boundary

std.topology.boundary · Level L1

The boundary of a subset A in a finite topology, as a 0/1 mask: cl A \ int A. A and its complement have the same boundary; ∅ and X have none.

∂A = cl A \ int A

Signature

boundary(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 closure minus interior in exact rational arithmetic, on all 40 test cases.
All 138 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

closure interior

Called by

—

sha256:d53bb669d92c6ea5514549c0f816966c05417eb8a6863dbaea53c5b0466f1735

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.boundary · Ω:boundary
Pins: sha256:8c4809afbd5da0b62ad562822c3b95802478e0261e5c5f945a0075fa5c8f5e64this graph and the 2 it reaches through calls
Evidence: sha256:50f8d7bd3c43bd2967b8f4ac70cee5b810a2abd145bf193abe7156dd7f0e5234the 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.