is_proper_coloring

std.linalg.is_proper_coloring · Level L1

Whether a colouring of the vertices is proper, as 1 or 0: no edge joins two vertices of the same colour. Vertices that are not adjacent may share a colour. A proper colouring with k colours shows χ(G) ≤ k, and only that.

[colour(u) ≠ colour(v) for every edge]

Signature

is_proper_coloring(A: f64[n, n], colors: f64[n]) → f64[]

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.
Equal to the reference no edge with equal colours at its ends in exact rational arithmetic, on all 40 test cases.
All 40 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:a4ce0d9a0bd684b3c45dd4f7d6ca1bb9a9f8148cf4c433234673344774862a5e

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.is_proper_coloring · Ω:is_proper_coloring
Pins: sha256:6e53c6b5bbed6f0b86b1ca300e8f6ff91f79515c008c2a6f357ae3a9ade07a8ethis graph alone
Evidence: sha256:a9761db0a1a140949edb23ecbe4a0be60d7df0b211456ff693e9dcee110c51b3the 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.