Generalized Atomic Weight Descriptor (GAWD)

GAWD (Generalized Atomic Weight Descriptor) is a deterministic, composition-first engine for direct computation of attenuation crossover coordinates from chemical formula only.

Scientific Position

GAWD was developed against legacy attenuation-reference behavior but does not depend on runtime legacy lookup to produce predictions. Its central claim is that a substantial portion of the attenuation crossover landscape can be recovered directly from stoichiometric moment structure, with bounded atomic-regime refinements where required.

Core Idea

GAWD reduces a compound to a compact family of composition moments built from:

• elemental mass fractions
• atomic number
• atomic mass

These moments drive direct laws for the main crossover coordinates. Where atomic-regime structure matters, GAWD applies tightly bounded shell-aware and actinide-edge refinements without replacing the core model with ad hoc patching or black-box inference.

Core Moment Definition

GAWD computes the pair–Compton crossover (Ex) and the photoelectric–scattering crossover (EPC) directly from stoichiometry, using composition-weighted atomic moments and bounded physics-based refinements. It is designed to replace repeated runtime table-search and interpolation with a compact, auditable computational model.

The generalized composition moments are defined by

$$ J_p = \sum_i \frac{w_i Z_i^p}{A_i} $$

where:

• (w_i) is the mass fraction of element (i)
• (Z_i) is the atomic number of element (i)
• (A_i) is the atomic mass of element (i)

Shell / Head-Tail Correction

$$R_{1s}(Z)=\frac{E_{1s}(Z)}{K Z^2} \qquad EPC_{shell2}=EPC_{pred}\,\exp(f)$$

Actinide Edge Correction

$$S_{\mathrm{closest}}(E)=\sum_i w_i \exp\!\left(-\min_{sh\in\{K,L1,L2,L3\}} \left|\ln E-\ln E_{i,sh}\right|\right) \qquad EPC_{final}=EPC_{shell2}\,\exp\!\bigl(b(S_{\mathrm{closest}}-S_0)\bigr)$$

What GAWD Does

Given a chemical formula, GAWD computes:

• Ex — the energy at which pair production equals incoherent (Compton) scattering
• EPC — the energy at which photoelectric attenuation equals total scattering
• supporting derived quantities for analysis, filtering, and comparison

The framework is deterministic. The same input formula always produces the same result.

Intended Use

GAWD is intended for:

• Direct estimation of attenuation crossover coordinates from formula
• Deterministic comparison of known materials
• Evaluation of hypothetical or previously untabulated compounds
• High-throughput screening workflows
• Materials ranking, filtering, and search

Architecture

GAWD is organized in layers:

1. Core predictor

Computes the base Ex and EPC estimates directly from composition moments.

2. Shell-aware refinement

Applies bounded correction logic where shell-regime structure materially affects EPC behavior.

3. Actinide-edge refinement

Adds a domain-specific edge correction for actinide-regime materials using independent atomic edge information.

4. Descriptor expansion

Generates additional composition-only descriptors for large-scale filtering, ranking, and analysis, while leaving the base predictions unchanged.

What GAWD Is Not

GAWD is not:

• a neural network
• a black-box surrogate
• a runtime wrapper around legacy attenuation table lookup
• a structure-dependent quantum simulation engine

It is a direct stoichiometric model.

Repository Scope

This repository contains the public GAWD engine and supporting code needed to compute crossover coordinates from chemical formula.

It does not document or expose private downstream search workflows, internal ranking pipelines, or unpublished application-specific deployment layers.

Status

GAWD is under active development. Public releases may expand the validation set, documentation, parser behavior, and supporting utilities, while preserving the deterministic composition-first core.

Inputs

GAWD accepts a chemical formula string as input (it does not need or care about charge).

Examples:

• H2O
• Bi2O3
• UO2
• LiH
• Ni0.52Cr0.19Fe0.18Nb0.05Mo0.03Ti0.01Al0.005

Outputs

Core Computed Quantities

These are the quantities GAWD computes directly from chemical formula and atomic constants.

Stoichiometric foundation

• Mass fractions (w_mass_fractions) — element-by-element composition weights derived from the input formula
• Composition moments (J1, J2, J3, J4) — the core stoichiometric invariants that drive the model

Primary crossover outputs

• Ex_pred_MeV — pair–Compton crossover energy
• EPC_pred_MeV — base photoelectric–scattering crossover energy
• EPC_shell2_MeV — shell-corrected EPC
• EPC_final_MeV — final EPC after bounded actinide-edge refinement

Shell and edge correction state

• Dlow / Dhigh — low-end and high-end shell drivers
• low_gate / high_gate — hard gate states controlling shell correction activation
• max_nsub — maximum subshell complexity proxy in the compound
• max_Z — highest atomic number present
• Sclosest_pred — mass-fraction-weighted edge-proximity score
• R1S_array — per-element shell structure values
• Shift_exponent — exponential shell-correction term applied to the base EPC

Derived Quantities from GawdApotheosis

These quantities are derived from the core GAWD outputs and are intended for search, ranking, filtering, and comparative analysis.

• Etot — total crossover span
  Etot = Ex_pred_MeV + EPC_final_MeV

• REB — relative energy balance
  REB = EPC_final_MeV / Ex_pred_MeV

• Sigma — edge-weighted crossover ratio
  Sigma = (Ex_pred_MeV / EPC_final_MeV) * Sclosest_pred

• R1s_weighted — weighted shell-structure summary across the compound

• delta_AN_raw — raw actinide-edge correction magnitude

• Variance_surrogate — composition-variance proxy
  Variance_surrogate = J2 - (J1 * J1)

• Gain — shell-correction amplification factor
  Gain = EPC_shell2_MeV / EPC_pred_MeV

• shell_val — compact encoded shell/regime classification

• VectorV3 / VectorV4 — grouped moment tuples for downstream analysis

Supporting Data File

material_descriptors.py is provided as a convenience file for users of GAWD. It contains commonly needed associated lookup information used alongside the software and does not itself constitute part of the core GAWD method.

Example Notebook

A companion notebook is included to demonstrate basic usage, derived-output examples, and related helper workflows. Users can download the Python files together with the notebook and begin working with the engine immediately.

Minimal Example

from GAWD import Gawd, GawdApotheosis

result = Gawd("Bi2O3")
print(result["Ex_pred_MeV"])
print(result["EPC_final_MeV"])

full = GawdApotheosis("UO2")
print(full["formula"])
print(full["Ex_pred_MeV"])
print(full["EPC_final_MeV"])
print(full["Sigma"])