Source: https://guthlabs.ai/docs/instruments/nuclear-binding-energy-calculator/mechanism/

instrument mechanism / verified-clean

# Nuclear Binding Energy Calculator mechanism

The inspectable method record for Nuclear Binding Energy Calculator, kept separate from implementation and qualification.

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

## Model scope

The energy relation E_b=Δm c² is standard, but the mass convention is not. The instrument should explicitly branch between nuclear-mass input, using Z m_p+N m_n−M_nucleus, and atomic-mass input, using Z m_H+N m_n−M_atom. Because the current specification claims to accept atomic masses while prescribing only the nuclear-mass formula, it fails verification. The honest label should disclose the atomic-versus-nuclear mass convention, the isotope-table source/version, and the neglected electron-binding-energy correction.

- The stated mass-defect formula Δm=Z m_p+N m_n−M_nucleus is correct only when M_nucleus is a nuclear mass excluding electrons. The inputs explicitly allow measured atomic masses and isotope-table presets, which normally are atomic masses including Z electrons.

- For an atomic mass M_atom, the standard formula is Δm=Z m_H+N m_n−M_atom, where m_H is the neutral hydrogen-atom mass; equivalently, electron masses and electron binding-energy corrections must be handled explicitly.

- The specification does not state the formula for binding energy per nucleon; it should be BE/A, with A=Z+N.

- The specification does not define the mass unit or the exact isotope-table mass convention, so numerical results are ambiguous.

## Units and conventions

- Test vectors use atomic masses in unified atomic mass units (u), with m_H=1.00782503223 u, m_n=1.00866491595 u, and 1 u c²=931.49410242 MeV.

- Atomic masses include the electrons associated with the Z protons; the corrected atomic-mass formula therefore uses neutral hydrogen-atom mass m_H rather than bare proton mass m_p.

- A=Z+N is dimensionless, mass defect is reported in u, total binding energy in MeV, and binding energy per nucleon in MeV/nucleon.

- Electron binding energies are neglected, as is standard for nuclear binding-energy calculations at this precision.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "Z": 1,
    "N": 0,
    "A": 1,
    "mass_type": "atomic",
    "measured_atomic_mass_u": 1.00782503223
  },
  "expected_outputs": {
    "mass_defect_u": 0,
    "binding_energy_MeV": 0,
    "binding_energy_per_nucleon_MeV": 0
  },
  "working": "Use Δm=Z m_H+N m_n−M_atom. Δm=(1)(1.00782503223)+(0)(1.00866491595)−1.00782503223=0 u. BE=0×931.49410242=0 MeV. BE/A=0/1=0 MeV/nucleon. This is the zero-binding edge case."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification exposes a division-by-zero case at A=Z+N=0 and does not clearly define whether the supplied measured mass is atomic or nuclear. Applying the stated nuclear-mass formula directly to an atomic mass produces materially incorrect binding energies.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/nuclear-binding-energy-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/nuclear-binding-energy-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/nuclear-binding-energy-calculator/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`