Empirical & Molecular Formula Finder mechanism

Model scope

The core stoichiometric equations are standard, but the product is not fully specification-complete. The exact ambiguities requiring review are the ratio-rounding tolerance and multiplier-search policy, treatment of zero elements, percentage normalization and validation, and acceptance criteria for the molecular multiplier.

• moles=mass/M is correct only when mass and molar mass use compatible units; the specification does not state this explicitly.
• Dividing every mole value by the smallest is correct for nonzero elemental amounts, but the specification does not define how zero-valued elements are handled.
• multiply to whole-number ratio is underspecified: it needs a tolerance for recognizing near-integer ratios and a defined multiplier-search limit. Blind multiplication can produce incorrect formulas from rounded composition data.
• n=M_molecular/M_empirical is correct only when the result is a positive integer within a defined tolerance. The specification does not require molecular molar mass to be at least the empirical formula mass or reject noninteger results.
• The percent-composition workflow does not explicitly state that percentages are placed on a common 100-mass-unit basis and that the percentages should sum to approximately 100%.

Units and conventions

• Mass and molar mass must use compatible units, such as grams and grams per mole; any common mass unit is acceptable if used consistently.
• Percentage composition is interpreted as grams of each element in a 100 g sample, or an equivalent common mass basis.
• Atomic weights are dimensionless relative atomic masses used numerically in g/mol for molar-mass calculations.
• Empirical-formula recognition requires a rounding tolerance because measured or rounded composition data rarely produce exact integer ratios.
• The molecular molar mass input is assumed to be in g/mol and uses the same atomic-weight table as the empirical-formula mass.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "composition_type": "percent",
    "percent_composition": {
      "C": 40,
      "H": 6.71,
      "O": 53.29
    },
    "atomic_weights": {
      "C": 12.011,
      "H": 1.008,
      "O": 15.999
    },
    "molecular_molar_mass_g_per_mol": 180.156
  },
  "expected_outputs": {
    "empirical_formula": "CH2O",
    "molecular_formula": "C6H12O6",
    "ratio_table": {
      "C": 1,
      "H": 1.999,
      "O": 1
    },
    "empirical_molar_mass_g_per_mol": 30.026,
    "molecular_multiplier": 6
  },
  "working": "Use a 100 g basis: C moles = 40.00/12.011 = 3.33028; H moles = 6.71/1.008 = 6.65675; O moles = 53.29/15.999 = 3.33083. Divide by the smallest value, 3.33028: C = 1.00000; H = 6.65675/3.33028 = 1.99886, approximately 2; O = 3.33083/3.33028 = 1.00017, approximately 1. Empirical formula = CH2O. Empirical mass = 12.011 + (2 x 1.008) + 15.999 = 30.026 g/mol. Molecular multiplier = 180.156/30.026 = 6. Molecular formula = C6H12O6."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-mass element produces a zero smallest-mole value and therefore undefined normalization; the instrument must reject it. Unit interpretation of molecular molar mass can also change the molecular formula by a factor of 1000 if not explicitly constrained.

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-tranche2/batch10-output.jsonl
• BOUNDARY_HAZARD_CATALOG.json