Elamur Groupantsworld-school-arithmetic-curriculum
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-arithmetic-curriculum-behavior-complement | behavior_complement | partial source model | behavior-complement |
world-school-arithmetic-curriculum-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
world-school-arithmetic-curriculum-coupling | constraint_relation | partial source model | coupling |
world-school-arithmetic-curriculum-observation-fiber | information_loss | partial source model | observation-fiber |
Model text
forward
Op::apply uses checked Add/Mul, checked Sub only when a>=b, and Div only for exact representable quotients. Problem::answer maps None to legacy zero. Fixed xorshift and template filtering assemble the elementary curriculum; revision sorts last.
invariant
Sub never returns negative; Div rejects zero, nonzero remainder and MIN/-1. Signed Add/Mul/Div results are allowed. PRACTICE and TEST have distinct complete strings, not disjoint vocabulary. Rng range requires a valid small inclusive range and pick a nonempty slice.
cost
Arithmetic O(1); template generation linear output bytes; lesson sorting O(L log L). Checked scalar arithmetic keeps the original asymptotic cost. No performance optimization claimed.
composition
Problem::answer and Student::answer share apply. Public Problem admits arbitrary i64, unlike bounded generators. The native oracle uses i128 for 25x25x4 rows; five extreme cases reject overflow. Template separation and revision order are constant-only checks.
epoch-memory
2026-10-30 initial school source-bound epoch. Prospective model: keep O(1) arithmetic/partition cost, widen aggregation scalars, and expose actual codecs without filesystem effects. Old native witnesses found unchecked operation, score, marginal vote, partition and duplicate-vote arithmetic; legacy serialization synthesized zero accumulators. Review found that dropping explicit zero accumulators also changed the prediction table. Both activation directions now have named tests. No speedup, approximate-error profile or general semantic proof is claimed. Unchecked update/world arithmetic retains representability premises.
checks
cargo test -p world --lib school::wave12_models -- --test-threads=1. Root evidence.md binds exact source/evidence hashes, repeated debug/release outcomes and a compiled production mutation. Named fixture domains appear in composition. Syntax is a source-bound partial projection; macros remain opaque. No semantic AST or live school execution.
behavior-complement
Subject/revision: manifest hash and byte scope. Universe: supplied finite inputs, fixed dependencies, successful allocation and the explicit arithmetic premises of this scope. Inner absent-behavior relation: Some(z) is absent for overflow, a<b subtraction, zero divisor, inexact division and MIN/-1. The model excludes results different from the exact representable equation. Invalid Rng inputs remain outside scope. These are source-derived constraints with finite named witnesses where indicated; external behavior remains unknown.
reverse-reconstruction
Subject/revision: manifest hash. Operator: compatible preimage/converse, holding dependencies and admissibility fixed. For fixed op,z retain all i64 pairs satisfying the operation equation and its guards. Add(z=0) includes (0,0),(1,-1); Mul(z=0) has both zero-axis fibers. Problem::answer(0) also admits invalid operations, so its scalar result cannot recover success. Partial relational description, not a complete inverse search or a unique causal history.
coupling
Subject/revision: manifest hash. Constraint relation on stage identities and ordered intermediate states: Problem::answer and Student::answer share apply. Public Problem admits arbitrary i64, unlike bounded generators. The native oracle uses i128 for 25x25x4 rows; five extreme cases reject overflow. Template separation and revision order are constant-only checks. Supplied native joins and source inspection are distinct evidence.
observation-fiber
Subject/revision: manifest hash. Domain: scoped inputs with the declared observation. The information-loss relation equates inputs whose observation agrees: Invalid arithmetic collides with genuine zero through Problem::answer's legacy fallback. Retain Option from apply when successful zero must remain distinguishable. Finite tests do not establish unrestricted completeness.
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