is_filtration

std.stats.is_filtration · Level L2

Whether a sequence of at least two partitions of one finite sample space (row t gives each outcome's block label at time t) is a filtration, as 1 or 0: each partition refines the one before, which is the inclusion F_s ⊆ F_t of the σ-algebras they generate, every pair of outcomes checked. A Scan of refine_step. A filtration only nests information; it does not make a process adapted, natural or Markov.

F_s ⊆ F_t for s ≤ t

Signature

is_filtration(L: f64[T, n]) → f64[]

Requires: T ≥ 2

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 with T ≥ 2.
Equal to the reference each partition refines the one before, every pair in 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

Calls

refine_step

Called by

martingale_check

sha256:a44f1023314637fc19f12e2b7d9963ebda383a07a25505c5c2b9f8616e249087

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.is_filtration · Ω:is_filtration
Pins: sha256:21a906950e579d9a3ce037abc69be5e3feeb92f6d39597fff2268c77831e38fdthis graph and the 1 it reaches through calls
Evidence: sha256:669599194ccbbd8162ede986be8676f9300c2698c3598856a4515f26452302bathe 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.