Purity Engine — Physical-Existence Floor Search

Numerical radial eigenstate—

Schrödinger ↔ Dirac energy—

Independent floor verdicts—

Integrity residual—

Existence search & veto log

Recursive calculation & audit chain

Numeric operator walk · electronic energy and forces

Audit roots to begin.

Integer/rational inputs → integrals → eigenproblem → normalization → forces → total Hamiltonian. Missing operators defer their dependent families; independent calculations continue. No material-name or geometry catalog.

Electronic calculations appear here.

Electron spin field (T): Bx By Bz

Branch and reconvergence graph

Every two-carrier solve compares separate spatial-spectrum routes, energy decomposition, normalization and particle-number reconstruction. Shared premises and blocked dependents are explicit.

Fermion occupation and finite-spectrum thermal audit

(Z,Ne)=(2,2), three spherical basis functions. Computed interacting levels, zero-field spin degeneracies. Not a complete physical equilibrium partition function.

θ=kBT/Eh

Dependency and proportionality audit

Expression-inferred dimensions, shared-root sensitivities, and model-specific scaling checks. Numeric configuration identities decode exactly. Geometry edits require a new Hamiltonian calculation.

Interacting two-carrier operator · fixed nuclear centre

Antisymmetric states; Coulomb and exchange integrals; 2S=0 and 2S=2; nested spherical bases. Nuclear existence and relativistic corrections remain unresolved.

Signed nuclear charge Basis exponent

Historical branch review

Reviewed three archived branches. Retained ideas: dependency floors, exact discrete arithmetic, total-energy differences, reversible checks and time response.

Excluded: geometric replacements for measured constants, modulo-selected defects/lattices, assumed occupations, invented rates and renormalized Euler propagation. Export includes source hashes and findings by function.

Projected molecular electric response · (1,1,1,2,1)

Constant axial field; two parity states; fixed nuclei. Ten numerical obligations check this projected operator. Full-space response remains unresolved.

Field (atomic units) Time (atomic units)

Equipped: (Z,N,Ne)=(1,0,1) radial operator and (Z1,Z2,Ne)=(1,1,1) fixed-nuclei variational energy/forces. The latter walks every positive rational separation and exponential-basis exponent by increasing integer complexity. Each step also solves nested 2, 4, 6 and 8 function bases and checks energy lowering, overlap conditioning and eigen-residuals. Analytic forces currently refer to the 2-function basis. A third interleaved domain walks integer Z and rational exponents for two interacting carriers in nested spherical bases, with both spin sectors and conjugate Hamiltonians. Full-basis convergence, periodic hosts and vacancy reconstruction require further operators.