interior

std.topology.interior · Level L1

The interior of a subset A in a finite topology, as a 0/1 mask: the union of all the open sets contained in A, the largest open subset of A. It depends on the topology; no metric is used.

int A = ∪{U ∈ τ : U ⊆ A}

Signature

interior(tau: f64[m, n], A: f64[n]) → 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 the union of the rows inside A in exact rational arithmetic, on all 40 test cases.
All 150 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

boundary closure is_neighborhood

sha256:9f8a936c9eccbd611040041fd3e2e3eeb55e4aea6bd2be3862fcde353f0a8852

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.interior · Ω:interior
Pins: sha256:85cd91d31e642f72d886aa3d42e92fa096f67271a6c472d01f236cf8f32cdf79this graph alone
Evidence: sha256:07eb2356422952042d549450cfb848c67ab9149c3d07ab3943986b45e6798acdthe 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.