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CVP reproduce

engineering.process.capability

Independent re-run pack: fixed input vectors, O3 expected values, oracle version, commands, and the last result summary. This is how a reader moves from “CalculatorX says it passed” to “I can reproduce why it passed.”

Reproduce JSON CVP Manifest O3 table Generator REST checker Calculator

Identity

Calculation version, protocol version, and evidence revision are distinct.

Calculation version
1.0.0
CVP protocol
1.0.0-proposed · proposed
Evidence revision
2026-09-16.o2-o3
Oracle
O3 · mpmath 1.4.1 · 80 dps
Generator
process-capability-mpmath-o3 · seed 20260916.process-capability-o3
Table SHA-256
0bfecdd4b6d6cc36cdb828de51869e94b4b4057ec539f0efb09dae25d24b6c2d

Numerical claim

O3 PASS is a tabulated-vector claim, not a whole-domain proof.

O2: design-stage Cp/Cpk/Cpu/Cpl vs separate-module identities (≤2 ULP). Not Pp/Ppk, not Cpm, not P/T=1/Cp, not Monte Carlo, not an in-control SPC study. ≤2 ULP vs O3 applies only to the published tabulated Cp/Cpk vectors (centered, off-center, negative Cpk, aliases, σ=2, shifted limits, tight). It is not a whole-domain guarantee and does not cover Pp/Ppk, Cpm, P/T, or Monte Carlo simulated indices.

  • Last O3 run 8 / 8
  • Max error observed 0 ULP
  • Threshold ≤ 2 ULP

Commands

Regenerate the table from the public generator. Independent REST check needs only this page's reproduce.json plus stdlib Python — no repo clone and no mpmath. The CVP runner remains a maintainer command.

Regenerate O3 table
python3 generate-process-capability-o3.py after downloading the public generator next to the table
Repo maintainer path
python3 scripts/lib/cvp/oracles/generate-process-capability-o3.py
Independent REST check
Compare POST /api/v1/calc/process-capability against /developers/cvp/reproduce/process-capability-o3-tables.json after downloading check-math-o3-rest.py next to process-capability-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP
npm run cvp:run -- --capability engineering.process.capability
REST check
POST https://www.calculatorx.com/api/v1/calc/process-capability with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 0bfecdd4b6d6cc36cdb828de51869e94b4b4057ec539f0efb09dae25d24b6c2d. Compare each expected_f64 to the production result within the declared ULP threshold.

Tabulated vectors

Every O3 vector used for the ≤2 ULP claim. Expected values come from the published mpmath table, not from the implementation under test.

IDKindInputsExpected (f64)ActualULPStatus
o3-centercentered{"lsl":0,"usl":12,"mu":6,"sigma":1}{"oracle_layer":"analytic","Cp":2,"Cpk":2,"Cpu":2,"Cpl":2}{"Cp":2,"Cpk":2,"Cpu":2,"Cpl":2,"lsl":0,"usl":12,"mu":6,"sigma":1}0PASS
o3-shiftoff-center-high{"lsl":0,"usl":12,"mu":8,"sigma":1}{"oracle_layer":"analytic","Cp":2,"Cpk":1.3333333333333333,"Cpu":1.3333333333333333,"Cpl":2.6666666666666665}{"Cp":2,"Cpk":1.3333333333333333,"Cpu":1.3333333333333333,"Cpl":2.6666666666666665,"lsl":0,"usl":12,"mu":8,"sigma":1}0PASS
o3-shift-lowoff-center-low{"lsl":0,"usl":12,"mu":4,"sigma":1}{"oracle_layer":"analytic","Cp":2,"Cpk":1.3333333333333333,"Cpu":2.6666666666666665,"Cpl":1.3333333333333333}{"Cp":2,"Cpk":1.3333333333333333,"Cpu":2.6666666666666665,"Cpl":1.3333333333333333,"lsl":0,"usl":12,"mu":4,"sigma":1}0PASS
o3-sigma2centered-wider{"lsl":0,"usl":12,"mu":6,"sigma":2}{"oracle_layer":"analytic","Cp":1,"Cpk":1,"Cpu":1,"Cpl":1}{"Cp":1,"Cpk":1,"Cpu":1,"Cpl":1,"lsl":0,"usl":12,"mu":6,"sigma":2}0PASS
o3-unitshifted-limits{"lsl":10,"usl":16,"mu":13,"sigma":1}{"oracle_layer":"analytic","Cp":1,"Cpk":1,"Cpu":1,"Cpl":1}{"Cp":1,"Cpk":1,"Cpu":1,"Cpl":1,"lsl":10,"usl":16,"mu":13,"sigma":1}0PASS
o3-negnegative-cpk{"lsl":0,"usl":12,"mu":14,"sigma":1}{"oracle_layer":"analytic","Cp":2,"Cpk":-0.6666666666666666,"Cpu":-0.6666666666666666,"Cpl":4.666666666666667}{"Cp":2,"Cpk":-0.6666666666666666,"Cpu":-0.6666666666666666,"Cpl":4.666666666666667,"lsl":0,"usl":12,"mu":14,"sigma":1}0PASS
o3-aliasalias{"LSL":0,"USL":12,"mean":6,"std":1}{"oracle_layer":"analytic","Cp":2,"Cpk":2,"Cpu":2,"Cpl":2}{"Cp":2,"Cpk":2,"Cpu":2,"Cpl":2,"lsl":0,"usl":12,"mu":6,"sigma":1}0PASS
o3-tighttight{"lsl":0,"usl":6,"mu":3,"sigma":0.5}{"oracle_layer":"analytic","Cp":2,"Cpk":2,"Cpu":2,"Cpl":2}{"Cp":2,"Cpk":2,"Cpu":2,"Cpl":2,"lsl":0,"usl":6,"mu":3,"sigma":0.5}0PASS