📐algorithm-dinic

The groupant beside algorithms/src/dinic/mod.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

Components

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.

Model text

descriptant

dinic mod.rs

Reject size caps, source, sink, same terminal, then first invalid edge. Allocate paired residual arcs. FIFO BFS fixes levels; monotone cursors and explicit path backtracking exhaust blocking flows. Augment bottlenecks with checked arithmetic. Return reverse residuals and final BFS reachability.

Epoch 2026-10-30: original code/fixtures; scientific attribution in mod.rs. O(V+E) initialization; each phase has O(V+E) failed scans and at most E paths of length at most V. Fewer than V reachable-sink phases: conservative O(V^2 E+V^2+E) time, O(V+E) storage. No recursion. u128 total <=1,000,000*u64::MAX; Overflow defensive under caps/invariants. Allocation failure untyped.

Composition: Reuses max_flow Edge/Flow identity; independent certificates plus secondary Edmonds-Karp values.

Two release runs, seven alternating-order batches: old/new median ratio 28.27/28.46 for 256 disjoint lanes (V=258,E=512,30 calls/batch), 119.88/120.98 for 1024 lanes (V=1026,E=2048,8 calls/batch). Single path V=256: 1.05/1.03 (100 calls/batch); one edge loses: 0.935/0.930, 199 ns versus 186/185 ns (2000 calls/batch). Allocations included, construction excluded. Shape-specific, shared-machine evidence; no universal speedup.

Prospective batching-cost prediction saved before implementation/timing. Wide independent paths support it; tiny cases expose overhead. Exact operations remain exact; no useful percentage-error surrogate metric identified. Partial syntax leaves macros opaque and does not resolve semantics.

approximant

Forward and cost

Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask.

Reject size caps, source, sink, same terminal, then first invalid edge. Allocate paired residual arcs. FIFO BFS fixes levels; monotone cursors and explicit path backtracking exhaust blocking flows. Augment bottlenecks with checked arithmetic. Return reverse residuals and final BFS reachability.

O(V+E) initialization; each phase has O(V+E) failed scans and at most E paths of length at most V. Fewer than V reachable-sink phases: conservative O(V^2 E+V^2+E) time, O(V+E) storage. No recursion. u128 total <=1,000,000*u64::MAX; Overflow defensive under caps/invariants. Allocation failure untyped.

invariant

Invariant

Each residual pair sums to original capacity. Flows respect capacities and conserve mass off terminals. Level paths strictly increase depth; loops have zero flow. Final saturated cut certifies optimum; source-side mask equals residual reachability.

catalog

Typed model family

behavior-complement

Type: behavior_complement. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: U is declared inputs/errors crossed with outputs. C=U minus forward relation R includes wrong first errors, infeasible witnesses and wrong optima/canonical fields. Exact specification, partial Rust correspondence only. Each residual pair sums to original capacity. Flows respect capacities and conserve mass off terminals. Level paths strictly increase depth; loops have zero flow. Final saturated cut certifies optimum; source-side mask equals residual reachability. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

reverse-reconstruction

Type: reverse_reconstruction. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Pre(y)={x in domain | R(x,y)} preserves every compatible input. Traversal history is omitted, graph redundancy creates multiple antecedents, and errors have whole first-failure fibers. No unique inverse or reconstruction executor claimed. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

residual-pairs

Type: conservation_certificate. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Fix e: r_forward+r_reverse=c_e and f_e=r_reverse. Conservation and terminal balance imply feasibility. Final residual cut capacity equals value; verify checks these separately. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

phase-progress

Type: blocking_flow_progress. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: With fixed BFS levels, cursors advance monotonically. Dead children are exhausted before their incoming arc is discarded. Each path saturates a level arc; reverse updates cannot reopen forward level arcs that phase. Next finite sink distance increases. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

tie-trace

Type: deterministic_witness. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Fixed ordered inputs determine FIFO and path selection. Edmonds-Karp comparison equates values, not vectors. A repeated cancellation fixture fixes one rerouted edge to zero. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

capacity-scaling

Type: positive_scale_equivariance. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Positive k with all u64 products fitting preserves residual zero tests and bottleneck order. Flows/value scale by k, source-side bits stay fixed. Fixture executes k=u64::MAX. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

value-fiber

Type: objective_projection_preimage. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Path capacities (1,b), b>=1, all give value 1. Test b=1..7. Objective cannot reconstruct slack capacities; even full Flow remains noninjective. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

validation

Type: first_failure_partition. Subject/revision: algorithms/src/dinic/mod.rs, SHA-256 672bc5ddd53b228e96dc9bcc1021af80ffc3e8ba084c9fe85e53e23dad2deb55. Domain: Directed u64-capacity edges and distinct indexed terminals, V and E at most 1,000,000. Return existing max_flow::Flow: u128 value, per-edge flows and residual source-side mask. Observation: complete public return or named harness result, restricted to the explicitly named projection. Operator: Size cap precedes source, sink, same terminal, then first edge error. Even zero-capacity endpoints are validated. Overflow is defensive, not an allocation guarantee. Approximation: exact specified relation, partial source correspondence; no numerical error budget. Assumptions: standard Rust semantics, successful allocation, trusted compiler/harness and declared coordinate identity. Evidence: Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity. See tests.md for compiled controls. Status: partial_source_derived_model; no semantic AST or general proof.

tests

Finite evidence

Five tests: 729 ternary-capacity three-vertex networks times six terminals (4374 comparisons), all 4096 four-vertex loop-free unit graphs. Independent cuts, conservation, relaxed residual reachability; secondary Edmonds-Karp values. Cancellation, loops, antiparallel/parallel edges, u64::MAX scaling, error precedence, 20,000-vertex path, value ambiguity.

2026-10-30: 356 library unit tests pass twice debug and twice release; identical normalized names/results SHA-256 56550bbf2b2f3d4999f9d5f3ea0230762f4ef2bb54a8a850d3687daf0129943c. This file contributes five tests or their production subject. Strict algorithm all-target Clippy and narrow rustfmt pass.

Compiled control: Initial zero value becomes one; exhaustive_weighted_cuts rejects. Log SHA-256 b496ace121fd13bf8bc0ec50c96f297d0a3c0024bd6edee016416f2c98ca9d12. Named assertion failure, not compile failure. Six mutants restored byte-for-byte before repeated positives.

Two release runs, seven alternating-order batches: old/new median ratio 28.27/28.46 for 256 disjoint lanes (V=258,E=512,30 calls/batch), 119.88/120.98 for 1024 lanes (V=1026,E=2048,8 calls/batch). Single path V=256: 1.05/1.03 (100 calls/batch); one edge loses: 0.935/0.930, 199 ns versus 186/185 ns (2000 calls/batch). Allocations included, construction excluded. Shape-specific, shared-machine evidence; no universal speedup.

Timing logs SHA-256 b3fca25c0729a0edecefdf1c4914f973f761be705db618171b159f4ac96ad7c3 and 9e8b9c417dfc0dfda48f1446825054bfca985f2aa96dea370843c1184e7b020d; Rust harness SHA-256 f78acc0796bf87f2e32ae559c46519badb9b3219b1ed449a56ca5362cb166799; prospective derivation SHA-256 41f9013788fa8bdce512d82f7922287ed2bd9c87bd84dbfca26180aa4d34a03d.

Raw logs external. No live parser/teacher/GPU/course/held-out runs.

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