Elamur Groupantsmath-qread-affine
The groupant beside math/src/qread.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| composition | partial | model.md |
| cost | partial | Cost |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
one_pass_substitution | one_pass_substitution | partial source derived model | one_pass_substitution |
key_classification | key_classification | partial source derived model | key_classification |
Parts
Model text
descriptant
math-qread-affine
add((c,x),(d,y),s)=(c+sd, prune(x+sy)); prune keeps exactly |a|>1e-12. subst replaces each original key once with its supplied Lin, preserving unsolved keys.
Epoch 2026-10-31: replaced duplicate catalog sentences with concrete exclusions, compatible-antecedent examples and two distinct scoped behavioral views. Source and prior execution evidence are unchanged; this revision ran no tests.
approximant
Scoped forward relation
add((c,x),(d,y),s)=(c+sd, prune(x+sy)); prune keeps exactly |a|>1e-12. subst replaces each original key once with its supplied Lin, preserving unsolved keys.
This source-derived relation is partial; no executable percentage surrogate or replacement is supplied.
invariant
Scoped domain and invariants
Finite map arithmetic is assumed for the pruning interpretation. Constant c is not pruned; map coefficients are. No global finite-value guarantee.
Cost
Each addition clones the left map, updates right keys through ordered-map operations, then scans retained entries. Substitution repeats additions for each replaced key; cost depends on total substituted support, not just original key count.
models
behavior_complement
For finite coefficients, canceled entries with |a|<=1e-12 cannot remain in add's output; subst cannot recursively substitute a newly introduced key within that same call. Numeric text parsing does not exclude nonfinite f64 values.
reverse_reconstruction
Output x={LEAF:1} admits both the original map and addition of equal-and-opposite unknown terms. subst({u:1},{u:v}) yields v even if the solution map also maps v to a leaf; one pass cannot identify a unique input equation.
one_pass_substitution
Let sol(u)=v and sol(v)=leaf0. subst(u,sol)=v, while a second call yields leaf0. The preimage relation therefore depends on substitution depth.
key_classification
unknowns selects keys<LEAF independently of coefficient value; var(LEAF) is a numeric leaf while var(LEAF-1) is an unknown. add may remove an unknown through pruning without solving an equation.
tests
Scoped evidence
Lin cancellation/subst, compound zero denominator and provenance only.
Named actual source fixtures: qread::wave28::{affine_provenance_and_gate_order; empty_query_and_compound_provenance}.
Parent tests.md records commands and paired profiles. No additional coverage inferred from parent fixtures outside this byte range; source-scoped numeric/parse properties remain partial.
Wave34 direct-helper refinement
Earlier source-only gaps and wave28 receipts above are historical. Current descendants add actual helper fixtures; see ../wave34-evidence.md and each descendant's Tests section. Full English parsing and general solver correctness remain gaps.
wave34-composition
Affine descendant composition
one-pass-images invokes support-pruning repeatedly through add. It iterates original keys in BTreeMap order; replacement keys are inserted into accumulated output but never become iteration inputs. Each addition can discard a coefficient, so a later replacement operates on the already pruned map. The constant follows a separate unpruned accumulation. unknowns then classifies keys below LEAF without validating leaf backing storage.
Inverse composition must retain every intermediate map satisfying the rounded addition and pruning relation. A dropped residual cannot be reconstructed uniquely. Replacing this ordered process by simultaneous exact substitution would change the observed relation. These are absolute pruning thresholds, not percentage error guarantees.
Cost
For each original key, count its replacement support, accumulated map clone and ordered updates/retention. Summing these add costs is appropriate; adding the full parent cost again is not. Map growth and cancellations determine actual storage.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/qread.rs.groupant/affine.groupant/