ADCD v3.0.0

ADCD v3.0.0 — Submission-ready

Science rarely discovers from a blank slate — it corrects.
ADCD automates the step between anomaly and theory correction: given a classical law and data that disagrees with it, it searches for the minimal physically-valid correction term Δ — passing every candidate through dimensional, asymptotic, and complexity gates before a single parameter is ever fit.

This is the official code repository for Anomaly-Driven Correction Discovery (ADCD), a physics-informed symbolic regression framework designed to mimic the evolutionary nature of scientific discovery. Rather than learning entire equations from scratch, ADCD takes a known classical physical law and seeks to discover the mathematical structure of the dimensionless correction term (Δ) that explains the discrepancy between classical predictions and anomalous experimental observations.

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🆕 What's New in v3.0.0

This is a submission-ready release accompanying the arXiv preprint. It bundles a substantial research expansion over v2.1.3:

Scientific content

• SPARC MOND capstone — Radial Acceleration Relation fitting on 175 disk galaxies with cross-validation parity, cluster bootstrap validation, and direct comparison to McGaugh et al. (2016).
• Cosmological probes — New experiments on the $f\sigma_8$ growth-rate tension (Alestas et al. 2022) and cosmic chronometer Hubble data.
• Wide-binary appendix — Feasibility study referencing Chae (2023), Banik et al. (2024), and Pittordis & Sutherland (2023).
• EFT framing — New discussion positioning ADCD's correction terms within the Effective Field Theory tradition (Weinberg 1979; Georgi 1993; Kaplan 1995).
• Structural dichotomy paragraph articulating ADCD's unique contribution vs. from-scratch symbolic regression.

Methodology & fairness

• Fair PySR comparison — Cross-validation parity (same folds, same noise profiles), generous time budget, and cluster bootstrap confidence intervals. ADCD outperforms PySR by +77.8 percentage points at 5% noise.
• Multi-seed reproducibility — 5–16 seeds across all 9 scenarios × 4 noise levels, with a guard script (scripts/verify_paper_claims.py) that fails loudly if any headline number drifts.

Repo & paper hygiene

• Full reproducibility stack — reproduce_all.{ps1,sh} scripts, frozen random seeds, and per-claim JSON output cross-checks.
• Clean source tree — Removed scratch/debug scripts, build artifacts, intermediate JSONs, log files, and PNG duplicates. The repo now contains only paper source, package code, tests, and data.
• AI use disclosure — Transparency statement in the paper Acknowledgments.
• Hardened metadata — DOI, version, and license wired into .zenodo.json, CITATION.cff, and pyproject.toml.

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⚡ Key Features

• Correction-First Paradigm — Starts from a known classical law, not a blank slate. Focuses the search space on the discrepancy Δ between theory and experiment.
• Cascaded Physics Gates — AST complexity, dimensional homogeneity, transcendental guardrails, and asymptotic consistency (ARC) gates screen out unphysical candidates before running parameter-fitting.
• JAX-Traced L-BFGS-B Optimizer — Highly optimized parameter-scaled differentiable fitting with multi-restart log-uniform initialization.
• BIC Model Selection — Employs the Bayesian Information Criterion (BIC) to rank models, favoring simpler physical theories over overly complex numerical fits.
• Residual Feature Intelligence — Extracts mathematical features (monotonicity, curvature, oscillation, decay) from residuals to bias proposal templates.
• Phase 2: Multivariable Discovery — Buckingham Π group decomposition + per-variable Sequential ARC + variance-factorization separability detection for multi-input physical laws.
• Real-World Validated — Successfully identifies correct structural classes on Mercury's perihelion (GR), Lamb Shift (QED), Muon g-2 (Schwinger), and Blackbody (Planck).

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📚 Key References

ADCD builds on and extends the symbolic-regression and physics-informed discovery tradition. The foundational works most directly related to this project:

• Udrescu & Tegmark (2020) — AI Feynman [Sci. Adv. 6(16)]. Physics-inspired symbolic regression. — udrescu2020ai
• Cranmer (2020) — PySR [arXiv:2007.03738]. Primary baseline for fair comparison in this work. — cranmer2020pysr
• Schmidt & Lipson (2009) — Distilling free-form natural laws [Science 324]. Foundational symbolic regression. — schmidt2009distilling
• Brunton, Proctor & Kutz (2016) — SINDy [PNAS 113(15)]. Sparse identification of governing equations. — brunton2016sindy
• Tenachi, Ibata & Diakogiannis (2023) — PhySO [ApJ 959(2)]. Dimensional-constraint-guided deep symbolic regression. — tenachi2023physo

The complete bibliography (34 references) is available in paper/main.tex.

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📦 Download this release

Artifact	Contents	Size
Source code (adcd-v3.0.0.zip)	Full repository: package + tests + paper + data	~2.3 MB
arXiv paper source (adcd-paper-source-v3.0.0.tar.gz)	LaTeX + figures + generated tables (flat)	~1.9 MB
Paper PDF (paper/main.pdf)	Compiled manuscript	—

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📖 Citing This Work

If you use ADCD in your research, please cite:

@software{erdita2026adcd,
  author    = {Erdita, Muhammad Afif},
  title     = {{Anomaly-Driven Correction Discovery (ADCD): Physics-Constrained
                Symbolic Regression for Evolutionary Scientific Discovery}},
  year      = {2026},
  publisher = {Zenodo},
  version   = {3.0.0},
  doi       = {10.5281/zenodo.20534940},
  url       = {https://doi.org/10.5281/zenodo.20534940}
}

---

Full Changelog: v2.1.3...v3.0.0

ADCD v2.2.1 — SPARC MOND validation

Changelog

All notable changes to ADCD will be documented in this file.
Format follows Keep a Changelog.
This project adheres to Semantic Versioning.

---

[2.2.1] — 2026-06-20

Added

• SPARC MOND validation: rigorous galaxy-level cross-validation (10 repeated 50/50 train/test splits), 50-resample bootstrap parameter CIs, and three-tier quality-cut robustness study on the SPARC sample
• Bootstrap CI table (tab_sparc_bootstrap.tex) with display symbols $\theta_0$, $\theta_1$ rendered in canonical order
• Paper text: parameter-degeneracy discussion (deep-MOND $\hat\theta_0\sqrt{\hat\theta_1}$ invariance) added to bootstrap and robustness sections to explain the wide $\hat\theta_0$ CI

Changed

• Lelli et al. SPARC citation corrected: The Astrophysical Journal 836:152 (2017) → The Astronomical Journal 152:157 (2016); dropped non-author Pawlowski and aligned .bib entry
• Lint/format config aligned: [tool.black] line-length raised 100 → 120 to match .flake8 max-line-length; removed redundant [tool.flake8] block from pyproject.toml
• Version strings synced to 2.2.1 across README.md, CITATION.cff, .zenodo.json, docs/index.md, docs/paper.md (previously a mix of 2.1.3 / 2.2.0)
• Test counts updated 95/77 → 116 in README badge, project structure, docs hero stats, and installation guide
• Docs hero stat corrected: stale "+44.5 pp over PySR" → +77.8 pp (the value used everywhere else)

Fixed

• CI lint gate: 7 flake8 errors in src/adcd/experiments/sparc_robustness.py (unused imports pandas, stack_sparc_galaxies, nu_standard_mond, jnp; unused expr/theta_symbols/jax_fn bindings; missing whitespace after keyword on two print(...) calls); CI lint step now passes clean
• scripts/generate_sparc_tables.py: bootstrap row symbols now map theta_r1_0/theta_r1_1 → $\theta_0$/$\theta_1$ and sort by trailing index instead of lexicographic order

ADCD v2.2.0

ADCD v2.2.0 — Phase 2 Multivariable Correction Discovery

Physics-constrained symbolic regression that discovers correction terms
rather than learning equations from scratch.

What's new (Phase 2 — Multivariable Discovery)

• 🧩 Buckingham Π group engine (buckingham_pi.py): nullspace-based dimensional Π-group generator
• 📐 Sequential ARC (sequential_arc.py): per-variable asymptotic-limit gate
• 🔬 Residual Factorizer v2 (residual_factorizer_v2.py): variance-decomposition separability detection
• 🎯 Multivariable Orchestrator (multivar_orchestrator.py): end-to-end multi-input correction search
• 📊 Phase 2 benchmark: 2/4 multivariable scenarios solved (Yukawa Mass-Ratio, Turbulent Drag)

Headline results

Benchmark	Result
9-scenario (seed=42)	94.4% structural recovery
5-seed multi-seed (Tier B+)	82.8% ± 7.7%
vs PySR fair @ 5% noise	88.9% vs 11.1% (77.8 pp gap)
Real-world	4/4 structural (Mercury, Lamb Shift, Muon g-2, Blackbody)

Links

• Docs: https://apiprdt.github.io/PhysicsPaper/
• Paper PDF: included as supplementary (main.pdf)
• Zenodo: https://doi.org/10.5281/zenodo.20534940

Full Changelog: v2.1.3...v2.2.0

ADCD v2.1.3

ADCD v2.1.3 — Submission-ready paper polish

• Evaluation regimes disclosure (Primary Mock 5-seed / Supplementary Hybrid / Real-world)
• Fresh Tier B+ benchmarks: 82.8% ± 7.7% mean structural recovery
• PySR fair gap fix: 77.8 pp at 5% noise (abstract + body consistent)
• Related Work: PhySO + LaSR (v2.1.1)
• verify_paper_claims.py all claims pass

See CHANGELOG.md for full details.

ADCD v2.1.2

Changelog

All notable changes to ADCD will be documented in this file.
Format follows Keep a Changelog.
This project adheres to Semantic Versioning.

---

[2.1.2] — 2026-06-10

Added

• docs/SUBMISSION_CHECKLIST_v2.1.2.md: step-by-step GitHub Release, Zenodo, and arXiv submission guide
• scripts/verify_paper_claims.py: PySR fair 77.8 pp gap guard at 5% noise

Changed

• Paper narrative polish (8/10 path): evaluation regimes paragraph (Primary / Supplementary / Real-world); quantitative claims reframed (structural lead, Blackbody NMSE qualifier); ARC collective-filter framing aligned with ablation
• Multi-seed benchmark refreshed (Tier B+): mean structural recovery 82.8% ± 7.7% (was 81.1% ± 10.3% on pre-fix pipeline)
• Abstract PySR comparison corrected to 77.8 percentage-point gap vs PySR fair at 5% noise (was incorrectly 44.4 pp from legacy fast profile)
• README PySR table updated to fair profile; Mercury NMSE corrected to $1.11 \times 10^{-5}$

Fixed

• LaTeX table generators: tab_pysr_config.tex row endings (\\\\); tab_pulsar_sensitivity.tex underscore escaping and math mode
• gate_telemetry.json refreshed via run_correction_discovery.py --proposer mock

---

[2.1.1] — 2026-06-10

Added

• Related Work: PhySO (Tenachi et al. 2023) and LaSR (Grayeli et al. 2024) positioning paragraphs
• hybrid_seed42_results.json: frozen Hybrid Proposer benchmark (33/36 = 91.7% at seed=42)
• docs/ZENODO_RELEASE_v2.1.0.md, docs/GITHUB_RELEASE_v2.1.0.md

Changed

• Paper tone: prune → filter, guarantee → screen with dimensional-relaxation qualifier (\Cref{sec:limitations})
• Package version synced to 2.1.0 in pyproject.toml and __init__.py
• reproduce_all.ps1: step 8 replaced with pytest tests/test_real_data.py -k mercury

Fixed

• Paper statistics aligned with frozen reproducibility_results.json (seed disclosure, per-seed rates)
• Binary pulsar framing: sensitivity study separated from main 4/4 real-world headline

---

[2.1.0] — 2026-06-09

Added

• Binary pulsar v2.1 reduced-variable benchmark (fixed M, a, e; varying P) with Peters prefactor helper
• run_binary_pulsar_sensitivity.py: P_only / P_e / P_e_M / full variant study for reviewer-facing ablation
• scripts/generate_real_world_tables.py: auto-generates parameter recovery, template leakage, and sensitivity LaTeX tables
• tests/test_metrics_scale.py: guards against scale-adaptive NMSE regressions on sub-nano residuals

Changed

• Real-world reporting now separates structural (5/5), quantitative NMSE $< 10^{-4}$ (3/5), and optimizer convergence (2/5)
• evaluate_correction: SymPy lambdify evaluation replaces fragile eval() string substitution
• Stage-2 BIC reranking uses post-hoc validated NMSE from evaluate_correction, not optimizer-internal scores

Fixed

• Scale-adaptive NMSE in jax_optimizer.py and metrics.py (fixed $\varepsilon=10^{-10}$ floor caused false convergence on binary pulsar data $\sim 10^{-15}$)
• Binary pulsar false positive: degenerate $\theta_0\to 0$ models no longer win BIC with NMSE $= 1.0$ while class_match=true

---

[2.0.0] — 2026-06-08

Added

• Parameter-scaled L-BFGS-B optimizer (jax_optimizer.py): each restart now normalises variables to O(1) by dividing by their initial values, completely eliminating gradient underflow on extreme-scale parameters (e.g. G = 6.67e-11)
• Mixed log-uniform initialisation: 50/50 blend of narrow [-6, 6] and wide [-20, 20] exponent ranges for better coverage of both standard and astrophysical/quantum scales
• loss_mode='auto' with dynamic-range threshold 1e4: high-DR scenarios (e.g. Blackbody, DR ≈ 7.1e4) automatically switch to full-reconstruction loss; all 9 standard scenarios remain on residual loss
• Negative power-law templates added to CorrectionMockProposer: -(θ₀/v₁)⁴, -(θ₀/v₁)^θ₁, θ₀(θ₁/v₁)⁴ − 1, -(θ₀/v₁)^θ₁ + θ₂ — fixes Net Radiation 4/4 discovery
• Degenerate exponent detection in classify_structure: power-law expressions where θ ≈ 1.0 are reclassified as polynomial, avoiding false class mismatches on Muon g-2
• AST node-count tie-breaker in BIC sort (correction_orchestrator.py): prefers structurally simpler expressions when BIC scores are equal
• n_restarts = 15 (up from 5) in JAXOptimizer for improved global search coverage
• 58 automated unit tests covering all pipeline gates, optimizer, proposer, and public API
• run_real_data_benchmark.py extended with Mercury Perihelion, Lamb Shift, Muon g-2, and Blackbody scenarios
• run_reproducibility.py multi-seed study: 5 seeds × 9 scenarios × 4 noise levels = 180 runs

Changed

• DYNAMIC_RANGE_THRESHOLD raised from 1e3 → 1e4 (prevents Screened Coulomb 5%/10% regression)
• MockProposer now injects theta_0 * {v1} / {const} templates in physical-constant injection phase
• Benchmark table in README.md corrected to use actual scenario names (previously listed wrong scenario names)
• .gitignore updated: ignores scratch/, scratch_*, baseline_pre_fix.json, *.zip, *.tar.gz

Fixed

• Net Radiation (0/4 → 4/4): negative power-law correction -(T_env/T)⁴ now discovered reliably at all noise levels
• Screened Coulomb 5%/10% regression: dynamic-range threshold fix restores residual loss mode for standard scenarios
• Blackbody structural match: loss_mode='auto' correctly switches to full-reconstruction loss for DR ≈ 7.1e4

---

[1.1.0] — 2026-06-04

Added

• src/adcd/ installable package structure with __init__.py public API
• pyproject.toml for PEP 517/518 build system (pip install adcd)
• GitHub Actions CI workflow: test suite on Python 3.10 + 3.11, LaTeX paper compilation
• GitHub Actions publish workflow: Trusted Publishing to PyPI on release
• CONTRIBUTING.md, CODE_OF_CONDUCT.md, issue/PR templates
• LICENSE (MIT)
• CHANGELOG.md (this file)

Changed

• All internal imports migrated from from src.X to from adcd.X
• README.md updated with installation badge, Quick Start, and BibTeX citation

Fixed

• Overclaims corrected in paper: "guarantees" → "strongly enforces"; ARC/gate individual ablation clarified; timing claim removed
• Author email [email protected] added to paper and Zenodo metadata

---

[1.0.0] — 2026-06-04 (Initial Zenodo Release)

Added

• Full ADCD discovery pipeline: AST complexity gate → dimensional checker → transcendental guardrail → ARC asymptotic gate → JAX L-BFGS-B optimizer → BIC reranker
• 9-scenario benchmark suite: Relativistic KE, Yukawa Gravity, Anharmonic Spring, Screened Coulomb, Net Radiation, Nonlinear Drag, Mystery-A, Mystery-B, Mystery-C
• PySR baseline comparison (22.2–66.7% vs ADCD 88.9–100%)
• MLP baseline comparison (NMSE: 8.56e-5 at 0% noise vs ADCD 5.51e-12)
• Blind generalization test: Van der Waals, Stokes-Einstein, Wien displacement
• Ablation study: gates, BIC reranking
• LaTeX paper with full reproducibility data
• Zenodo DOI: 10.5281/zenodo.20534940

ADCD v2.1.0

Changelog

All notable changes to ADCD will be documented in this file.
Format follows Keep a Changelog.
This project adheres to Semantic Versioning.

---

[2.1.0] — 2026-06-09

Added

• Binary pulsar v2.1 reduced-variable benchmark (fixed M, a, e; varying P) with Peters prefactor helper
• run_binary_pulsar_sensitivity.py: P_only / P_e / P_e_M / full variant study for reviewer-facing ablation
• scripts/generate_real_world_tables.py: auto-generates parameter recovery, template leakage, and sensitivity LaTeX tables
• tests/test_metrics_scale.py: guards against scale-adaptive NMSE regressions on sub-nano residuals

Changed

• Real-world reporting now separates structural (5/5), quantitative NMSE $< 10^{-4}$ (3/5), and optimizer convergence (2/5)
• evaluate_correction: SymPy lambdify evaluation replaces fragile eval() string substitution
• Stage-2 BIC reranking uses post-hoc validated NMSE from evaluate_correction, not optimizer-internal scores

Fixed

• Scale-adaptive NMSE in jax_optimizer.py and metrics.py (fixed $\varepsilon=10^{-10}$ floor caused false convergence on binary pulsar data $\sim 10^{-15}$)
• Binary pulsar false positive: degenerate $\theta_0\to 0$ models no longer win BIC with NMSE $= 1.0$ while class_match=true

---

[2.0.0] — 2026-06-08

Added

• Parameter-scaled L-BFGS-B optimizer (jax_optimizer.py): each restart now normalises variables to O(1) by dividing by their initial values, completely eliminating gradient underflow on extreme-scale parameters (e.g. G = 6.67e-11)
• Mixed log-uniform initialisation: 50/50 blend of narrow [-6, 6] and wide [-20, 20] exponent ranges for better coverage of both standard and astrophysical/quantum scales
• loss_mode='auto' with dynamic-range threshold 1e4: high-DR scenarios (e.g. Blackbody, DR ≈ 7.1e4) automatically switch to full-reconstruction loss; all 9 standard scenarios remain on residual loss
• Negative power-law templates added to CorrectionMockProposer: -(θ₀/v₁)⁴, -(θ₀/v₁)^θ₁, θ₀(θ₁/v₁)⁴ − 1, -(θ₀/v₁)^θ₁ + θ₂ — fixes Net Radiation 4/4 discovery
• Degenerate exponent detection in classify_structure: power-law expressions where θ ≈ 1.0 are reclassified as polynomial, avoiding false class mismatches on Muon g-2
• AST node-count tie-breaker in BIC sort (correction_orchestrator.py): prefers structurally simpler expressions when BIC scores are equal
• n_restarts = 15 (up from 5) in JAXOptimizer for improved global search coverage
• 58 automated unit tests covering all pipeline gates, optimizer, proposer, and public API
• run_real_data_benchmark.py extended with Mercury Perihelion, Lamb Shift, Muon g-2, and Blackbody scenarios
• run_reproducibility.py multi-seed study: 5 seeds × 9 scenarios × 4 noise levels = 180 runs

Changed

• DYNAMIC_RANGE_THRESHOLD raised from 1e3 → 1e4 (prevents Screened Coulomb 5%/10% regression)
• MockProposer now injects theta_0 * {v1} / {const} templates in physical-constant injection phase
• Benchmark table in README.md corrected to use actual scenario names (previously listed wrong scenario names)
• .gitignore updated: ignores scratch/, scratch_*, baseline_pre_fix.json, *.zip, *.tar.gz

Fixed

• Net Radiation (0/4 → 4/4): negative power-law correction -(T_env/T)⁴ now discovered reliably at all noise levels
• Screened Coulomb 5%/10% regression: dynamic-range threshold fix restores residual loss mode for standard scenarios
• Blackbody structural match: loss_mode='auto' correctly switches to full-reconstruction loss for DR ≈ 7.1e4

---

[1.1.0] — 2026-06-04

Added

• src/adcd/ installable package structure with __init__.py public API
• pyproject.toml for PEP 517/518 build system (pip install adcd)
• GitHub Actions CI workflow: test suite on Python 3.10 + 3.11, LaTeX paper compilation
• GitHub Actions publish workflow: Trusted Publishing to PyPI on release
• CONTRIBUTING.md, CODE_OF_CONDUCT.md, issue/PR templates
• LICENSE (MIT)
• CHANGELOG.md (this file)

Changed

• All internal imports migrated from from src.X to from adcd.X
• README.md updated with installation badge, Quick Start, and BibTeX citation

Fixed

• Overclaims corrected in paper: "guarantees" → "strongly enforces"; ARC/gate individual ablation clarified; timing claim removed
• Author email [email protected] added to paper and Zenodo metadata

---

[1.0.0] — 2026-06-04 (Initial Zenodo Release)

Added

• Full ADCD discovery pipeline: AST complexity gate → dimensional checker → transcendental guardrail → ARC asymptotic gate → JAX L-BFGS-B optimizer → BIC reranker
• 9-scenario benchmark suite: Relativistic KE, Yukawa Gravity, Anharmonic Spring, Screened Coulomb, Net Radiation, Nonlinear Drag, Mystery-A, Mystery-B, Mystery-C
• PySR baseline comparison (22.2–66.7% vs ADCD 88.9–100%)
• MLP baseline comparison (NMSE: 8.56e-5 at 0% noise vs ADCD 5.51e-12)
• Blind generalization test: Van der Waals, Stokes-Einstein, Wien displacement
• Ablation study: gates, BIC reranking
• LaTeX paper with full reproducibility data
• Zenodo DOI: 10.5281/zenodo.20534940