Source: https://guthlabs.ai/docs/instruments/1d-2d-inelastic-collision-solver-coefficient-of-restitution/implementation/

instrument implementation / implementation-contract

# 1D/2D Inelastic Collision Solver (coefficient of restitution) implementation

A source-bound implementation contract for 1D/2D Inelastic Collision Solver (coefficient of restitution); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-215

**Effect**: Computation or source lookup only

## Input and validation requirements

Zero total mass causes division by zero and an underdetermined collision, so the solver must reject that input. The e>1 branch is also outside the stated physical domain and must be rejected rather than silently treated as an ordinary inelastic collision.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "m1": 2,
    "m2": 3,
    "v1": 5,
    "v2": -1,
    "e": 0.5,
    "mass_units": "kg",
    "velocity_units": "m/s"
  },
  "expected_outputs": {
    "v1_prime": -0.4,
    "v2_prime": 2.6,
    "energy_lost": 16.2
  },
  "working": "M=m1+m2=2+3=5. Initial momentum p=2(5)+3(-1)=10−3=7. Initial relative velocity v1−v2=5−(−1)=6. Final relative velocity v2'−v1'=e(v1−v2)=0.5(6)=3. Solve v1'=(p−m2·3)/M=(7−3·3)/5=(7−9)/5=−0.4. Solve v2'=v1'+3=−0.4+3=2.6. Initial KE=0.5(2)(5²)+0.5(3)((−1)²)=25+1.5=26.5 J. Final KE=0.5(2)((−0.4)²)+0.5(3)(2.6²)=0.16+10.14=10.3 J. Energy lost=26.5−10.3=16.2 J."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/1d-2d-inelastic-collision-solver-coefficient-of-restitution/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/1d-2d-inelastic-collision-solver-coefficient-of-restitution/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/1d-2d-inelastic-collision-solver-coefficient-of-restitution/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`