orbit_stabilizer
std.algebra.orbit_stabilizer · Level L3The orbit-stabilizer theorem on a finite action, for the point x: |G·x|, |Stab(x)|, and whether |G| = |G·x|·|Stab(x)|, as 1 or 0. It holds for every action, faithful or not: g ↦ g·x maps G onto the orbit, and the fibre over y = g₀·x is the coset g₀·Stab(x).
Signature
orbit_stabilizer(T: i64[n, n], A: i64[n, k], x: f64[]) → f64[], f64[], 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
the set of g·x and the count of g fixing xin exact rational arithmetic, on all 40 test cases. - All 120 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
sha256:855679207be638919c97716075db61770c7eb6badb9e499b8c312e2d6382e50bThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.algebra.orbit_stabilizer · Ω:orbit_stabilizer
- Pins
sha256:619a8c62c8381c0d56cb1c03e01b930c637771f63314a0ff03f36ec11da8a426this graph and the 1 it reaches through calls- Evidence
sha256:5ac729a44c49435746950da1c2fe758d6161efc9a75f64d2d1c915ac54d9a61athe 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.