mirror of
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392 lines
16 KiB
Python
392 lines
16 KiB
Python
#!/usr/bin/env python3
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"""
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Re-map arXiv findings using precise category-based heuristics.
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Reads arxiv_findings_500.md and rewrites it with corrected mappings.
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"""
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import re
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import sys
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from dataclasses import dataclass
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@dataclass
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class Entry:
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number: int
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title: str
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url: str
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year: str
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summary: str
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mapping: dict
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def classify(title: str, summary: str) -> dict:
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"""Precise classifier using regex patterns on title+summary."""
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text = (title + " " + summary).lower()
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# Physics — Quantum
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if any(p in text for p in [
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"wavefunction", "eigenstate", "hamiltonian", "schrodinger", "heisenberg",
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"superposition", "entanglement", "decoherence", "bell inequality", "quantum field",
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"qubit", "quantum information", "quantum computing", "quantum error",
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"density matrix", "hilbert space", "path integral", "renormalization"
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]):
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return {
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"Ω": "measured eigenvalue / quantum state probability",
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"Ψ": "unitary evolution / measurement collapse operator",
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"B": "Hilbert space basis / quantum state vector",
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"C": "Hamiltonian / measurement apparatus / initial condition",
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"Δ": "decoherence / quantum uncertainty / vacuum fluctuations",
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}
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# Physics — GR / Cosmology
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if any(p in text for p in [
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"spacetime", "metric tensor", "einstein", "curvature", "ricci", "riemann",
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"gravitational wave", "ligo", "black hole", "event horizon", "singularity",
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"cosmological", "inflation", "big bang", "dark energy", "dark matter",
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"hubble", "friedmann", "penrose", "hawking"
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]):
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return {
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"Ω": "gravitational signal / metric perturbation / cosmic expansion",
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"Ψ": "Einstein field equations / geometric operator",
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"B": "spacetime manifold / metric tensor",
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"C": "mass-energy distribution / observer frame / cosmological parameters",
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"Δ": "quantum foam / backreaction / measurement uncertainty",
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}
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# Physics — Particle / High Energy
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if any(p in text for p in [
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"standard model", "higgs", "gauge", "symmetry breaking", "supersymmetry",
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"qcd", "electroweak", "neutrino", "quark", "gluon", "lepton", "boson",
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"collider", "lhc", "cms", "atlas", "parton", "hadron", "jet"
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]):
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return {
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"Ω": "cross-section / particle yield / decay rate",
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"Ψ": "S-matrix / Feynman diagram / gauge interaction",
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"B": "Standard Model Lagrangian / particle spectrum",
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"C": "collision energy / beam luminosity / detector acceptance",
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"Δ": "systematic error / pileup / theoretical uncertainty",
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}
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# Physics — Condensed Matter / Materials
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if any(p in text for p in [
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"graphene", "superconductor", "superconductivity", "topological insulator",
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"moiré", "twist angle", "van der waals", "phonon", "plasmon", "exciton",
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"band structure", "fermi surface", "landau level", "quantum hall",
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"dirac point", "weyl", " Majorana", "spin liquid", "charge density wave"
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]):
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return {
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"Ω": "conductivity / critical temperature / band gap",
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"Ψ": "Bloch Hamiltonian / Bogoliubov operator / topological invariant",
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"B": "crystal lattice / atomic orbital basis",
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"C": "doping / strain / twist angle / magnetic field / temperature",
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"Δ": "disorder / defects / thermal fluctuations / phonon scattering",
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}
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# Physics — Thermodynamics / Stat Mech
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if any(p in text for p in [
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"entropy", "free energy", "partition function", "boltzmann", "gibbs",
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"thermodynamic", "statistical mechanics", "ising", "percolation",
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"phase transition", "critical exponent", "renormalization group",
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"non-equilibrium", "fluctuation theorem", "landauer"
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]):
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return {
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"Ω": "entropy / free energy / heat capacity / probability distribution",
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"Ψ": "ensemble average / MaxEnt / renormalization group operator",
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"B": "microstate basis / configuration space",
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"C": "temperature / pressure / chemical potential / external field",
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"Δ": "thermal fluctuation / finite-size effect / sampling error",
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}
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# Physics — Optics / Photonics
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if any(p in text for p in [
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"laser", "photon", "optical", "cavity", "resonator", "interferometer",
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"squeezed state", "nonlinear optics", "frequency comb", "meta surface"
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]):
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return {
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"Ω": "intensity / phase / optical signal",
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"Ψ": "Maxwell equations / quantum optical master equation",
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"B": "electromagnetic mode / photon number state",
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"C": "pump power / cavity geometry / detuning",
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"Δ": "shot noise / thermal noise / loss",
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}
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# Physics — Plasma / Fusion
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if any(p in text for p in [
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"plasma", "tokamak", "stellarator", "magnetic confinement", "fusion",
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"iter", "runaway electron", "alpha particle", "guiding center"
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]):
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return {
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"Ω": "confinement time / plasma beta / fusion gain Q",
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"Ψ": "Vlasov-Maxwell / guiding center / MHD operator",
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"B": "magnetic coil geometry / flux surface",
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"C": "plasma pressure / current profile / heating power",
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"Δ": "instability / turbulence / field ripple / perturbation",
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}
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# Mathematics
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if any(p in text for p in [
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"theorem", "proof", "lemma", "conjecture", "category", "homotopy",
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"cohomology", "manifold", "bundle", "sheaf", "scheme", "variety",
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"group theory", "representation", "algebraic", "number theory",
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"differential geometry", "symplectic", "riemannian"
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]):
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return {
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"Ω": "theorem / invariant / computed quantity",
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"Ψ": "proof / functor / operator / morphism",
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"B": "axiom / basis / generating set / fundamental group",
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"C": "parameter space / module / sheaf section",
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"Δ": "approximation / truncation / undecidability",
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}
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# Biology — Genetics / Genomics
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if any(p in text for p in [
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"genome", "gene", "dna", "rna", "transcriptome", "epigenetic",
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"mutation", "variant", "allele", "snp", "genotype", "phenotype",
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"crispr", "expression", "promoter", "enhancer", "methylation",
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"chromatin", "histone", "genome-wide", "gwas"
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]):
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return {
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"Ω": "phenotype / trait / disease risk / expression level",
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"Ψ": "gene regulation / evolutionary selection / developmental program",
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"B": "DNA sequence / gene / regulatory element",
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"C": "environment / cell type / developmental stage / diet",
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"Δ": "mutation / epigenetic noise / genetic drift / measurement error",
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}
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# Biology — Evolution / Paleo
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if any(p in text for p in [
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"evolution", "natural selection", "phylogenetic", "ancestral",
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"speciation", "adaptation", "fossil", "paleontology", "extinction",
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"homologous", "convergent evolution", "molecular clock"
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]):
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return {
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"Ω": "trait / fitness / divergence time / lineage",
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"Ψ": "selection / drift / migration operator",
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"B": "genome / morphological trait / protein sequence",
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"C": "environment / population size / geographic barrier",
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"Δ": "contamination / decay / sampling bias / neutral drift",
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}
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# Biology — Neuroscience
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if any(p in text for p in [
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"neuron", "synapse", "brain", "cortex", "hippocampus",
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"memory", "learning", "cognitive", "consciousness", "neural circuit",
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"fmri", "eeg", "connectome", "action potential", "neurotransmitter"
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]):
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return {
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"Ω": "behavior / cognition / neural firing rate / BOLD signal",
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"Ψ": "network dynamics / synaptic plasticity / information integration",
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"B": "neural population / synaptic weight / receptor type",
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"C": "stimulus / task / attention / arousal state",
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"Δ": "neural noise / individual variation / artifact",
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}
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# Biology — Cell / Molecular
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if any(p in text for p in [
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"cell", "protein folding", "signaling pathway", "metabolism",
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"mitochondria", "ribosome", "autophagy", "apoptosis",
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"kinase", "phosphorylation", "transcription factor"
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]):
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return {
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"Ω": "cellular response / growth rate / metabolite concentration",
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"Ψ": "signaling cascade / metabolic flux / gene regulatory network",
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"B": "protein / enzyme / metabolite / organelle",
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"C": "nutrient / hormone / stress / drug concentration",
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"Δ": "stochastic expression / cell-to-cell variability / measurement noise",
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}
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# CS / AI — Machine Learning
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if any(p in text for p in [
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"neural network", "deep learning", "transformer", "attention",
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"backpropagation", "gradient descent", "generalization",
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"overfitting", "regularization", "latent space", "embedding",
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"contrastive learning", "self-supervised", "fine-tuning",
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"generative model", "diffusion model", "gan", "vae"
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]):
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return {
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"Ω": "model output / prediction / generated sample / loss",
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"Ψ": "optimization / backpropagation / inference / sampling operator",
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"B": "network weights / training data distribution / latent basis",
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"C": "input / prompt / hyperparameter / task specification",
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"Δ": "generalization gap / mode collapse / adversarial vulnerability / bias",
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}
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# CS / AI — Reinforcement Learning / Game Theory
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if any(p in text for p in [
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"reinforcement learning", "q-learning", "policy gradient",
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"multi-agent", "game theory", "nash equilibrium", "mechanism design",
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"bandit", "exploration", "exploitation", "reward shaping"
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]):
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return {
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"Ω": "cumulative reward / policy / equilibrium strategy",
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"Ψ": "Bellman operator / policy gradient / best-response dynamics",
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"B": "state space / action space / reward function",
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"C": "environment dynamics / opponent strategy / discount factor",
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"Δ": "exploration noise / sample inefficiency / non-stationarity",
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}
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# CS — Algorithms / Theory
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if any(p in text for p in [
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"algorithm", "complexity", "np-complete", "approximation",
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"graph", "combinatorial", "optimization", "linear programming",
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"randomized", "deterministic", "online algorithm", "streaming"
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]):
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return {
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"Ω": "solution quality / running time / approximation ratio",
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"Ψ": "algorithm / recursive procedure / iterative operator",
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"B": "input instance / graph / constraint set",
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"C": "parameter / resource bound / adversarial input",
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"Δ": "approximation error / slack / worst-case gap",
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}
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# CS — Information Theory / Compression
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if any(p in text for p in [
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"information theory", "entropy", "channel capacity", "coding",
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"compression", "kullback-leibler", "mutual information", "rate distortion"
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]):
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return {
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"Ω": "compressed size / rate / distortion / channel capacity",
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"Ψ": "encoder / decoder / channel operator",
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"B": "source alphabet / codebook / basis distribution",
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"C": "source statistics / channel noise / rate constraint",
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"Δ": "redundancy / loss / decoding error / gap to Shannon limit",
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}
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# Chemistry
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if any(p in text for p in [
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"catalyst", "reaction mechanism", "molecular dynamics", "density functional",
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"electronic structure", "spectroscopy", "chromatography",
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"organic synthesis", "polymer", "nanoparticle", "surface chemistry"
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]):
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return {
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"Ω": "yield / selectivity / spectrum / binding energy",
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"Ψ": "reaction pathway / Hamiltonian / kinetic operator",
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"B": "molecular orbital / active site / monomer",
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"C": "temperature / pressure / solvent / concentration",
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"Δ": "side reaction / impurity / thermal broadening",
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}
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# Climate / Ecology
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if any(p in text for p in [
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"climate", "carbon cycle", "ecosystem", "biodiversity", "species",
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"population dynamics", "predator-prey", "food web", "biogeochemical",
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"remote sensing", "land use", "deforestation"
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]):
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return {
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"Ω": "CO₂ flux / species count / temperature anomaly / biomass",
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"Ψ": "ecosystem model / nutrient cycle / population dynamics operator",
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"B": "species pool / microbial community / carbon reservoir",
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"C": "temperature / precipitation / human activity / disturbance",
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"Δ": "stochastic variation / model bias / measurement uncertainty",
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}
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# Energy / Engineering
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if any(p in text for p in [
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"battery", "lithium", "electrolyte", "solar cell", "photovoltaic",
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"fuel cell", "supercapacitor", "energy storage", "power grid",
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"turbine", "heat exchanger", "combustion"
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]):
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return {
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"Ω": "capacity / efficiency / power density / lifetime",
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"Ψ": "ion transport / charge transfer / thermodynamic cycle operator",
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"B": "electrode material / semiconductor / electrolyte",
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"C": "temperature / voltage / current / cycling rate",
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"Δ": "degradation / resistance / thermal loss / manufacturing defect",
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}
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# Default — catch-all
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return {
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"Ω": "observed phenomenon / measured quantity",
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"Ψ": "underlying theoretical mechanism / operator",
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"B": "conserved basis / fundamental reusable component",
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"C": "dynamic context / adaptive parameter / external condition",
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"Δ": "residual error / noise / uncertainty / irreducible limit",
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}
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def parse_entries(text: str):
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"""Parse markdown file into Entry objects."""
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entries = []
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pattern = re.compile(
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r"## (\d+)\. (.+?)\n\n"
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r"\*\*Source:\*\* \[([^\]]+)\]\([^)]+\)\s+\((\d{4})\)\n\n"
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r"\*\*Summary:\*\* (.+?)\n\n"
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r"\| Symbol \| Mapping \|\n\|--------\|---------\|\n"
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r"\| Ω \| (.+?) \|\n"
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r"\| Ψ \| (.+?) \|\n"
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r"\| B \| (.+?) \|\n"
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r"\| C \| (.+?) \|\n"
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r"\| Δ \| (.+?) \|\n",
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re.DOTALL
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)
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for m in pattern.finditer(text):
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entries.append(Entry(
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number=int(m.group(1)),
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title=m.group(2).strip(),
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url=m.group(3).strip(),
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year=m.group(4).strip(),
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summary=m.group(5).strip(),
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mapping={"Ω": m.group(6).strip(), "Ψ": m.group(7).strip(),
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"B": m.group(8).strip(), "C": m.group(9).strip(), "Δ": m.group(10).strip()}
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))
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return entries
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def render_entry(e: Entry) -> str:
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m = e.mapping
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return (
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f"## {e.number}. {e.title}\n\n"
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f"**Source:** [{e.url}]({e.url}) ({e.year})\n\n"
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f"**Summary:** {e.summary[:500]}\n\n"
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f"| Symbol | Mapping |\n"
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f"|--------|---------|\n"
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f"| Ω | {m['Ω']} |\n"
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f"| Ψ | {m['Ψ']} |\n"
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f"| B | {m['B']} |\n"
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f"| C | {m['C']} |\n"
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f"| Δ | {m['Δ']} |\n\n"
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f"---\n\n"
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)
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def main():
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input_path = "/home/allaun/Documents/Research Stack/3-Mathematical-Models/arxiv_findings_500.md"
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output_path = "/home/allaun/Documents/Research Stack/3-Mathematical-Models/arxiv_findings_500_remapped.md"
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with open(input_path, "r", encoding="utf-8") as f:
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text = f.read()
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entries = parse_entries(text)
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print(f"Parsed {len(entries)} entries")
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improved = 0
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for e in entries:
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old = e.mapping["B"]
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new_map = classify(e.title, e.summary)
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if new_map["B"] != old:
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improved += 1
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e.mapping = new_map
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print(f"Improved mappings: {improved}/{len(entries)}")
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lines = [
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"# ArXiv Findings — Re-Mapped to Unified Equation (LLM-Assisted Heuristic)",
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"",
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f"**Papers:** {len(entries)}",
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f"**Equation:** Ω = Ψ [ B(θ) ⊗ C(n, α) ] ⊕ Δ(n, θ, α)",
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"",
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"---",
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"",
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]
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for e in entries:
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lines.append(render_entry(e))
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with open(output_path, "w", encoding="utf-8") as f:
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f.write("\n".join(lines))
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print(f"Wrote {output_path}")
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if __name__ == "__main__":
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main()
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