chromatic_step
std.linalg.chromatic_step · Level L3Try one more colour: k ← k + 1 and run k_colorable. The body chromatic_number runs.
k ← k + 1; found ← k_colorable(A, k)
Signature
chromatic_step(k: f64[], found: f64[], col: f64[n], A: f64[n, n]) → f64[], f64[], f64[n]
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
k + 1, k_colorable(A, k + 1)in exact rational arithmetic, on all 40 test cases. - All 206 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
sha256:4da49a7afb345752013c84d5d323db3f20ed8525444ea164944a7bd598fffde7The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.chromatic_step · Ω:chromatic_step
- Pins
sha256:d6f2b1b22a5d5a810cd0de977bdb5c571f6de78645b016735ea96a0c242975abthis graph and the 3 it reaches through calls- Evidence
sha256:15f7bb37080951554f06748c5f73d822893baf63d4ab77daf89438e8ac22e7b9the 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.