1D Elastic Collision Solver mechanism

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

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