flow_check

std.linalg.flow_check · Level L2

Whether f is a feasible flow in the network with capacities C, from vertex 0 to vertex n − 1, as 1 or 0: 0 ≤ f ≤ C on every edge, and inflow equals outflow at every inner vertex. Also its value twice, as the source's net outflow and as the sink's net inflow; for a feasible flow the two are equal.

0 ≤ f ≤ C; Σᵤ f(u, v) = Σ_w f(v, w) for v ≠ 0, n − 1

Signature

flow_check(C: f64[n, n], f: f64[n, n]) → f64[], f64[], f64[]

Requires: n ≥ 2

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
Equal to the reference capacity and conservation checks; the source's net outflow and the sink's net inflow in exact rational arithmetic, on all 40 test cases.
All 120 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:7c68034637dc7d5f9b3cb8c914e25c03cfb34cddcebda4e782f3e4c8f3d6549b

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.flow_check · Ω:flow_check
Pins: sha256:92b35017fc0e3c3ed677ebb6863b04002ca487c975fb4dba3bce44b5c7ff1da1this graph alone
Evidence: sha256:fc8f3606f9639b23c8dec695fa5d85c1290005b089884f64800b8de13cac99a8the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.