is_open

std.topology.is_open · Level L1

Whether a subset A (a 0/1 mask) is open in a finite topology τ, as 1 or 0: A is one of the listed open sets.

[A ∈ τ]

Signature

is_open(tau: f64[m, n], A: 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 A among the rows 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_closed quotient_open

sha256:10831a2d591dcc0eef694689d312aa2fbfe0412c50abf1e584d7c8932edfcf7f

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

Control handle

Symbol: Ω:std.topology.is_open · Ω:is_open
Pins: sha256:27edd3940430955fa0a289fcfd3815a23f4c0cd0bb976631472f6f026d03ed39this graph alone
Evidence: sha256:51eb767a7b74d5e297f951421663fc1c47781e266dcdb46fbeb15e6bcc3c4894the 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.