# Kalika — Systems Deep Dive

> The `libs/kalika/` area: ~96 Nx projects making up Oshun's scientific-research
> platform — a symbolic-algebra core, two Rust compute kernels, a Python/Jupyter
> SDK surface, and a broad library of mathematics, theoretical-physics, and
> materials-science code. This page is the entity-catalog view; the narrative
> architecture lives in the
> [Kalika domain space](../../docs/domains/kalika/deep-dive/architecture.html).

## What this area is

Kalika is the layer underneath Oshun's consumer domains: the symbolic
representation, the provenance model, the compute kernels, the reactive research
notebooks, the autonomous research agents, and a very wide library of
mathematics and physics implementations. The organising idea is the
**reproducibility-and-auditability gap** in computational science — a bare
number is not a result; the derivation chain, assumptions, units, tolerance, and
verification status are. `@kalika/core`'s `ProvenResult<T>` and `Expr` AST carry
that metadata through the stack.

The area is unusually large and **unevenly integrated**, and the most important
honest fact about it (documented at length on the domain architecture page) is
that it holds **two parallel compute substrates that are not yet wired to each
other at runtime**: the Rust kernels (`@kalika/cas-engine`,
`@kalika/numerical-engine`) and a hand-written TypeScript symbolic/numeric stack
built on `@kalika/core`. The Rust kernels are genuinely deep (tens of thousands
of lines), but with one exception (`@kalika/electronic-structure` depends on
`@kalika/numerical-engine`) no TypeScript package imports them — the
`'@kalika/cas-engine'` strings in packages like `@kalika/arithmetic` and
`@kalika/calculus` are **backend-name labels/metadata, not imports**.

A handful of packages are deliberately thin: **facade/aggregator packages** that
only re-export sibling libraries (e.g. `@kalika/mathematical-physics`,
`@kalika/operators`, `@kalika/cohomology`) or declare a capability/metadata
constant (`@kalika/arithmetic`, `@kalika/calculus`), and one near-empty
**scaffold** (`@kalika/wannier`). The bulk, however, are substantial: dozens of
TypeScript libraries in the multi-thousand-line range with real, domain-specific
module decompositions (named explicitly per entity below).

## How it fits the wider system

These libraries are consumed by the Kalika applications (`apps/kalika/*` — the
compute service, notebook backend, research-agent runners) and by the
TypeScript/Python SDKs (`@kalika/sdk`, `kalika-sdk-python`,
`kalika-jupyter-kernel`). Internally they form a dependency cone rooted at
`@kalika/core` (the `Expr` AST, provenance, rewrite engine): the math/physics
libraries build on `core` and on each other, the facade packages re-export them
into convenient umbrellas, and the platform libraries (`@kalika/database`,
`@kalika/knowledge-graph`, `@kalika/renderer`, `@kalika/notebooks`,
`@kalika/research-agents`, `@kalika/training-data`) compose the computational
libraries into storage, visualization, notebook, and agentic-research surfaces.
Walk the "used by" edges on any node below to see exactly who depends on it.

Two further families sit alongside the mathematics/physics cone:

- **First-principles materials science** — `@kalika/crystallography` plus the
  lattice-dynamics chain (`phonons`, `phonons-dfpt`, `phonons-anharmonic`,
  `phonons-special`, `thermal-transport`, `electron-phonon`, `eliashberg`,
  `polarons`) and the many-body/correlated-electron chain (`many-body`, `gw`,
  `bse`, `response`, `tddft`, `dmft`, `qmc`, `cc-solids`, `embedding`,
  `molecular-dynamics`, benchmarked by `many-body-benchmarks`). Real named
  algorithms in TypeScript (tetrahedron DOS, CT-HYB, Allen-Dynes, fixed-node
  DMC), mostly compact/formula-level rather than plane-wave-scale solvers;
  DFT-engine execution and GPU kernels are explicit fail-loud seams, and
  `molecular-dynamics` carries Rust crates not yet bridged to TS.
- **Lab automation / self-driving lab** — `@kalika/experiment-orchestration`
  (the shared type backbone) with `doe`, `protocols`, `instrument-control`,
  `lab-safety`, `sample-ops`, `closed-loop-experiments`, and `research-ops`:
  design, compile, safety-gate, track, and close the loop on experiment
  campaigns. Honestly a control-plane/policy layer — typed models, validators,
  and planners; no live instrument transport is implemented (drivers are
  interface seams).

## Entity reference

### @kalika/core

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.

### @kalika/cas-engine

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.

### @kalika/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.

### @kalika/sdk

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.

### kalika-sdk-python

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`.

### kalika-jupyter-kernel

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`.

### @kalika/database

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.

### @kalika/knowledge-graph

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.

### @kalika/research-agents

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.

### @kalika/training-data

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.

### @kalika/notebooks

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.

### @kalika/renderer

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.

### @kalika/citations

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

### @kalika/typesetting

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

### @kalika/hpc-orchestrator

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.

### @kalika/formal-verification

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.

### @kalika/utils

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

### @kalika/autodiff-core

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

### @kalika/autodiff

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.

### @kalika/algebra

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`.

### @kalika/arithmetic

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.

### @kalika/calculus

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.

### @kalika/number-theory

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.

### @kalika/combinatorics

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

### @kalika/algebraic-combinatorics

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

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

### @kalika/algebraic-geometry

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.

### @kalika/analysis

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`.

### @kalika/approximation

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

### @kalika/numerical

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`.

### @kalika/measure-theory

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

### @kalika/probability

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

### @kalika/optimization

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.

### @kalika/optimal-transport

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

### @kalika/sdp-core

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.

### @kalika/surrogate

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

### @kalika/category-theory

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`.

### @kalika/higher-categories

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

### @kalika/cohomology

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.

### @kalika/differential-geometry

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`.

### @kalika/geometric-analysis

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

### @kalika/lie-theory

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`.

### @kalika/quantum-groups

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

### @kalika/noncommutative-geometry

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

### @kalika/spectral-geometry

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`.

### @kalika/symplectic

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

### @kalika/topology

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`).

### @kalika/three-manifolds

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

### @kalika/tropical

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

### @kalika/vertex-algebras

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

### @kalika/periods

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

### @kalika/integrable-systems

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

### @kalika/matrix-models

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

### @kalika/positive-geometry

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

### @kalika/operators

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.

### @kalika/tensor

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.

### @kalika/classical-mechanics

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.

### @kalika/electrodynamics

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

### @kalika/optics

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

### @kalika/fluid-dynamics

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

### @kalika/plasma-physics

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

### @kalika/thermodynamics

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

### @kalika/statistical-mechanics

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`.

### @kalika/quantum-mechanics

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`.

### @kalika/quantum-field-theory

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`).

### @kalika/quantum-chaos

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

### @kalika/quantum-gravity

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

### @kalika/quantum-computing

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.

### @kalika/open-quantum-systems

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

### @kalika/entanglement

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

### @kalika/information-theory

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

### @kalika/topological-qc

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

### @kalika/general-relativity

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.

### @kalika/gravitational-waves

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

### @kalika/cosmology

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`).

### @kalika/astrophysics

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

### @kalika/bbn

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

### @kalika/neutrino-physics

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

### @kalika/hep-phenomenology

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`).

### @kalika/particles

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.

### @kalika/feynman

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.

### @kalika/string-theory

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`).

### @kalika/supersymmetry

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

### @kalika/non-perturbative

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`).

### @kalika/bootstrap

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).

### @kalika/resurgence

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

### @kalika/mathematical-physics

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.

### @kalika/nonlinear-dynamics

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

### @kalika/lattice

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

### @kalika/tensor-networks

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.

### @kalika/condensed-matter

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

### @kalika/electronic-structure

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`.

### @kalika/atomic-physics

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

### @kalika/xc-functionals

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.

### @kalika/neural-physics

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.

### @kalika/symbolic-regression

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.

### @kalika/wannier

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.

### @kalika/bse

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.

### @kalika/cc-solids

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.

### @kalika/closed-loop-experiments

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.

### @kalika/crystallography

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.

### @kalika/dmft

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.

### @kalika/doe

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).

### @kalika/electron-phonon

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`.

### @kalika/eliashberg

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.

### @kalika/embedding

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.

### @kalika/experiment-orchestration

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.

### @kalika/gw

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.

### @kalika/instrument-control

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.

### @kalika/lab-safety

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.

### @kalika/many-body

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.

### @kalika/many-body-benchmarks

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.

### @kalika/molecular-dynamics

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.

### @kalika/phonons

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.

### @kalika/phonons-anharmonic

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`.

### @kalika/phonons-dfpt

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.

### @kalika/phonons-special

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.

### @kalika/polarons

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.

### @kalika/protocols

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.

### @kalika/qmc

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.

### @kalika/research-ops

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.

### @kalika/response

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.

### @kalika/sample-ops

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.

### @kalika/tddft

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.

### @kalika/thermal-transport

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.