is_hausdorff
std.topology.is_hausdorff · Level L2Whether a finite topological space is Hausdorff, as 1 or 0: every two distinct points x ≠ y lie in disjoint open sets U ∋ x and V ∋ y, every pair checked. One failing pair disproves it. A finite Hausdorff space is discrete, which does not carry over to infinite spaces; the empty space and a single point are Hausdorff.
Signature
is_hausdorff(tau: f64[m, 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
for every pair of points, a disjoint pair of open setsin 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.
- 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:aeb1d24ca1dda96e763c72dd59526f00cac7286dd51ab24a4b7c276e30322e87The 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_hausdorff · Ω:is_hausdorff
- Pins
sha256:5ca58dc9281a5cb36d65c062182bd3a9298425beaa3605b1192e5ff07cfb16a7this graph alone- Evidence
sha256:b0d60d06e62c02ad1e230caf519c3da15f207b734fcfeb9ac5dae57363a350cdthe 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.