basis_step
std.topology.basis_step · Level L3One row of the basis check: for the basis element B_i and every B_j, each point of B_i ∩ B_j lies in some basis element inside B_i ∩ B_j. The body is_basis scans.
x ∈ B_i ∩ B_j ⇒ ∃B_k: x ∈ B_k ⊆ B_i ∩ B_j
Signature
basis_step(ok: f64[], i: f64[], B: 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
every point of every B_i ∩ B_j, against every B_kin 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
sha256:34a3ca8b1b066cf9116cbffc1a63dece463d894ca95228f786e2c9ce90ddb59dThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.topology.basis_step · Ω:basis_step
- Pins
sha256:8872e4eb64191fdc1df76e447ef213d4c911466e7a6d025aa8775ea85830a510this graph alone- Evidence
sha256:fe5983910cede09ee304226b9edc0c3f5d992da550d8b3b4ce205970eea0e2c6the 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.