kalika library

Abstract & linear algebra (libs/kalika/algebra/src, ~22 files, ~10.7k lines): linear-algebra, matrix-functions, rings, modules, field-extensions, galois, finite-groups + finite-group-atlas, decompositions, spectral.

Algebraic combinatorics (libs/kalika/algebraic-combinatorics/src): matroids

• matroid-kazhdan-lusztig, posets, and ehrhart (Ehrhart polynomials).

A large algebraic-geometry library (libs/kalika/algebraic-geometry/src, ~37 files): schemes, sheaves, divisors, cohomology, derived categories/functors, bridgeland-stability, fourier-mukai, moduli-spaces, git-quotients, homotopy-continuation, numerical-irreducible-decomposition, with msolve/dmodule interfaces.

Real/complex/functional analysis (libs/kalika/analysis/src, ~25 files): complex-analysis, conformal-mapping, riemann-surfaces, hilbert-space, operator-theory, distribution-theory, fourier/laplace/integral-transforms, asymptotics, dispersion-relations, and series.

Approximation theory (libs/kalika/approximation/src): chebyshev-technology, polynomial-approximation, and rational-approximation.

A thin facade/metadata package (libs/kalika/arithmetic/src/index.ts, ~10 lines): exports only package/backend-name constants and a frozen ARITHMETIC_CAS_ENGINE_CAPABILITIES list naming @kalika/cas-engine as the intended backend. No arithmetic is implemented here — it is a capability label, not an import.

Astrophysics (libs/kalika/astrophysics/src): stellar-structure, tov (neutron-star structure), compact-objects, accretion-disk, and a mesa interface.

Atomic & molecular physics (libs/kalika/atomic-physics/src): hartree-fock, molecular-physics, and spectroscopy.

Higher-level autodiff (libs/kalika/autodiff/src, ~14 files): forward/reverse mode plus CAS-adjoint, ODE-adjoint, PDE-adjoint, and numerical-compatibility layers tying AD into the symbolic and numeric engines.

Core automatic differentiation (libs/kalika/autodiff-core/src): forward-mode and a namespaced reverse-mode — the low-level AD primitives.

Big-Bang nucleosynthesis (libs/kalika/bbn/src): reaction-network, abundance-prediction, and bsm-constraints.

The conformal/S-matrix bootstrap (libs/kalika/bootstrap/src, ~14 files): conformal-blocks, crossing-equations, analytic-bootstrap, navigator-function, s-matrix-bootstrap, and sdp-bootstrap (numerical bootstrap via SDP).

Bethe-Salpeter excitonic optics (libs/kalika/bse/src, ~13 files): electron-hole kernel assembly (bareExchangeElement, screenedDirectElement, buildBseHamiltonian), Tamm-Dancoff (solveTdaBse) and full A/B-block solutions (solveFullBse, beyondTdaCorrection), a Haydock-Lanczos spectrum path (lanczosCoefficients), and optical outputs — absorption, oscillator strengths, exciton binding energies and radiative lifetimes — plus 2D keldyshPotential screening, singlet-triplet and spin-orbit excitons, and kernel interpolation / k-grid extrapolation.

A thin facade/metadata package (libs/kalika/calculus/src/index.ts, ~10 lines): like @kalika/arithmetic, only package/backend-name constants and a frozen CALCULUS_CAS_ENGINE_CAPABILITIES list. The actual calculus lives in the Rust cas-engine (not wired) and the live TS engine; this package is metadata.

A real Rust computer-algebra kernel (libs/kalika/cas-engine, ~43k lines of Rust across three crates: kalika-cas-core plus kalika-cas-native (napi-rs) and kalika-cas-wasm (wasm-bindgen) bridges). kalika-cas-core mirrors the @kalika/core AST with arbitrary-precision integers, canonical ordering, hash-consed storage and the URN1 binary envelope. Substantial and benchmarked, but per the domain architecture page not imported by any TypeScript package at runtime today — it is a built-but-not-wired substrate.

Category theory (libs/kalika/category-theory/src, ~19 files): category, abelian-categories, monoidal-categories, universal-constructions, topos-theory, string-diagrams, zx-calculus, tqft, and compositional-systems.

Coupled-cluster for solids (libs/kalika/cc-solids/src, ~730 lines): canonical/spin-adapted/Laplace-transform MP2 (canonicalMP2, laplaceMP2 with its own Laplace quadrature), CCSD correlation energy with DIIS acceleration (ccsdCorrelationEnergy, diisExtrapolate), perturbative triples and EOM-CCSD excitations (perturbativeTriples, eomCcsdExcitations), and local-correlation/finite-size machinery — DLPNO pair-natural-orbital domains, two-point CBS extrapolation, structure-factor finite-size corrections. Compact, formula-level implementations; the CCD/FCI "two-electron" functions are analytic 2×2 minimal models used as exactness anchors.

Citation/bibliography management (libs/kalika/citations/src, ~19 files): arxiv/doi/inspire resolvers, a citation manager, normalization, formats, a local database, and graph visualization.

Classical mechanics (libs/kalika/classical-mechanics/src, ~35 files): lagrangian/hamiltonian, poisson, canonical-transformations, noether, hamilton-jacobi, kam-theory, birkhoff-normal-form, celestial & restricted-three-body mechanics, perturbation theory, and a symbolic layer.

Closed-loop autonomous-experiment coordination (libs/kalika/closed-loop-experiments/src/index.ts): orchestrateExperimentComputeLoop turns DoE candidate runs plus new measurements into ranked recommendations, protocol requests, and a QC-gated execution queue; updateSurrogateModels applies weight-averaged moment-based posterior mean/variance updates — deliberately lightweight Bayesian bookkeeping, not the GP regression that lives in @kalika/surrogate — and learnDiscrepancyModel fits per-modality simulation-vs-experiment residual statistics. Four domain planners (planBatteryClosedLoopCampaign, planCatalystClosedLoopCampaign, thin-film, structural-alloy) template concrete campaigns.

An aggregator facade (libs/kalika/cohomology/src/index.ts, ~11 lines): re-exports @kalika/topology and @kalika/algebraic-geometry under namespaces and declares a COHOMOLOGY_SOURCE_MODULES constant. No cohomology code of its own — it is an umbrella over the two real libraries.

Combinatorics (libs/kalika/combinatorics/src): enumerative, graphs, species, and tableaux modules.

Condensed-matter physics (libs/kalika/condensed-matter/src): tight-binding, hubbard-model, bcs-superconductivity, quantum-hall, and topological-band.

The symbolic foundation (libs/kalika/core/src, ~62 files): the Expr AST (expr.ts), hash-consing arena, e-graph/rewrite engine (egraph.ts, rewrite-rule.ts, rewrite-strategy.ts, pattern.ts, matching.ts), provenance (derivation.ts, proven-result.ts, verification-badge.ts), numerical compiler, and many interchange formats (openmath, mathml, smtlib, tptp, scscp, serialization). The most heavily depended-on package in the area; everything symbolic is rooted here.

Cosmology (libs/kalika/cosmology/src, ~20 files): friedmann, inflation, cmb-power-spectrum, dark-energy, structure-formation, cosmological likelihoods, and Boltzmann-code interfaces (class-interface, camb-interface, cobaya-interface).

A very large crystallography & solid-state library (libs/kalika/crystallography/src, ~209 files, ~25.6k lines): Bravais lattices with Niggli reduction (lattice/niggli-core.ts), the 230 space groups with Hall symbols, detection and xyz operator algebra (space-group/), Hinuma-convention Brillouin-zone k-paths (reciprocal/hinuma.ts), diffraction with form factors, systematic absences and Le Bail fitting (diffraction/lebail.ts), crystal chemistry (bond valence, coordination polyhedra, porosity, prototypes), surfaces/interfaces (Wulff construction, CSL grain boundaries, moiré), magnetic Shubnikov groups, space-group irreps/corepresentations and distortion modes, and symmetry-adapted tensor properties (Neumann, elastic, Landau). Structure I/O covers CIF/POSCAR and more, with COD and Materials-Project database clients.

The persistence + ingestion layer (libs/kalika/database/src, ~40 files): computation cache, embedding service, schema, migrations, vector search, and a suite of scientific-database importers (lmfdb, oeis, hepdata, knotinfo, kreuzer-skarke, sxs-catalog), plus privacy-preserving computation logging.

An aggregator facade (libs/kalika/differential-geometry/src/index.ts, ~9 lines): re-exports @kalika/general-relativity under a namespace plus a source- modules constant. The differential-geometry machinery actually lives in @kalika/general-relativity.

Dynamical mean-field theory (libs/kalika/dmft/src, ~20 files): a Bethe-lattice runDmft self-consistency loop with Matsubara Green's functions and chemical-potential adjustment, a segment-representation CT-HYB hybridization-expansion Monte-Carlo impurity solver (runCtHyb, deterministic Mulberry32 PRNG), exact-diagonalization and Wilson-chain NRG solvers (nrgIterativeDiagonalization on a logarithmic mesh), analytic continuation by Padé / MaxEnt / Nevanlinna / stochastic methods, cRPA/cLDA interaction- parameter estimation with Slater-Kanamori conversion, and extended-DMFT / DFT+DMFT workflow glue with quasiparticle-weight and Mott-transition observables.

Design of experiments for lab campaigns (libs/kalika/doe/src/index.ts, ~1.9k lines, single module): classical designs — full/fractional factorial, plackettBurmanDesign, Taguchi arrays, latinHypercubeDesign, greedy dOptimalDesign over a candidate set, central-composite responseSurfaceDesign — filtered by lab-aware constraints (applyDoeConstraints: forbidden combinations, simplex/mixture, process windows, equipment throughput, precursor inventory), then Bayesian-optimization candidate ranking with expected-improvement / UCB / constrained-EI acquisitions, active-learning planning, adaptive replicate allocation, portfolio scheduling, and campaign outputs (plate maps, batch sheets, instrument queues, requisitions).

Classical electrodynamics (libs/kalika/electrodynamics/src, ~16 files): maxwell, fdtd, green-functions, multipole-expansion, radiation, static-solvers, and waves.

Electron-phonon coupling (libs/kalika/electron-phonon/src, ~860 lines): deformation-potential and Fröhlich matrix elements with Bloch↔Wannier transforms and a long-range polar correction for interpolation (froehlichMatrixElement, blochToWannier), the Eliashberg spectral function α²F with λ, ω_log and mode-resolved decomposition (alpha2F, couplingConstant), Fan-Migdal + Debye-Waller self-energies for zero-point/temperature band-gap renormalization, SERTA and iterative-BTE phonon-limited mobility with Seebeck-Mott and Hall-factor helpers, and Kohn-anomaly/nesting analysis. Compact but named-formula real; the full gap solvers live in @kalika/eliashberg.

A pseudopotential / crystallography-and-DFT-types library (libs/kalika/electronic-structure/src, ~73 TS files, ~17.9k lines). Its implemented code (everything index.ts re-exports) lives in types (the bulk: crystallographic and DFT data structures — atoms, lattices, k-point grids/paths, space groups, symmetry finding, wavefunctions, charge density, band-structure and DFT-calculation types), pseudopotential (relativistic pseudopotential physics — Dirac radial solver, spin-orbit Hamiltonians, delta-factor / equation-of-state validation, library registry), io (POSCAR/CONTCAR, CIF, Quantum-ESPRESSO, XYZ, ABINIT and Materials-Project parsers/writers), runtime (kernel loader), and constants (physical constants). The sibling directories scf, plane-wave, band-structure, charge-analysis, xc, wannier, parallel, and optimization are empty placeholder directories (each holds only a .gitkeep, no .ts, none exported) — reserved slots, not yet a working DFT solver. The one TS library that depends on the Rust @kalika/numerical-engine.

Eliashberg superconductivity (libs/kalika/eliashberg/src): isotropic imaginary-axis Matsubara gap equations (solveEliashberg, criticalTemperature, gap-vs-temperature), McMillan and Allen-Dynes Tc with Morel-Anderson μ* (allenDynesTc, morelAndersonMuStar), multiband and anisotropic gap equations (solveMultibandEliashberg, solveAnisotropicEliashberg), Padé analytic continuation plus a direct real-axis solver with tunneling DOS (solveRealAxisEliashberg), and derived properties — gap ratio, specific heat, isotope exponent, strong-coupling shape factor.

Multiscale embedding (libs/kalika/embedding/src, ~375 lines): frozen-density embedding with Thomas-Fermi / von Weizsäcker kinetic functionals and freeze-and-thaw cycles (fdeEmbeddingPotential, freezeAndThaw), QM/MM with electrostatic embedding, hydrogen link atoms and ONIOM2/3 subtractive layering, and many-body/defect embedding — Manby-Miller projectionEmbedding, Green's-function defect embedding, the Freysoldt-Neugebauer-Van de Walle fnvCorrection, defect formation energies and transition levels. Compact scalar-and-small-matrix formula implementations, not a full SCF engine.

Entanglement measures (libs/kalika/entanglement/src): von-neumann-entropy, renyi-entropy, negativity, mutual-information, and topological-entropy.

The typed backbone of the lab-automation family (libs/kalika/experiment-orchestration/src): model.ts defines campaigns, hypotheses, budgets, facility constraints, ExecutableProtocol steps with tolerances/branches/QC gates, sample-lineage graphs, InstrumentSession, and the SafetyEnvelope rule types that @kalika/instrument-control and @kalika/lab-safety import; integration.ts builds an ExperimentStackManifest (createExperimentStackManifest) linking a campaign to @kalika/notebooks, @kalika/research-agents and @kalika/knowledge-graph. Honestly a schema-plus-constructors model layer — the coordination contract, not an executor.

An aggregator facade (libs/kalika/feynman/src/index.ts, ~11 lines): re-exports @kalika/quantum-field-theory and @kalika/renderer under namespaces plus a source-modules constant. The Feynman-diagram math/rendering lives in those two libraries.

Fluid dynamics (libs/kalika/fluid-dynamics/src, ~16 files): euler-equations, navier-stokes, ideal-mhd, shallow-water, turbulence-models, vortex-dynamics, and standard solutions.

A broad formal-methods bridge (libs/kalika/formal-verification/src, ~56 files): SMT solver, first-order ATP, decision procedures, model/computability theory, derivation-to-tactic, Lean (lean-process-manager, lean-source-parser, lean-to-kalika/kalika-to-lean, Mathlib lemma DB), and bridges to Coq, Isabelle, Metamath, SymPy, Sage, Oscar, Symbolica, Wolfram, plus cross-CAS/cross-prover verification.

A large GR library (libs/kalika/general-relativity/src, ~52 files): tensor algebra, curvature tensors, covariant derivative, exact solutions, ADM/BSSN formalisms, geodesic solver, black-hole + cosmological perturbation, gravitational-wave extraction, post-Minkowskian scattering/EOB, Killing vectors, Penrose-Carter, and benchmark suites. The home of the tensor-calculus machinery that @kalika/tensor and @kalika/differential-geometry alias.

Geometric analysis (libs/kalika/geometric-analysis/src): geometric flows — ricci-flow, mean-curvature-flow, harmonic-map-flow, yang-mills-flow, and perelman-functionals.

Gravitational-wave science (libs/kalika/gravitational-waves/src): waveform-models, nr-surrogates, data-analysis, detector-models, and source-modeling.

GW quasiparticle theory (libs/kalika/gw/src, ~27 files): Adler-Wiser RPA χ₀ (assembleRpaChi0, head/wing/body blocks), dielectric matrix and screened interaction with Coulomb truncation, plasmon-pole models — Hybertsen-Louie, Godby-Needs, and Engel-Farid multipole — one-shot G0W0 (solveG0W0, spectral functions, DFT-starting-point analysis), static COHSEX, full-frequency self-energies, eigenvalue-self-consistent GW and QSGW (runQsgw, with a BSE hand-off), space-time-method pieces, and convergence tooling (band-count / G-cutoff / k-point extrapolation, static-remainder correction) under a runGwWorkflow driver.

HEP phenomenology (libs/kalika/hep-phenomenology/src, ~44 files, ~16.8k lines): PDG database, spectrum generator, flavor physics, dark-matter/axion modules, electroweak precision, and a wide set of HEP file-format and tool bridges (lhef, hepmc3, lhapdf, root-file, fits-file, yoda, openloops, collier, checkmate, smodels, higgsbounds-signals).

Higher category theory (libs/kalika/higher-categories/src): simplicial-sets, quasicategories, stable-infinity-categories, and homotopy-algebras.

Compute orchestration (libs/kalika/hpc-orchestrator/src): job scheduler, distributed computation, resource monitor, and a computation cache — the substrate for farming out long-running scientific jobs.

Information theory (libs/kalika/information-theory/src): quantum-information, entanglement, information-geometry, and thermodynamic-geometry.

A typed instrument control plane (libs/kalika/instrument-control/src/index.ts, ~1.2k lines): InstrumentDriver capability/command schemas with parameter validation (validateInstrumentCommand), a connection-state machine, a STANDARD_ACQUISITION_ADAPTERS catalog spanning XRD/Raman/XPS/SEM/TEM/AFM/electrochemistry modalities, facility sessions with manifest export and archive sync, calibration assessment (assessCalibration), acquisition-template materialization, in-run QC that emits reacquisition commands (evaluateInRunQc), and streaming partial-dataset dispatch. Honestly a control-plane model: no VISA/serial/ vendor-SDK transport is implemented here — InstrumentDriver is the seam a real hardware driver must fill.

Classical/quantum integrable systems (libs/kalika/integrable-systems/src): lax-pair, inverse-scattering, soliton-solutions, hirota-bilinear, classical-r-matrix, and bethe-ansatz.

A mathematical knowledge graph (libs/kalika/knowledge-graph/src, ~31 files): ontology, concept linking, analogy/gap detection, graph-RAG, prerequisite computation, theorem-dependency graph, Lean-theorem registration and Mathlib dependency extraction, with persistence and query layers.

Fail-closed safety gating for autonomous lab work (libs/kalika/lab-safety/src/index.ts, ~1.25k lines): a chemical/process hazard knowledge base compiled into a SafetyEnvelope (buildSafetyEnvelope), protocol-DSL validation against incompatibility/PPE/exposure rules (validateProtocolSafety), per-step execution gating with operator credentials and approval signatures (gateProtocolStep), pre-flight review packets, an incident/near-miss ledger, and exportable audit traces. Pure policy/validation logic over @kalika/protocols documents — it decides and blocks; it does not actuate hardware.

Lattice gauge theory (libs/kalika/lattice/src, ~14 files): gauge-theory, fermions, hmc (hybrid Monte Carlo), monte-carlo, measurements, and gauge-configuration I/O.

Lie theory (libs/kalika/lie-theory/src, ~20 files): lie-groups, lie-classification, representations, root-operations, structure-constants, weyl-group, casimir, homogeneous-spaces, and exceptional-constructions.

The shared numerical substrate of the GW/BSE family (libs/kalika/many-body/src, ~56 files, ~7.6k lines): Matsubara/real-axis Green's functions, χ₀ polarizability and the ε(G,G′,q,ω) dielectric matrix with dense inversion and local-field ε_M, bare/truncated Coulomb v(q+G), radix-2 Cooley-Tukey FFT with exact-DFT fallback, k-point / imaginary-time / Matsubara grids, ScaLAPACK-style block-cyclic parallel-layout, HDF5 checkpointing, a BerkeleyGW bgw-compat layer, and wavefunction I/O for VASP, Quantum ESPRESSO, ABINIT, GPAW and Wannier90. The compute-backend GPU path is a fail-loud seam: selectComputeBackend currently always falls back to the real CPU kernels because the napi-rs/wgpu addon is not bundled — it never fabricates GPU output.

Validation-only companion to the many-body family (libs/kalika/many-body-benchmarks/src, ~475 lines): reference-data.ts stores literature reference values (semiconductor and transition-metal-oxide gaps, exciton binding energies, HEG energy per electron, SrVO₃ Hubbard bands, diamond cohesive energy) and benchmarks.ts scores computed results against them (gw100Benchmark, tmoGapBenchmark, bseOpticalSpectraBenchmark, srvo3Benchmark) via errorStatistics pass/fail verdicts. A testing/validation library — it checks results; it computes no physics of its own.

An aggregator facade (libs/kalika/mathematical-physics/src/index.ts, ~19 lines): re-exports six physics libraries (classical-mechanics, electrodynamics, general-relativity, quantum-field-theory, statistical-mechanics, string-theory) under namespaces plus a source-modules constant — a top-level umbrella, no implementation of its own.

Matrix models (libs/kalika/matrix-models/src): one-cut-solver, topological-recursion, and the jt-syk (JT gravity / SYK) module.

Measure theory (libs/kalika/measure-theory/src): measure-spaces, integration-theorems, and ergodic-theory.

Atomistic simulation (libs/kalika/molecular-dynamics/src, ~71 TS files, ~7.1k lines, plus ~6.2k lines of Rust in rust/crates/{md-core,md-potentials,md-analysis}): the TS layer carries VelocityVerlet + MDRunner classical-MD orchestration, enhanced sampling (metadynamics BiasPotential, nudgedElasticBand, string method, WHAM/MBAR), free-energy estimators (thermodynamicIntegration, bennettAcceptanceRatio, Jarzynski/Crooks), coarse-graining (DPD, iterative Boltzmann inversion, force matching), random-search structure prediction, and wide trajectory I/O (PDB/GRO/DCD/TRR/LAMMPS-data/POSCAR/restart). The Rust crates implement EAM/Stillinger-Weber/Tersoff potentials, thermostats/PBC, and Green-Kubo thermal conductivity / shear viscosity (green_kubo.rs) — but are cargo-tested only, with no napi/wasm bridge into the TS layer yet.

Physics-informed machine learning (libs/kalika/neural-physics/src, ~16 files): pinn + separable-pinn, deeponet, fourier-neural-operator, neural-operator-pipeline, differentiable-physics, and training infrastructure.

Neutrino physics (libs/kalika/neutrino-physics/src): oscillation-probability, cross-sections, mass-mechanisms, leptogenesis, and sphaleron-rate.

Non-perturbative field theory (libs/kalika/non-perturbative/src, ~28 files): instantons (bpst-instanton, instanton-calculus, adhm, nekrasov), monopoles, vortices, skyrmions, kinks, topological defects, and anomaly machinery (chiral-anomaly, anomaly-polynomial/-descent/-inflow).

Noncommutative geometry (libs/kalika/noncommutative-geometry/src): spectral-triples, cyclic-cohomology, cstar-k-theory, noncommutative-algebras, and a standard-model application module.

Nonlinear dynamics & chaos (libs/kalika/nonlinear-dynamics/src): dynamical-systems, lyapunov, poincare, fractals, route-to-chaos, and standard systems.

The reactive research-notebook model (libs/kalika/notebooks/src, ~53 files): reactive engine, CAS kernel, cell execution, dependency locking, reproducibility

• provenance, Jupyter/Mathematica/Pluto interoperability, LaTeX paper import, collaboration/comments/sharing/versioning, reproducible export.

Computational number theory (libs/kalika/number-theory/src, ~40 files): elliptic curves + L-functions, modular forms/symbols/Hecke, number fields, local fields, rings of integers, factorization, primality, Mordell-Weil, and high-precision/general L-function machinery.

Numerical computing in TypeScript (libs/kalika/numerical/src, ~28 files): arbitrary-precision arithmetic, computational geometry, Taylor models, verified computation, Mellin-Barnes, plus interfaces (gmsh, hdf5) and benchmark/ validation suites (linear-algebra, ODE, PDE, Monte-Carlo). The TS numeric path, distinct from the Rust numerical-engine.

A real Rust dense/sparse linear-algebra kernel (libs/kalika/numerical-engine; the core crate's lib.rs is ~27k lines covering matrix decompositions, error types, SIMD paths). Unlike cas-engine, it is declared as a runtime dependency in @kalika/electronic-structure's package.json (cas-engine is absent there — it appears only in the looser project.json implicitDependencies, alongside numerical-engine), so it is the one Rust kernel with a TypeScript consumer.

Open quantum systems (libs/kalika/open-quantum-systems/src): lindblad, beyond-lindblad, and noise-channels.

An aggregator facade (libs/kalika/operators/src/index.ts, ~11 lines): re-exports @kalika/analysis and @kalika/quantum-mechanics under namespaces plus a source-modules constant — an umbrella for operator-theory consumers, with no implementation of its own.

Optics (libs/kalika/optics/src): geometric-ray-optics, fourier-optics, nonlinear-optics, and quantum-optics.

Optimal transport (libs/kalika/optimal-transport/src): sinkhorn, wasserstein, monge-ampere, and displacement-interpolation.

Optimization (libs/kalika/optimization/src, ~22 files, ~15.9k lines): linear / semidefinite (with sdpb-interface) / convex / nonlinear / global + verified-global programming, least-squares fitting, variational discretization, and quantum-variational methods.

An aggregator facade (libs/kalika/particles/src/index.ts, ~11 lines): re-exports @kalika/hep-phenomenology and @kalika/quantum-field-theory under namespaces plus a source-modules constant — an umbrella, no implementation of its own.

Periods and polylogarithms (libs/kalika/periods/src, ~14 files): polylog + elliptic-polylog, mzv (multiple zeta values), hyperint, single-valued, and feynman-coaction.

Harmonic lattice dynamics (libs/kalika/phonons/src, ~58 files, ~6.7k lines): finite-displacement force constants with symmetry-reduced displacement sets and orbit averaging (generateDisplacements, extractForceConstants), acoustic-sum-rule enforcement and space-group symmetrization, dynamical matrices with Born-charge LO-TO non-analytic correction and Gonze-Lee damping (dynamicalMatrixWithNAC), dispersion/DOS with linear tetrahedron integration (tetrahedronDOS), instability detection, and thermodynamics — harmonic free energy, Grüneisen parameters, and quasi-harmonic runQHA over Birch-Murnaghan EOS fits (Gibbs energy, Cp). Parses VASP OUTCAR / QE forces and phonopy BORN files.

Anharmonic lattice dynamics (libs/kalika/phonons-anharmonic/src, ~1k lines): third-order force-constant extraction from irreducible displacement triplets with permutation symmetrization and a third-order acoustic sum rule (extractThirdOrderFC), three-phonon matrix elements with Bose factors and normal/Umklapp classification (classifyProcess), scattering rates turned into linewidths, lifetimes and frequency shifts, joint DOS, and adaptive-broadening / cutoff / q-mesh convergence analysis. A direct dependency of @kalika/thermal-transport.

DFPT phonons (libs/kalika/phonons-dfpt/src, ~700 lines): a Sternheimer linear-response kernel — conduction-projected sternheimerSolve, first-order density, selfConsistentResponse — Fourier interpolation of dynamical matrices over Wigner-Seitz vectors with polar splitting (interpolateDynamicalMatrix), response properties (Raman tensor, elastic and piezoelectric constants from strain response), and a checkpointed SCF → ph.x → force-constant recovery → dispersion pipeline (runDfptWorkflow) with longest-processing-time q-point load balancing. The DFT stages are supplied as engine callbacks (Quantum ESPRESSO or another engine); a missing callback fails loud rather than simulating the run.

Phonons in special systems (libs/kalika/phonons-special/src, ~1.1k lines): Kapitza interface conductance via acoustic-mismatch and diffuse-mismatch models plus atomistic-Green's-function transmission and Landauer conductance (ammConductance, dmmConductance, agfTransmission), alloy/disorder tools (VCA averaging, SQS pair-correlation error, CPA self-energy, band-unfolding weights), spectroscopy (Raman/IR, one-phonon INS/IXS with powder averaging, dynamical structure factor), surface slab phonons, 2D flexural ZA-mode dispersion/DOS, and pressure/strain/temperature conditions.

Plasma physics (libs/kalika/plasma-physics/src): vlasov, dispersion-relation, mhd-equilibrium, and transport.

Polaron physics (libs/kalika/polarons/src, ~660 lines): Fröhlich weak-coupling perturbation energy plus the all-coupling Feynman path-integral variational bound minimized over (v, w) (weakCouplingEnergy, feynmanEnergy), Holstein small polarons via the Lang-Firsov transformation with independent-boson ground state and tridiagonal-Lanczos lowest eigenvalues (langFirsov, polaronCrossover), bipolaron binding / effective mass / BEC temperature, and transport — thermally activated hoppingMobility, band-to-hopping crossover, photoemission phonon sidebands and quasiparticle residue.

Positive geometry (libs/kalika/positive-geometry/src): amplituhedron, associahedron, cosmological-polytope, positroid, and a general positive-geometry module.

Probability (libs/kalika/probability/src, ~13 files): distributions, markov-chains, stochastic-processes, random-matrix, and Schramm-Loewner evolution (schramm-loewner, sle-cft).

The experiment-protocol DSL and execution model (libs/kalika/protocols/src/index.ts, ~1.6k lines): typed step kinds (synthesis, annealing, mixing, deposition, curing, transfer, characterization) in a ProtocolDslDocument, compileProtocol to backend commands, dryRunProtocol simulation against a declared environment (inventory, equipment, QC gates), a stateful execution machine (createProtocolExecution, startNextProtocolStep, sign-offs, pause/resume, exceptions + recovery plans, evidence, checkpoints), and connector planners for liquid handlers (dispense commands, dilution trees, tip management), thermal/deposition processes, and robotic transfer. Connector "plans" are typed command sequences for downstream drivers — no vendor hardware I/O lives here.

Quantum Monte Carlo (libs/kalika/qmc/src, ~1.4k lines): Metropolis VMC with cusp-conditioned Jastrow factors and Slater log-determinants (runVmc, jastrowFactor), fixed-node importance-sampled DMC with drift-diffusion moves, population control, and time-step extrapolation (runDmc, validated against the exact hydrogen −0.5 Ha ground state), phaseless AFQMC (discrete Hubbard-Stratonovich decomposition, phaselessWeight, back-propagation), solid-state machinery (Ewald energy, B-spline orbitals, Hellmann-Feynman + Pulay forces, twist averaging, KZK and MPC finite-size corrections), and blocking-analysis error bars with autocorrelation times (blockingAnalysis), all on a deterministic Mulberry32 PRNG.

Quantum chaos (libs/kalika/quantum-chaos/src): level-statistics, otoc, spectral-form-factor, spectral-unfolding, and quantum-billiards.

An aggregator facade (libs/kalika/quantum-computing/src/index.ts, ~11 lines): re-exports @kalika/quantum-mechanics and @kalika/information-theory under namespaces plus a source-modules constant — an umbrella, not its own implementation.

A very large QFT library (libs/kalika/quantum-field-theory/src, ~82 files, ~27k lines): Feynman-rule application, diagram topology, Dirac/color algebra, IBP reduction, Passarino-Veltman, one-loop scalar integrals, renormalization / RGE (automated-rge, renormalization-group), Dyson-Schwinger, EFT matching, NLO automation, and external-tool bridges (amflow, finiteflow).

Quantum gravity (libs/kalika/quantum-gravity/src): loop-quantum-gravity, causal-dynamical-triangulations, and asymptotic-safety.

Quantum groups (libs/kalika/quantum-groups/src): drinfeld-jimbo, crystal-bases, r-matrix, and kazhdan-lusztig.

Quantum mechanics (libs/kalika/quantum-mechanics/src, ~35 files): hilbert-space, operators, time-(in)dependent Schrödinger solvers, perturbation-theory, path-integral, scattering-formalism, angular-momentum-coupling, spherical-harmonics, spin-algebra, hybrid quantum-classical, and a quantum-hardware-interface.

Scientific visualization (libs/kalika/renderer/src, ~40 files): function/data plotting, complex visualization, vector/field plots, plus physics-specific diagram renderers (feynman-diagram, tikz-feynman, dynkin-diagram, penrose-carter-diagram, spacetime-diagram, quantum-circuit-diagram, tensor-network-diagram, young-diagram), gltf, pgfplots, and time-evolution animation.

Autonomous research agents (libs/kalika/research-agents/src, ~60 files): conjecture formulation/validation, FunSearch-style generation, proof agent / proof-search-tree / proof-repair, retrieval-augmented proving, multi-agent orchestration, plus literature clients (arxiv, inspire-hep, semantic-scholar, openalex, oeis) and paper-claim/reproduction verifiers.

Federated research operations (libs/kalika/research-ops/src, ~1.9k lines): a FederatedSiteRegistry with access-policy evaluation and cross-site replication planning, SHA-256 content-hash provenance signing (canonicalize/contentHash, signProvenance), an ImmutableArtifactRegistry with integrity reports, retention classes and checkpoint-cadence rules, execution-environment capture exported as Spack/Nix/container recipes with validation, workflow replay bundles gated by a fail-loud assertProductionReady, and a LicenseAwareScheduler with fair-share priorities. Governance and bookkeeping logic — it does not itself run the computations it tracks.

Linear-response and dielectric properties (libs/kalika/response/src, ~340 lines): the Dyson equation for the interacting susceptibility (dysonResponse), static Lindhard function, charge susceptibility and compressibility, macroscopic dielectric constant / loss function / optical constants and joint DOS, plus sum-rule diagnostics — f-sum and conductivity sum rules, plasma frequency, and a Kramers-Kronig transform with residual check (kramersKronigResidual). A compact formula-level companion to @kalika/many-body's full ε(G,G′,q,ω) machinery.

Resurgence / asymptotic-series summation (libs/kalika/resurgence/src): borel-summation, borel-pade, transseries, alien-calculus, and perturbative-coefficients.

Sample lifecycle operations (libs/kalika/sample-ops/src/index.ts, ~1.5k lines): hazard-aware inventory assessment against facility rules (assessInventory), sample registration with barcode/QR/RFID tags over @kalika/experiment-orchestration lineage types, plate/wafer/single-sample container builders with position maps, a digitally signed chain-of-custody ledger (appendChainOfCustodyEvent), batch/queue planning for characterization, annealing and beamtime, and contamination-rule co-processing validation (validateCoProcessing). Pure typed ledger/planning logic — the LIMS brain, not a robot.

The TypeScript client SDK (libs/kalika/sdk/src): engine, numeric, physics, sdk, types, and wasm-kernel modules — the developer-facing surface for driving Kalika computations.

A focused semidefinite-programming core (libs/kalika/sdp-core/src): a single substantial semidefinite-programming module (~2.5k lines) — the SDP solver primitives reused by bootstrap/optimization consumers.

Spectral geometry (libs/kalika/spectral-geometry/src, ~18 files): heat-kernel, laplace-beltrami, index-theorem + index-applications, eta-invariant, spectral-zeta, spin-geometry, and curved-spacetime-qft.

Statistical mechanics (libs/kalika/statistical-mechanics/src, ~20 files): partition-functions, classical-lattice-models, mean-field-theory, quantum-statistical-mechanics, non-equilibrium, RG, exact results, and a stat-mech-lattice-bridge.

A large string-theory library (libs/kalika/string-theory/src, ~48 files, ~14.9k lines): ads-cft, conformal-field-theory, virasoro, calabi-yau-geometry, mirror-symmetry, toric-geometry, flux/orbifold compactification, BCFW recursion, spinor-helicity, generalized unitarity, color-kinematics, and ML-assisted modules (neural-calabi-yau-metric, ml-hodge-prediction, rl-string-landscape).

Supersymmetry (libs/kalika/supersymmetry/src): grassmann, superspace + n2-superspace, superfields, and SUSY lagrangian construction.

Surrogate modelling (libs/kalika/surrogate/src): a single substantial gaussian-process module (~1.7k lines) for GP regression/emulation.

Symbolic regression / equation discovery (libs/kalika/symbolic-regression/src, ~17 files): genetic-programming, transformer-symbolic-regression, llm-guided-symbolic-regression, physics-equation-discovery, separability/symmetry detection, and AI-Feynman benchmarks.

Symplectic geometry (libs/kalika/symplectic/src): symplectic-manifold, floer-homology, symplectic-capacities, hamiltonian-reduction, and geometric-integrators.

Time-dependent DFT (libs/kalika/tddft/src, ~420 lines): Casida-equation excitations in full and Tamm-Dancoff form (solveCasida), exchange-correlation kernels — ALDA, gradient-corrected, hybrid, and long-range-corrected with α from ε∞ (aldaKernel, lrcKernel) — real-time propagation via unitary Crank-Nicolson steps with dipole-to-absorption spectra, Bloch current, and an Ehrenfest nuclear step (crankNicolsonStep, ehrenfestStep), plus a TDDFT-vs-BSE spectrum comparison and kernel ranking (compareTddftBse). Formula-level model dimensions, not a plane-wave TDDFT code.

An aggregator facade (libs/kalika/tensor/src/index.ts, ~7 lines): re-exports @kalika/general-relativity and declares TENSOR_SOURCE_MODULES = ['@kalika/general-relativity']. Tensor-calculus code lives in the GR library; this is a thin alias.

Tensor networks (libs/kalika/tensor-networks/src, ~15 files): mps, peps, mera, dmrg, lattice-gauge, a generic tensor-network (the einsum engine), and XXZ benchmarks.

Lattice thermal conductivity (libs/kalika/thermal-transport/src, ~1.1k lines, depends on @kalika/phonons + @kalika/phonons-anharmonic): phonon-BTE solvers from RTA through iterative, direct, and variational-bound forms (kappaRTA, iterativeBTE, directBTE, variationalBound), mode-resolved and temperature-dependent κ, scattering mechanisms — Tamura isotope mass-variance, Casimir boundary, alloy, T-matrix and four-phonon rates combined by Matthiessen's rule — and spectral analysis: mean-free-path accumulation, a Wigner coherent-transport contribution (wignerCoherentKappa), and ballistic-diffusive suppression.

Thermodynamics (libs/kalika/thermodynamics/src): equations-of-state, phase-diagrams, thermodynamic-cycles, and thermodynamic-potentials.

3-manifold topology (libs/kalika/three-manifolds/src): heegaard-floer, wrt (Witten-Reshetikhin-Turaev), and interfaces to regina and snappy.

Topological quantum computing (libs/kalika/topological-qc/src): anyon-model, braiding-simulation, gate-compilation, topological-entanglement, and standard models.

Topology (libs/kalika/topology/src, ~26 files): simplicial-complex, cw-complex, homotopy, cohomology, Morse theory/homology, discrete Morse, knot-theory, persistent-homology, and TDA applied to cosmic structure / phase transitions (cosmic-structure-tda, phase-transition-tda).

ML training-data pipeline for math models (libs/kalika/training-data/src, ~74 files): arXiv-LaTeX extraction, dedup, domain balancing, proof-pile, tokenizer extension, embedding/instruction-tuning/reward-model training, RLVF, constitutional AI, model A/B testing, serving/routing, speculative decoding, KV-cache. A large self-contained ML-ops corner of the area.

Tropical geometry (libs/kalika/tropical/src, ~16 files): semiring, polynomial, convexity, newton-polytope, variety, grassmannian, and a feynman (tropical-Feynman) module.

LaTeX typesetting and import (libs/kalika/typesetting/src): equations, derivation, latex + latex-import, and paper modules for rendering Kalika results and ingesting papers.

Shared scientific utilities (libs/kalika/utils/src): dimensions, physical-constants, and physical-quantity (units-and-dimensions support used across the physics libraries).

Vertex algebras (libs/kalika/vertex-algebras/src): vertex-operator-algebra, module-theory, w-algebras, standard-constructions, and moonshine.

A near-empty scaffold (libs/kalika/wannier/src/index.ts is a single line exporting WANNIER_PACKAGE_NAME = '@kalika/wannier', plus a trivial spec). No Wannier-function implementation lives here — and none lives anywhere else either: electronic-structure/src/wannier/ is itself an empty placeholder directory (.gitkeep only), and the only wannier references in Kalika TS are the unrelated Wannier-center-flow (condensed-matter) and Kramers-Wannier duality (statistical-mechanics/notebooks) uses, not Wannier-function machinery. Shown as a reserved/placeholder slot, not a working library.

DFT exchange-correlation functionals (libs/kalika/xc-functionals/src, ~36 files, ~8.1k lines): organised by rung — lda, gga, and meta-gga modules exposing many named functionals through the barrel.

Python bindings (libs/kalika/sdk-python/src/kalika_sdk) exposing a SymPy-like surface (symbols, diff, integrate, solve); the default backend shells out to the TypeScript SDK via a Node/tsx subprocess (_bridge.ts, backends.py, client.py, expressions.py). Nx project name is the un-scoped kalika-sdk-python.

A Jupyter kernel (libs/kalika/jupyter-kernel/src/kalika_jupyter, ~600 lines Python) that runs Kalika CAS computations from notebook cells (simplify, diff, integrate, solve, eval) while preserving derivation chains and verification metadata in rich output bundles. Nx project name kalika-jupyter-kernel.