Share encoded atom powers across recursive child spectator extents

[tekuuu]

Scoped implementation and source-action optimization for a missing recursive preparation component.

The actual Layout.child_extents constructs three spectator cardinalities using multiply_atom_power. Its old loop runs the complete encoded radix validator separately for every atom. This applies standard loop interchange to runtime encoded exponents and shares one validator across all three powers. A single owned blank Counter role is reused and returned erased; exponents, Ring operands, borrowed heads and every original geometry guard are preserved.

This directly follows the child-geometry handoff left open by #4025 and #4062. It adds a callable multi-power kernel and an authenticated adapter to the actual frozen source method. Frozen/shared code is unchanged.

Complete same-input geometry/cleanup comparisons include encoded size division, Geometry/Layout construction, marginal outputs and all disposal:

Case	Original source actions	Shared source actions
Width70 internal-child geometry, n321/q3/w2	7,046,111	5,038,964
q5/even-column geometry	2,334,453	1,042,650
No remainder, rank42	84,977	34,668

Across fifteen declared pairs, total retained record/residue/index reads, writes and unit moves decrease 28.49%–59.20%. Added counter probes, index copies and countdowns are fully charged, with negative savings lanes retained. All tested additional per-bank numerical peaks remain index21/residue6. These are source-action invoices, not a physical-step tariff or a measured production speedup.

PROOF.md proves the uniform successful-input identity and exact old-minus-new invoice. A separate checker imports no primary/runtime code: it reconstructs integer geometry, marginal outputs and counter costs by individual trailing-zero cases. It takes the complete source-measured radix invoice as a parameter, rather than reimplementing the Ring arithmetic. Thirty control groups include26 actual source Counter calibrations, all six geometry guards in both variants, an omitted-output adapter, alias/reentrancy, source/inventory/typed-receipt corruption and overwrite refusal. An actual same-output exponent-one losing control prevents a universal speedup interpretation.

python3.12 -B scripts/research_package.py --package research/encoded-child-spectators

All three registered commands pass. The official committed export/check and25-file source-history/byte preflight pass at head 90b658330f0357975337b41d67927ae84b72c851. All three optimized commands pass from a read-only Git-free final export with an empty effective PATH and import-shadow trap; all27 files remain unchanged. Kernel/adapter/primary receipt freeze: 69a07699bc39e6f2ea40db446c7f1e165500dcc5. Exact canonical base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Eight live source files have sealed SHA256/Git blob pins, authenticated before execution. No pending-PR executable is imported.

Scope: these are valid geometry instances, including a child width above64, not a completed GL64 packet or proof of every chosen source's top-level reachability. The source-level compiler, physical control/allocator tariff, dirty acquisition, actual capsule/payload copies, original-width stock, numerical precision and full supplier admission remain separate. Malformed contexts retain rejection, but loop interchange can change partial outputs and does not add transactional rollback. A tiny kernel can lose; callers must prove the complete budget at their site and pay any dispatch rule. No new κ is claimed.

VERIFICATION.md gives the explicit same-runtime API and next join with #4062's Context/directory/admission work. The cheap selected-baseline inventory was attempted but the sparse checkout omits research/complex-sw4-frame8; no selected cold replay is claimed. Source inputs used here are complete and authenticated.

Credit David Arias/PR2753 for ordered child geometry; Jose Manuel/jmbarrancoml for the fixed-role caller and retained runtime; ToikY/PR4025 for the fixed-d² shared-radix precedent, following ywz65/PR2590; Chris R/Clear1nsight/PR4062 for the preparation composition and released handoff; and the retained record/codec/source/caller lineage. New variable-exponent kernel, source-method integration, tariff proof and checks by Tekalign (tekuuu) with substantial OpenAI Codex assistance. Apache-2.0. No independent human or formal-kernel acceptance is claimed.