Elamur Groupantsworld-school-scenario-assessment-fold-residues
The groupant beside world/src/school.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 source model | forward |
| ast | partial | ../../syntax.json |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | partial source model | checks |
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 |
|---|---|---|---|
world-school-scenario-assessment-fold-residues-behavior-complement | behavior_complement | partial source model | behavior-complement |
world-school-scenario-assessment-fold-residues-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
world-school-scenario-assessment-fold-residues-partition_membership | set_relation | partial source model | partition_membership |
world-school-scenario-assessment-fold-residues-affine_collapse | domain_boundary | partial source model | affine_collapse |
world-school-scenario-assessment-fold-residues-repeat_wrap | arithmetic_boundary | partial source model | repeat_wrap |
world-school-scenario-assessment-fold-residues-group_information | information_loss | partial source model | group_information |
Model text
Wave34, 2026-10-31. Source-bound helper model; no universal proof or approximation-error certificate. Historical parent epoch remains intact.
forward
folds=0 returns None. Otherwise ungrouped result is (indexp[repeat mod 5]+repeat) mod folds in u128. Grouped result is (hash XOR wrapping64(repeatC)) mod folds; index is ignored.
invariant
Result lies in [0,folds) and equal group hashes stay together for fixed repeat/folds. Composite folds with noncoprime p may have empty residues. Hash grouping cannot prove semantic nonleakage.
cost
Constant arithmetic, no allocation; native word sizes and widening are part of the model.
composition
cross_check_k applies the same helper to row selection for both learn !=fold and check ==fold. No dataset or training is executed; helper membership does not certify the provenance of hashed text or extra training rows.
behavior-complement
Exclude Some for zero folds, out-of-range residues for positive folds, or different folds for identical hash/repeat/folds at different indices. Do not exclude empty folds when gcd(p,folds)>1.
reverse-reconstruction
Ungrouped observed j admits indices solving p*i ≡ j-repeat mod folds; if gcd divides the RHS there are gcd residue classes, otherwise none. Grouped fiber is all hashes whose XOR-mixed value has residue j; zero-fold None admits every index/hash/repeat.
partition_membership
For one positive fold count, equality with the returned residue defines exactly one check partition and folds-1 learn partitions per row.
affine_collapse
repeat=1 uses multiplier7; folds=7 makes all ungrouped indices return1. A partition assignment invariant is weaker than balanced coverage.
repeat_wrap
Grouped repeatC is explicitly wrapping u64 before XOR; ungrouped indexp uses u128. Debug and release must agree at machine-word edges.
group_information
Equal hash enforces co-location but distinct texts may collide; fold alone cannot reconstruct a hash, index or source record.
checks
Exact world library selections: school::wave12_models::assessment_partition_has_exactly_one_check_fold. Current repeated debug/release outcomes and compiled controls are in the root sidecar wave34-evidence.md. Only these supplied-input tests are current evidence; older parent module-wide receipts are historical. Macro bodies remain opaque.
epoch-memory
Prospective model saved before edits. This epoch deepens one existing node rather than renaming it. Production implementation unchanged; tests add helper-boundary observations where stated. No live lessons, frozen suites, model loading, teacher or network. Read-only symbolic relations are broader than the finite native domain.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/world/src/school.rs.groupant/scenario-assessment.groupant/fold-residues.groupant/