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CVP reproduce

mechanical.statics.end_triangle_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
end-triangle-deflection-mpmath-o3 · seed 20260927.end-triangle-deflection-o3
Table SHA-256
6434e57a2e1935caf683d5c007751aa7b58c5cac0826eedff054bfc709310a92

Numerical claim

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

O2: delta vs a separate-module identity (≤2 ULP). Not center-peaked triangle, not a cantilever, and not a station curve. ≤2 ULP vs O3 applies only to the published tabulated end-triangle-deflection vectors.

  • Last O3 run 8 / 8
  • Max error observed 1 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-end-triangle-deflection-o3.py after downloading the public generator next to the table
Repo maintainer path
python3 scripts/lib/cvp/oracles/generate-end-triangle-deflection-o3.py
Independent REST check
Compare POST /api/v1/calc/end-triangle-deflection against /developers/cvp/reproduce/end-triangle-deflection-o3-tables.json after downloading check-math-o3-rest.py next to end-triangle-deflection-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP
npm run cvp:run -- --capability mechanical.statics.end_triangle_deflection
REST check
POST https://www.calculatorx.com/api/v1/calc/end-triangle-deflection with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 6434e57a2e1935caf683d5c007751aa7b58c5cac0826eedff054bfc709310a92. 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{"w0":"640","L":"1","E":"1","I":"1"}{"oracle_layer":"analytic","delta":3,"w0":640,"L":1,"E":1,"I":1}{"model":"end_triangle_deflection","w0":640,"L":1,"E":1,"I":1,"delta":3,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-SISI{"w0":"1000","L":"2","E":"200e9","I":"1e-5"}{"oracle_layer":"analytic","delta":0.0000375,"w0":1000,"L":2,"E":200000000000,"I":0.00001}{"model":"end_triangle_deflection","w0":1000,"L":2,"E":200000000000,"I":0.00001,"delta":0.0000375,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-aliasalias{"w":"1280","span":"1","modulus":"1","Ix":"1"}{"oracle_layer":"analytic","delta":6,"w0":1280,"L":1,"E":1,"I":1}{"model":"end_triangle_deflection","w0":1280,"L":1,"E":1,"I":1,"delta":6,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-awkwardawkward{"w0":"13.7","L":"3.5","E":"210000","I":"0.83"}{"oracle_layer":"analytic","delta":0.000055288733057228915,"w0":13.7,"L":3.5,"E":210000,"I":0.83}{"model":"end_triangle_deflection","w0":13.7,"L":3.5,"E":210000,"I":0.83,"delta":0.00005528873305722891,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}1PASS
o3-negsigned{"w0":"-640","L":"1","E":"1","I":"1"}{"oracle_layer":"analytic","delta":-3,"w0":-640,"L":1,"E":1,"I":1}{"model":"end_triangle_deflection","w0":-640,"L":1,"E":1,"I":1,"delta":-3,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-smallsmall{"w0":"10","L":"1","E":"1000","I":"0.01"}{"oracle_layer":"analytic","delta":0.0046875,"w0":10,"L":1,"E":1000,"I":0.01}{"model":"end_triangle_deflection","w0":10,"L":1,"E":1000,"I":0.01,"delta":0.0046875,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-stiffstiff{"w0":"500","L":"1.5","E":"210e9","I":"2e-4"}{"oracle_layer":"analytic","delta":2.825055803571429e-7,"w0":500,"L":1.5,"E":210000000000,"I":0.0002}{"model":"end_triangle_deflection","w0":500,"L":1.5,"E":210000000000,"I":0.0002,"delta":2.825055803571429e-7,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS
o3-longlong{"w0":"200","L":"4","E":"70e9","I":"5e-5"}{"oracle_layer":"analytic","delta":0.00006857142857142857,"w0":200,"L":4,"E":70000000000,"I":0.00005}{"model":"end_triangle_deflection","w0":200,"L":4,"E":70000000000,"I":0.00005,"delta":0.00006857142857142857,"solver":"simply supported end-peaked triangle","convention":"Simply supported span. Intensity is w0 at both supports and 0 at midspan. Midspan δ = 3 w0 L⁴/(640 E I). Added to the center-peaked triangle of the same w0, this recovers the uniform load w0. Positive w0 is the positive deflection direction. I is an input."}0PASS