Factorized numerator restoration validation

Lifecycle

investigation

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Ownership decision required

Review

2026-09-17 · ac2c553c36309e02529574812e70d4bdaa37eba8

Freshness

frozen-evidence

Evidence

capture date unavailable · ac2c553c36309e02529574812e70d4bdaa37eba8

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No verified code scopes recorded

Measured on 2026-09-21 at 20974534251153e805c00ed017dfd874a29626d5, using native binary SHA256 415c94c32ac8297ac22fca1169fc5d5e5a19df7c8b48d236dd27d85eb300d874.

Representation

Numerators remain shared functions of affine energy arguments, including signs, integer sampling nodes, and external-energy coefficients. Complete energy maps define branches; arguments may span the whole graph. This retains the structure needed for future LTD maps without implementing LTD.

NumeratorAtomExt::series_preserving_factors retains expansion-independent factors and shared numerator coefficient families. Expansion-dependent energy arguments remain visible to differentiation; Symbolica supplies the Laurent algebra. Both local UV routes use this machinery.

Evaluator preparation contracts closed parametric numerator contexts before component enumeration. Closed sums are prepared from the inside out and remain opaque in their parent products. Shared bodies retain factorized numerator sums, separate formals and private indices per occurrence, and existing chain/trace scopes. Scalar weights, inverse denominators, selectors, and independent closed products keep their boundaries. Open interfaces use ordinary component preparation; only reachable functions and scalar aliases are retained.

Family calls are lowered by their validated function head and tags. Exact formal arguments are bound simultaneously, including function-valued arguments; the catalog rejects duplicate formals. Lowering does not scan every family’s generic replacement pattern at every node of the outer expression.

After outer tensor contraction and factor collection, repeated complete scalar functions and powers may become retained aliases when the stored definition and references use fewer bytes. The root and each retained definition are visited once, preserving existing alias keys without unfolding the dependency graph. Any candidate containing a residue selector, orientation guard, theta, or IF remains visible, so subsequent branch preparation still encloses each inverse use in its lazy conditional. This sharing is applied after Taylor operations and formal-argument pruning; it does not hide momentum dependence from differentiation. Extraction stops at whole functions and powers, stores their bodies unchanged in AliasedAtom, and preserves exact parameter and existing-alias keys. Recursive subexpression extraction is unsuitable here: it can rewrite arguments used as exact function tags before evaluator lookup. Furthermore, Symbolica Horners alias definitions; candidates containing algebraic parameter or tag keys are excluded so that this pass cannot change their exact identity. Known ordinary arguments, including the OnShellEnergy invariant, remain eligible. FunctionMap enforces one tag count per function head; calls absent from the recorded catalog conservatively treat every argument as a tag. No numerator expansion is performed. Sharing reduces preparation storage; Symbolica may still inline definitions while building its evaluation tree.

A projected-4D scalar can already be wholly stored in a Spenso alias, leaving only its handle at the root. Factor collection therefore also visits each retained scalar body before sharing. Sharing rewrites the root and existing bodies together, while storing every newly extracted factor verbatim. This closes the root-only coverage gap observed in the September 26 projected-4D retry; the compact-energy validation record retains that memory-limited baseline.

Generated scalar numerator components and coefficient functions use Symbolica’s InliningPolicy::Always by default. Setting inline_numerator_functions = false uses Never for ordinary evaluators: distinct argument tuples call one retained evaluator body. Hyperdual builds always use Always: the pinned Symbolica implementation cannot vectorize retained sub-evaluators. This choice is made after Taylor operations, so it does not change symbolic momentum dependence or the Taylor algebra.

Function metadata records both inlining policy and caller-scope alias identity. Rebuilds and standalone archives preserve both; algebraic function-map replacement excludes Never definitions. Aliases still resolve in the caller’s parameter scope. The saved-state manifest and standalone archive versions change with this metadata layout. Generated scripts pin Symbolica, Numerica and Graphica to the generator’s revision.

Evaluator milestones distinguish root/alias bytes from recorded function-body bytes and report how many functions retain shared bodies. The optional evaluator_input debug tag captures factorized roots, aliases, recorded function definitions, parameters and optimization settings for an isolated replay. Registrations supplied only through an opaque FunctionMap are outside those recorded-body metrics. Reported instruction operation counts cover the root program; retained callee bodies are additional code.

Integrated UV preparation reduces color algebra before lowering chain/trace shorthands for Vakint. This removes reducible traces before repeated dummy-index materialization, without globally expanding the numerator.

Comparison protocol

Live main was checked as 312cf6aaf4cd1414f6742ad87ce39922c497a0b6 immediately before the runs. Its reused native binary was built from 226b7bea45398023f767fb4e53a1b5c6c3a43a2d, through unchanged child checkout 6fbfe7cd89839ca6b9f10bdd1e5bbc9eba1152f1. Rust sources, assets, Cargo manifests, lockfile, and toolchain match main312; the eight intervening changed files concern CI and contributor guidance. Timing measurements were fresh.

Both sides use Rust 1.98.1, Symbolica 3.0.0, native dev-optim, one generation core, and no evaluator compilation. Main uses sparse_atom_aware; the candidate uses intermediate_cost. Binary, card, graph, and effective-setting identities were checked. Runs were sequential with summary logging; this task ran no concurrent builds or tests. Each row is one observation on a shared host.

GL1 generation

The direct-3D card keeps local UV subtraction enabled and toggles integrated UV. Durations are seconds. Peak memory is native process RSS sampled every 100 ms, not the separate watchdog’s process-tree measurement. Symbolica time means evaluator construction.

Native generation is 5.67 times faster with integrated UV off and 2.75 times faster with it on. These derivative-UV timings are not equal-physics numerical comparisons with main, which lacks the required higher numerator energy powers.

Numerical controls

Eligible comparisons with main use GL1 without UV and the logarithmic-only GL0 top-quark photon box. The latter has UV degree zero, no proper loop subgraphs, and no Taylor derivatives. Graphs, runtime settings, and model parameters match; each side produced two identical, finite, nonzero inspections at the fixed point.

Raw complex results, written as (real, imaginary), are:

• GL1: main (0, 1.818545415743298e-6), candidate (0, 1.818545415743152e-6).
• GL0: main (-2.4834308873547831e-29, -8.71033584620754e-10), candidate (-1.6648052328444753e-29, 8.71033584620754e-10).

The predeclared phase (-1)^L is +1 for GL1 and −1 for GL0. Raw relative differences are 8.03e-14 and 2.0; phase-adjusted differences are 8.03e-14 and 4.76e-20, both below 1e-12. GL0′s opposite raw sign is retained explicitly. Native peak RSS rises slightly in these controls: 0.0396/0.0433 GiB for main/candidate GL1 and 0.0801/0.0973 GiB for GL0.

Same-physics derivative GL1 inspections against raised-energy revision 11fe63d82a13abc0fc16c2fc6296c880a52c0572 agree to 3.4933e-16 with integrated UV off and on, using phase +1. Both repeat inspections agree, inputs match, and saved states remain unchanged. This is a single-point sanity check.

Projected local-4D and validation status

The established projected-4D card, with integrated UV off and explicit orientation summation, takes 12.337 s native generation, 13.658 s command wall, and 1.290 GiB native peak RSS. Its expression/Spenso/Symbolica phases are 6.600/4.336/1.401 s. Main lacks this route and explicit-sum option; its 45.517 s direct-3D reference above is a generation-cost comparison, not equal-route numerical validation.

Local formatting and Clippy passed, together with 1,005 selected Idenso/GammaLoop unit tests; 84 tests were skipped. Final review additionally requires a successful just ci-checks-and-upload run before publishing CI-enabled work; the PR records that result. These measurements establish no numerical evaluator throughput claim or isolated speedup attributable to any single preparation step.