--- title: "algorithm-li-chao-tree-tests — Mova code model" description: "Mova code model of algorithms/src/li_chao_tree/tests.rs: components with their labels, obernants and the model text." url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/li_chao_tree/tests.rs.groupant/" --- Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants** This page as HTML: # algorithm-li-chao-tree-tests The groupant beside algorithms/src/li_chao_tree/tests.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 - **kind:** groupant - **status:** partial source derived instance - **source:** [`algorithms/src/li_chao_tree/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/li_chao_tree/tests.rs) - **source SHA-256:** `18732adb45262302…` - **repository folder:** [`algorithms/src/li_chao_tree/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/li_chao_tree/tests.rs.groupant) - **repository commit:** `855da7bd4a7b` > **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 | [Forward](#forward) | | **ast** | partial | `syntax.json` | | **cost** | conditional | [Cost](#cost) | | **descriptant** | present | [descriptant](#descriptant) | | **invariant** | partial | [Invariant](#invariant) | | **tests** | bounded executed | [evidence](#evidence) | ## 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 relational specification | [behavior_complement](#behavior-complement) | | `reverse_reconstruction` | reverse_reconstruction | partial relational specification | [reverse_reconstruction](#reverse-reconstruction) | | `oracle_independence` | oracle_independence | partial relational specification | [oracle_independence](#oracle-independence) | | `control_scope` | control_scope | partial relational specification | [control_scope](#control-scope) | ## Model text ### descriptant #### li_chao_tree epoch memory 2026-10-30: choose exact bounded integer computation before implementation. 15625 triples, 234375 exact query comparisons, plus 2^20 identical insertions and accepted/rejected coordinate cap fixtures. Finite bounded test cost; no timing benchmark. Retain the distinction between observation and internal representation: query ties preserve insertion identity; connectivity results preserve only partitions. The compiled faulty reduction/rollback controls establish sensitivity at named assertions. Original code follows the classic descriptions cited in module documentation; no copied solution. No performance gain or approximate substitute claimed. These small files use file-level models, with no nested fragments. Source-bound partial syntax is generated twice identically; macro expansion and semantic AST remain absent. Allocation-failure behavior is not fault-injected. ### model ## li_chao_tree tests.rs ### Forward Execute all 25^3 ordered triples of slopes/intercepts in -2..=2. After each insertion query five coordinates and compare literal enumeration of all inserted lines, retaining earliest ID. Add MIN/MAX, duplicate-coordinate, empty/unknown, cap and tie fixtures. ### Invariant Fixture order and integer arithmetic deterministic; independent oracles do not invoke production helpers. Test outcome observes scheduled assertions only, not all possible inputs or allocation effects. ### Cost 15625 triples, 234375 exact query comparisons, plus 2^20 identical insertions and accepted/rejected coordinate cap fixtures. Finite bounded test cost; no timing benchmark. ### behavior_complement Universe: implementations paired with normal/panic outcomes on the fixed fixtures. Normal completion is excluded if a returned value/ID disagrees with direct enumeration, if a tie selects a later ID, or boundary errors/cap state preservation differ. Unsampled implementations remain unconstrained. ### reverse_reconstruction Normal completion retains all implementations agreeing on the finite observations, including different algorithms and faults outside these fixtures. A failing named assertion yields a concrete witness, not a unique faulty source reconstruction. Finite success does not recover implementation identity. ### oracle_independence Execute all 25^3 ordered triples of slopes/intercepts in -2..=2. After each insertion query five coordinates and compare literal enumeration of all inserted lines, retaining earliest ID. Add MIN/MAX, duplicate-coordinate, empty/unknown, cap and tie fixtures. ### control_scope One compiled production mutation is required to fail a named assertion. Exact saved bytes are restored before repeated positive runs. This witnesses sensitivity to that fault only; no exhaustive fault detection follows. ### evidence #### Evidence, 2026-10-30 Source SHA-256: 18732adb4526230276350a3c3a452f515e061ec84a5ac4c6956e604659c4e05f. Three tests for this algorithm pass twice debug and twice release with identical normalized names/results. Strict all-target Clippy and narrow rustfmt pass. One production mutant per algorithm compiles and fails a named assertion, then exact source bytes are restored. 15625 triples, 234375 exact query comparisons, plus 2^20 identical insertions and accepted/rejected coordinate cap fixtures. Finite bounded test cost; no timing benchmark. Li Chao mutant changes query min reduction to max and fails exhaustive_envelopes. Connectivity mutant suppresses rollback and fails rollback_and_lifecycle. Six tests and two production controls total across the two algorithms. Finite evidence is not general correctness proof. No live parser/teacher/GPU, full-course or performance evidence. External raw log hashes: - li_chao_tree-debug-1.log: 687640980e1bf24e31543834663e3c5cbe1e5a7bf2f6cc1222b97853776fe233 - li_chao_tree-debug-2.log: 72852b921325550691d13252bc4c347c280f77b7e63f8b16dec50db5d1363de2 - li_chao_tree-release-1.log: 6d888dbb1cf62c740a1a7a550c6af192310831d058877a028d485b243514a7b9 - li_chao_tree-release-2.log: f2a4cd2701f54bb3d33a54356ef487d748e7398b73ba2188c6a3c6a6ac412fb3 - mutant-li_chao_tree.log: 9a3bd984ae011320809e9937a4af599b90a46409e39c402374477d59448858a4 - clippy.log: 999837d8357e2d33f39923fa376807b31cc10864ed60f5c06e089e5eae83c248 - check.log: 3b85fdb7533db33eb312c32b2094a66227d8ed4399e049ad5930461499eaf4de Structural receipts: four file sidecars, eighteen typed views (five per production file, four per tests file), zero fragments, four source-bound partial syntax projections. Each syntax artifact and groupant report generated twice identically. Temporary scaffold includes the base registry unchanged; no shared registry edits committed. Initial own-only scaffold was rejected for excluding existing ownership declarations, then corrected by including base nodes. - groupants-1.json: 07c0b20d6224715f6344d25485b47d19a0bca2cf20e787b5cd4848c073d4d3cf - groupants-2.json: 07c0b20d6224715f6344d25485b47d19a0bca2cf20e787b5cd4848c073d4d3cf - changed.json: 2684631f0c0110701eb8bfc5d8a70f9973f8634f19c5aa6c24c59a7e6f377c15