Truss Determinacy Checker mechanism

Model scope

The exact ambiguity is whether this instrument is intended to report only the planar Maxwell count or to make a definitive structural classification. As written, it claims definitive classification but lacks assumptions and geometry/connectivity checks. Revise the honest label to something such as 'preliminary planar truss determinacy count' unless full stability and rank analysis is added.

• m+r=2j is the planar Maxwell count, not a sufficient test for determinacy, indeterminacy, or stability. Connectivity, support arrangement, member geometry, and joint geometry must also be checked.
• The formulas require an explicit planar, pin-jointed, ideal-truss assumption. A spatial truss generally uses m+r=3j instead.
• m+r>2j indicates a positive count of excess constraints only if the truss is stable and the constraints are independent; it does not by itself prove static indeterminacy.
• m+r<2j indicates a constraint deficiency or possible mechanism, but does not by itself prove instability for every geometry.
• For m+r<2j, m+r-2j is a negative deficiency/index, not technically a degree of static indeterminacy. The output definition must distinguish these.

Units and conventions

• m, r, and j are dimensionless, nonnegative integer counts: members, independent reaction components, and joints.
• The count assumes a planar pin-jointed truss analyzed with two equilibrium equations per joint.
• Each reaction component is counted independently; a pin support normally contributes two reactions and a roller support normally contributes one in a planar model.
• No length, force, or other physical units are involved.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "m": 3,
    "r": 3,
    "j": 3
  },
  "expected_outputs": {
    "classification": "determinate",
    "degree_of_indeterminacy": 0
  },
  "working": "m+r = 3+3 = 6. 2j = 2×3 = 6. Since 6 = 6, classification = determinate. Degree = (m+r)−2j = 6−6 = 0."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The classifier has no division-by-zero operation, but extreme counts overflow JavaScript arithmetic and produce an infinite degree. More importantly, the meaning of r is convention-sensitive: counting supports instead of scalar reaction components can change the computed reaction count and classification unless the support model is explicitly defined.

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