process_joint
std.stats.process_joint · Level L3The two-time joint law P(X_{t1} = s, X_{t2} = s′) of a finite-horizon process given by its complete list of paths and their probabilities.
P(X_{t1} = s, X_{t2} = s′)
Signature
process_joint(paths: i64[N, T], p: f64[N], states: f64[k], t1: i64[], t2: i64[]) → f64[k, k]
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 masses of the paths through s at t1 and s′ at t2in exact rational arithmetic, on all 40 test cases. - All 1,008 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
—
Called by
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sha256:2f6c3feec76ac60b4647bbc0b6565b5b53394bcfd2a4867dee12b7a4328d8803The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.stats.process_joint · Ω:process_joint
- Pins
sha256:f1ad5604485e08761ad93359dd3eca8a9efdcab962b9f3a1b66c2714445096aethis graph alone- Evidence
sha256:a0adb972331cf8c163ce1647c12de45b4dc54f098813ff71fad4ed2260a3e463the 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.