Source: https://guthlabs.ai/docs/instruments/1d-elastic-collision-solver/mechanism/

instrument mechanism / verified-clean

# 1D Elastic Collision Solver mechanism

The inspectable method record for 1D Elastic Collision Solver, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The collision formulas are correct under the stated physical assumptions. Verdict is NEEDS_REVIEW because the exact v2' formula and the KE-check definition/tolerance are ambiguous, and the honest label is 'n/a' despite the claim requiring explicit assumptions about isolation, one-dimensionality, and perfect elasticity.

- The v1' formula is standard for a perfectly elastic 1D collision, but v2' is specified only as 'analogous'; it should be explicitly stated as v2'=((m2-m1)v2+2m1v1)/(m1+m2).

- The advertised KE check has no defined formula, comparison criterion, or numerical tolerance. A standard check would compare KE_initial=0.5*m1*v1^2+0.5*m2*v2^2 with KE_final=0.5*m1*v1'^2+0.5*m2*v2'^2.

## Units and conventions

- m1 and m2 must be positive masses expressed in the same unit; SI kilograms are assumed for the test vectors.

- v1 and v2 must be signed velocities in the same one-dimensional inertial frame, preferably m/s.

- The formulas assume an isolated collision with negligible external impulse and perfectly elastic behavior.

- KE outputs are in joules when masses are in kilograms and velocities are in m/s.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "m1": 2,
    "m2": 3,
    "v1": 5,
    "v2": -1
  },
  "expected_outputs": {
    "v1_prime": -2.2,
    "v2_prime": 3.8,
    "KE_initial": 26.5,
    "KE_final": 26.5,
    "KE_conserved": true
  },
  "working": "m1+m2=2+3=5. v1'=((2-3)*5+2*3*(-1))/5=(-5-6)/5=-11/5=-2.2. v2'=((3-2)*(-1)+2*2*5)/5=(-1+20)/5=19/5=3.8. KE_initial=0.5*2*5^2+0.5*3*(-1)^2=25+1.5=26.5 J. KE_final=0.5*2*(-2.2)^2+0.5*3*(3.8)^2=4.84+21.66=26.5 J."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The formulas produce undefined results when m1+m2=0, and the specification gives no stated input validation for zero or negative masses. The solver also has no explicit collision-applicability branch for receding inputs and no stated sign convention.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/1d-elastic-collision-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/1d-elastic-collision-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/1d-elastic-collision-solver/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`

- `BOUNDARY_HAZARD_CATALOG.json`