refine_step

std.stats.refine_step · Level L1

One step of a filtration check: the later partition (labels b2) refines the earlier one (labels a), so two outcomes in one block later were in one block before. The body is_filtration scans.

b2(x) = b2(y) ⇒ a(x) = a(y)

Signature

refine_step(ok: f64[], a: f64[n], b2: 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 every pair together later is together earlier 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

—

Called by

is_filtration

sha256:e4dc5bb2bf3d70dc46814558e743305bfcb92cf9e837436d6958660338c64fb0

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

Control handle

Symbol: Ω:std.stats.refine_step · Ω:refine_step
Pins: sha256:074ec08c08a27c50a02226103f98dfe60587bff79f21d174a6317b00b1b38702this graph alone
Evidence: sha256:d9e2ef72694d37252949fbaf7b094ea1130aba993be6fd4d5a27f8637d95da2bthe 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.