Elamur Groupantsmathematical-correspondence
The groupant beside models/mathematical-correspondence.groupant 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 | not materialized | |
| composition | partial source model | Composition |
| cost | partial source model | Cost |
| descriptant | present | 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 |
|---|---|---|---|
correspondence-behavior-complement | behavior_complement | partial source model | behavior-complement |
correspondence-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
correspondence-domain-obligations | endpoint_type_constraint | partial source model | domain-obligations |
correspondence-missing-formulas | formalization_gap | partial source model | missing-formulas |
correspondence-finite-evidence | assurance_partition | partial source model | finite-evidence |
correspondence-composition-fibers | information_loss_relation | partial source model | composition-fibers |
wave39-transport_condition_intersection | intermediate_domain_intersection | partial source derived model | transport_condition_intersection |
wave39-finite_kernel_and_image | finite_fiber_image_composition | partial source derived model | finite_kernel_and_image |
Model text
Migration: consolidated into model.md, 2026-11-04, operator decision; fresh hash-bound references to the former files were rebound to the sections below.
model
Mathematical correspondence composition
Forward
A source snapshot, ownership registry and reviewed formula catalogue enter the scanner. Binding gates require the declared source and model bytes, groupant ownership and confined artifact paths. Each admitted formula has finite named endpoint sorts and explicit observation, assumptions and effects. Core validation precedes canonical relation rewriting and finite interpretation. The scanner compares compatible algorithm/application roles and explores admitted typed compositions; the CLI writes one new report. Missing formalizations are reported rather than replaced with interpretations of prose.
Composition
Core relation semantics feeds scanner admission and pair construction; CLI argument selection and exclusive output writing wrap that computation. The native bridge harness binds selected finite tables to actual algorithm and math calls on declared inputs. All source-to-formula assumptions remain explicit. Independent finite-matrix checks validate the interpreter on bounded universes, while abstract Lean laws in formal/RelationComposition.lean justify only their stated relational identities. A source hash proves a byte binding, not the correctness of a mathematical abstraction. The LCS bridge separately compares actual text and algorithm APIs with a brute-force subsequence oracle; its byte, character and token domains remain distinct.
The ownership tree is separate from the correspondence graph. Formula comparisons and composition edges do not change source ownership or install a production implementation. Algorithm source files, ordinary source files, pure group tiers and mixed ancestors have different denominators. A pair opportunity is a counted possibility, not an evaluated equation.
Invariant
Endpoint names and ordered finite values remain part of the type. Converse exchanges endpoints; composition preserves the exact intermediate type. Complement is relative to the declared finite rectangle. Assumptions, effects, observations and source bindings are retained. An unknown formula remains unknown. Structural canonical equality, coincident finite tables, counterexamples, native source probes and abstract proofs have distinct evidence scopes. The scanner records exact declared converse/complement derivations only when the owner, full source binding and endpoint/observation/assumption/effect contracts agree. Every matching forward base remains visible. Derived records count as model coverage, not as independent source evidence; unrecognized constructions imply no independence either.
Cost
Let B be bound input bytes, N registry nodes, F catalogue formulas, T total AST nodes, K comparable formula pairs and U maximum finite endpoint cardinality. Admission traverses the ownership/data bindings and formula trees; matrix composition can require O(U^3) work per composition node. Pair discovery and rendering scale with admitted records, not merely the inexpensive full-grid count. Exact construction provenance can compare O(F²) candidate bases, with expression equality additionally bounded by T. A separate 100,000-edge budget rejects excess output before inserting the next edge; accepted reports retain every matching base. This step is not a constant-cost independence oracle. Caps reject excessive work rather than silently approximate it. Repository inventory and hashing costs remain separate from the finite-core caps. No whole-system latency or learning improvement is claimed.
behavior-complement
For the fixed snapshot and admitted relation universes, excluded report pairs include success with stale bindings, incompatible intermediate endpoints, a unique inverse for a noninjective projection, or a universal Rust-equivalence claim inferred only from a finite table. These are a partial excluded-behavior model; unmodeled filesystem/process failures remain outside it.
reverse-reconstruction
Given a report, retain every source/model snapshot and catalogue that passes its bindings and could generate the reported finite interpretations. Hashes constrain bytes under the usual collision-resistance assumption; an observed table does not uniquely reconstruct code, prose, formula syntax or unobserved behavior.
domain-obligations
Equal printed values do not identify equal scalar theories. Rational and finite-field endpoint types remain distinct. Floating-point reassociation, cancellation at zero and changing a Result error policy require additional proofs or source probes. Compatible endpoints are necessary for composition and do not prove that a source-level adapter exists.
missing-formulas
A groupant without a catalogue record has no machine-admitted formula in this prototype. Missing forward, reverse reconstruction and behavior complement roles stay separate. Registry coverage and mathematical formalization coverage are different quantities.
finite-evidence
Equality on all pairs in a declared finite rectangle is exact for that supplied finite relation, conditional on its table. It says nothing about values outside that rectangle or whether its table describes real source behavior. A structural normalization result additionally depends on the soundness and implementation of the stated rewrite rules. Lean and independent finite controls address separate parts of these obligations.
composition-fibers
For a function graph R, applying R then its converse returns the equal-output fiber relation. It is identity only when the function is injective on the chosen domain. Reversing that order yields identity only on the image. Behavioral complements do not generally distribute through composition; the Lean counterexample and executable controls retain this failed idea as useful evidence.
Checks
Focused core, scanner, CLI and actual-source bridge tests are listed in child groupants. Integration additionally repeats deterministic public/private-composed scans, checks stale bindings and exclusive output, materializes source syntax projections, and runs modelcheck registration and groupant validation. Evidence for this epoch is recorded separately after execution. No live corpus, teacher, training, GPU or held-out assessment run is part of this subsystem experiment.
Epoch memory
2026-10-31: the initial mathematical comparison catalogue deliberately covers a small reviewed subset while exposing the larger formalization backlog. Existing reviewed graph/assignment transfers remain prior evidence. Formula-level coincidence can suggest model reuse even when it yields no code speedup. Rejected domain matches and lossy inverse assumptions are useful findings, not failed coverage to hide.
The next integrated checkpoint adds bounded canonical output, typed totality/surjectivity, conservative construction provenance and two admitted LCS comparisons. Wave37 evidence separates finite relation results, actual-source tests and measured allocation/timing behavior. The whole-registry review records source-grounded model expansion and the remaining review queue; structural coverage is not semantic completion.
2026-11-01 paired diagnostic memory: a forward normalization vidtvorant preserves a finite relation, while resource-boundary reasoning separately requires admitted output syntax. The wave37 converse-chain counterexample showed that semantic preservation alone did not imply node-budget closure. Keep the bounded fallback, fixed limits and source witnesses in the composed explanation. Likewise, matching a forward relation and its mechanically derived converse/complement supplies dependent model evidence, not two independent source confirmations. The practical diagnostic cases connect this result with observed runtime repairs in other subsystems; they add explanation, not a new native run or an automatic equivalence proof.
wave36-evidence
Typed correspondence experiment — 2026-10-31
Baseline: 84c814109ed8bef07972dc768431b723ea22f388. Prospective hypothesis: an explicit typed relation AST and finite interpretation can expose reusable observations and reject inverse/domain confusion cheaply. General source extraction and universal equivalence were outside the experiment. The result includes a concrete repair: public arbitrary-integer math::nt::gcd(0,0) now returns zero consistently with extended Euclid and its independent certificate. The original regression failed with the dependency panic before the guard was added.
Integrated results
The public registry contains 896 Rust sources and 80 composed groups. Four new source groupants belong to this subsystem; the number-theory groupant and affected ancestors were refreshed. Public registration, changed-file coverage and groupant validation pass. Local overlays were checked separately without adding their source paths to public artifacts. Five source syntax projections were regenerated twice with identical bytes. Syntax is a partial Rust projection, distinct from the declared mathematical relation AST.
The scanner inventories 200 algorithm implementations against 477 nonalgorithm source nodes: 95,400 pair opportunities per direction. It separately reports 57 pure nonalgorithm groups and three mixed ancestors. The 16-formula catalogue covers eight production files. There are 2,199 missing typed roles across its inventoried tiers; these remain explicit gaps, not parsed or proved formulas.
Nine catalogue pairs are admitted to comparison/composition exploration: six finite coincidences, one concrete counterexample and two incompatible equality contracts. No normalized structural match occurs between these separately named atoms. Four composition orders are admitted; twelve are incompatible. Cross forward/reverse gcd composition yields a 35-pair equal-output fiber relation on nine input pairs, while the reverse order is identity on the three represented output values. This demonstrates preserved ambiguity and image scope. The Horner overflow pair refutes a full-behavior replacement. Different rational/modular endpoint theories are excluded by indexing and independently refuted by native probes.
Two public scans produced byte-identical reports in 0.119 and 0.120 seconds. These are whole-command warm-cache CPU snapshots on one host, not a baseline comparison or a claim about learning speed. Counting unformalized pair opportunities is cheap; it is not evaluating 95,400 source equivalences.
Executed checks
- Integrated Rust tests: eight core, six scanner and six actual-source bridge tests, each in debug and release. The repaired number-theory boundary adds two focused tests in both profiles: 44 successful test executions over 22 identities.
- Native bridges include 4,225 gcd inputs plus maximum-u64 boundaries, 3,905 polynomial/derivative cases, 288 preflight-admitted head maps plus dispatch-boundary shapes, and rational/modular system checks. Each catalogue row is tied to declared labels and computed public API results.
- Independent linked scalar Boolean-matrix oracle: 21,092 checks and 103 negative controls; repeated counts agree, zero failures. Its coordinate-loop oracle differs from the production row-bitset composition. Final core/scanner source hashes match the independent review snapshot.
- Cached Lean compilation: ten abstract theorem reports, only standard foundations, no admitted proofs. Both false-formula controls fail with Lean errors. These theorems are about abstract relations and conditional error propagation, not arbitrary Rust extraction.
- CLI controls reject a stale source hash and existing public/local report outputs; existing report bytes remain intact. Core/scanner unit controls cover incompatible fields/endpoints/contracts, inverse ambiguity, complement non-distribution, foreign/symlink models and duplicate identities.
The first integrated groupant gate rejected the new parent manifest because its status field was absent. The metadata was corrected and the complete gates rerun successfully. The failed report remains in the external attempt record. This was a schema repair, not a production algorithm failure.
Evidence boundary
The scanner binds source/model bytes and ownership; symbol and section strings remain unresolved annotations. A well-typed but false table can still pass its structural gate. Native source bridges, manual review and independent oracles are separate evidence, and finite observations do not establish general numeric error certificates. No production implementation is automatically replaced. No teacher, training, GPU, live corpus or held-out assessment was run.
The external run retains raw logs, numeric exits, deterministic reports, timings and source bindings. Repeating review follows the bounded workflow; catalogue details and mathematical scope are in the native bridge description.
wave39-digits
Digit/Horner correspondence composition — wave39
transport_condition_intersection
The adapter maps (MSB integer coefficients, integer base) to (reversed f64 coefficients, f64 base) and projects a successful pair to its value. Domain is an intersection of conversion exactness, every value multiplication/addition's exactness, and successful paired arithmetic; small listed fixtures additionally have exact derivative arithmetic. Neither equal final values nor individually representable endpoints establish the intersection. Counterexamples retain intermediate rounding, base aliasing and derivative overflow as distinct boundaries. A full Result contract would compare error outcomes and derivative meaning too; the integer fold has neither. These limitations are observations at this parent, not unproved substitution permissions.
finite_kernel_and_image
Let R be the finite listed algorithm value relation, S the independently checked integer value relation. They coincide on twelve inputs. R;S-converse relates equal-valued input descriptions: [] at base10, [0] at base10 and [1,2] at base-2 all map to0. Hence this composition is neither identity nor functional. R-converse;S is identity on the seven listed output labels because every label is observed. This is a finite image property, not recovery of coefficients. Converse/complement equalities derived from the exact forward ASTs are dependent evidence. Rectangle complements exclude wrong listed pairs only; omitted inputs, unlisted outputs and source failures remain unsupported. The ownership tree is unchanged; source-linked relation edges form the separate discovery graph.
Evidence: actual API tests plus independent positional-power sums and Opus's separate Rust probe. No universal Rust correctness proof, source AST equivalence, new executable percentage surrogate or throughput gain is claimed.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/models/mathematical-correspondence.groupant/