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CVP reproduce

mechanical.statics.cantilever_outer_at_deflection

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.”

Identity

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

Calculation version
1.0.0
CVP protocol
1.0.0-proposed · proposed
Evidence revision
2026-09-27.o2-o3
Oracle
O3 · mpmath 1.4.1 · 80 dps
Generator
cantilever-outer-at-mpmath-o3 · seed 20260927.cantilever-outer-at-o3
Table SHA-256
760a68748162e936b5d9dbb6fcc4988c431502b53fcefa3d43faab7aeebf9be1

Numerical claim

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

O2: delta vs a separate-module identity (≤2 ULP). Not tip-only under the same outer uniform load, and not a simply supported span. ≤2 ULP vs O3 applies only to the published tabulated cantilever-outer-at vectors.

  • Last O3 run 8 / 8
  • Max error observed 2 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-cantilever-outer-at-o3.py after downloading the public generator next to the table
Repo maintainer path
python3 scripts/lib/cvp/oracles/generate-cantilever-outer-at-o3.py
Independent REST check
Compare POST /api/v1/calc/cantilever-outer-at against /developers/cvp/reproduce/cantilever-outer-at-o3-tables.json after downloading check-math-o3-rest.py next to cantilever-outer-at-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP
npm run cvp:run -- --capability mechanical.statics.cantilever_outer_at_deflection
REST check
POST https://www.calculatorx.com/api/v1/calc/cantilever-outer-at with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 760a68748162e936b5d9dbb6fcc4988c431502b53fcefa3d43faab7aeebf9be1. 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-checkcheck{"w":"24","a":"1","x":"2","L":"2","E":"1","I":"1"}{"oracle_layer":"analytic","delta":41,"w":24,"a":1,"x":2,"L":2,"E":1,"I":1}{"model":"cantilever_outer_at_deflection","w":24,"a":1,"x":2,"L":2,"E":1,"I":1,"delta":41,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}0PASS
o3-SISI{"w":"1000","a":"1","x":"2","L":"2","E":"200000000000","I":"0.00001"}{"oracle_layer":"analytic","delta":0.0008541666666666667,"w":1000,"a":1,"x":2,"L":2,"E":200000000000,"I":0.00001}{"model":"cantilever_outer_at_deflection","w":1000,"a":1,"x":2,"L":2,"E":200000000000,"I":0.00001,"delta":0.0008541666666666665,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}2PASS
o3-aliasalias{"intensity":"48","span":"2","modulus":"1","Ix":"1","a":"1","x":"2"}{"oracle_layer":"analytic","delta":82,"w":48,"a":1,"x":2,"L":2,"E":1,"I":1}{"model":"cantilever_outer_at_deflection","w":48,"a":1,"x":2,"L":2,"E":1,"I":1,"delta":82,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}0PASS
o3-awkwardawkward{"w":"13.7","a":"1.2","x":"1.5","L":"2","E":"210000","I":"0.83"}{"oracle_layer":"analytic","delta":0.00007784064113597246,"w":13.7,"a":1.2,"x":1.5,"L":2,"E":210000,"I":0.83}{"model":"cantilever_outer_at_deflection","w":13.7,"a":1.2,"x":1.5,"L":2,"E":210000,"I":0.83,"delta":0.00007784064113597245,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}1PASS
o3-negsigned{"w":"-24","a":"1","x":"2","L":"2","E":"1","I":"1"}{"oracle_layer":"analytic","delta":-41,"w":-24,"a":1,"x":2,"L":2,"E":1,"I":1}{"model":"cantilever_outer_at_deflection","w":-24,"a":1,"x":2,"L":2,"E":1,"I":1,"delta":-41,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}0PASS
o3-smallsmall{"w":"10","a":"0.5","x":"1","L":"2","E":"1000","I":"0.01"}{"oracle_layer":"analytic","delta":0.6901041666666666,"w":10,"a":0.5,"x":1,"L":2,"E":1000,"I":0.01}{"model":"cantilever_outer_at_deflection","w":10,"a":0.5,"x":1,"L":2,"E":1000,"I":0.01,"delta":0.6901041666666667,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}1PASS
o3-stiffstiff{"w":"500","a":"1","x":"2","L":"2","E":"210e9","I":"2e-4"}{"oracle_layer":"analytic","delta":0.00002033730158730159,"w":500,"a":1,"x":2,"L":2,"E":210000000000,"I":0.0002}{"model":"cantilever_outer_at_deflection","w":500,"a":1,"x":2,"L":2,"E":210000000000,"I":0.0002,"delta":0.00002033730158730159,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}0PASS
o3-longlong{"w":"200","a":"1","x":"2","L":"4","E":"70e9","I":"5e-5"}{"oracle_layer":"analytic","delta":0.0006309523809523809,"w":200,"a":1,"x":2,"L":4,"E":70000000000,"I":0.00005}{"model":"cantilever_outer_at_deflection","w":200,"a":1,"x":2,"L":4,"E":70000000000,"I":0.00005,"delta":0.0006309523809523809,"solver":"cantilever outer uniform at a station","convention":"Unloaded from the wall to a, then uniform intensity w to the tip. The curve is the full uniform curve minus the partial-from-wall curve. x = L is the outer-uniform tip page. a = 0 is the full uniform curve."}0PASS