-05	5.2111890493145e-05
Bit saving	5.2035506438388e-05	5.2114606283958e-05
h23 / h25 auxiliary roles	27075 / 35500	27032 / 35431
Physical width W	133289600	133068501

kappa = 10422378098629/200000000000000000, which is 15818321591/200000000000000000
absolute (+0.152%) above the pinned 5203279888519/100000000000000000, and
+0.72% above PR76's 5.1738676045141e-05. The improvement also survives on the
coarser 1e-11 grid (5.211188e-05, still above the pinned fine-grid value).

The candidate is narrower than the pin and has fewer auxiliary roles, so
this is not a width effect: the region order changes which rank-one blocks the
profiler extracts from the same physical path, and the moment inequality
sum_t count_t (t/m)^(1-s) / W < 1 is decided by that profile shape.

How the orders were selected

Region orders were scored by recompiling axes and evaluating the unchanged
exact arithmetic: 12 h23 orders (9 keys plus 4 hash-seeded random orders, with
cover-core reproducing the pinned axis-23 word byte for byte) crossed with 10
h25 orders, 120 pairs in total, at 8-20 minutes of compilation per axis. The
best pair is node-asc with width-node; at h25 the node-asc and
width-node keys happen to produce the same order.

Coordinate relabelling was searched separately as an independent lever: more
than 500 hill-climbing and random relabel draws on the pinned words never beat
the identity relabel, so the pinned order-23.json and order-25.json are
retained unchanged. Only the region order moved the number.

What is verified

research/envelope-scheduled/verify.py replays both words (XOR word, dirty
basis, frame incidence), rebuilds the transition and fixed-basis profile
receipts, recomputes the profile of each axis exactly against the shipped
profiles-23.json / profiles-25.json, rebuilds the complete
child-multiplicity profile, re-derives the 1e-18 grid saving with the inherited
rational binary search, checks both moment enclosures, the independent
log-enclosure audit bound, the fixed-width bridge and the balanced assembly,
and asserts all 47 strict inequalities, the seven margins, the next-grid kappa
rejection and the independent-bound separation. --regenerate recompiles both
axes through this directory's compiler.py (role counts 27032 and 35431) and
asserts the regenerated words are byte-identical to the shipped ones; the
recorded run is regen.log. test_controls.py adds 15 controls: a duplicated
coordinate, an inconsistent mapping, unrelabelled source values or outputs, a
missing terminal synthesis, an aliased terminal, an unknown region order, a
region order that breaks the topological or carrier constraints, and a stale
bridge field are all rejected, while the recorded kappa is accepted and its
next 1e-18 grid value is rejected. CI runs both in the same three Python
versions as the pinned workflow.

Scope and limits

The arithmetic downstream of the words is inherited unchanged: the PR48
rational logarithm enclosures, the PR65 moment/assembly/audit code, the
fixed-tape transfer, routing and recovery interfaces, prime selection and the
all-size compiler argument. Only heuristic selection among legal region orders
changed, under the same topological and carrier-candidate assertions. Nothing
in research/envelope-balanced/ is modified; compiler.py and
flag_engine.py are copies of the pinned files in this directory, and the
copied flag engine keeps the pinned check_flag_engine assertion. The one
harness difference is that the oracle subprocess is awaited with a generous
timeout instead of ten seconds, because the pinned ten-second wait aborts an
already completed compilation at its shutdown step under parallel load,
before the word is written; it cannot change the word, which is fully
determined before that step.

This remains a conditional finite witness: no global optimality over region
orders and no measured practical speedup is claimed.

Region-order selection and verification with Codebuff (Buffy) assistance.
Inherited sources, notices and licenses remain unchanged.

[Mister-Meeseeks]

Thank you @maxime-fleury. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Dependency-valid region ordering and saved-word resynthesis.

Review and limits: Exact-head CI evidence; actual DAG compatibility retained.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 2b4dca843b7a719512595896aab29de28bc4ea1f. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.