REFLEX

Reflexive Equilibrium Fixed-point Learning for Endogenous eXchanges (ie. financial markets).

A machine learning framework for markets where the data distribution is not fixed, but is generated by the model itself. In OTC corporate bond markets, a dealer's quoting policy reshapes future trade flow, spreads, and liquidity, breaking the standard ML assumption that the data-generating process is independent of the learner.

REFLEX reframes learning as solving for a self-consistent equilibrium: a fixed point where the market dynamics induced by a trading policy are stable under repeated interaction with that same policy.

Built by Vignesh Nagarajan and Shriraghav Ashok.

Tech Stack

_{AI / ML & Scientific Computing:}

_{Language, Config, Testing & Verification:}

_{Tooling & Docs:}

_{Initial Prototype (archive/edl_simulator_v1):}

Functionality

• Endogenous Distribution Learning: replaces exogenous data D_{t+1} = P(·|D_t) with a policy-dependent system D_{t+1} = T(D_t, π_θ).
• Learned market response operator T_θ: a differentiable, trainable operator over stochastic market transitions, replacing hand-built simulators.
• Structurally-anchored performative correction: the learned loop fits the market model's own response families to its deployment history and ascends the estimated corrected gradient - stable where blind retraining diverges.
• Fixed-point objective: solve (π*, D*) = argmin_π E_D[R(π)] s.t. D = T(D, π).
• Stability-aware training: penalizes distribution collapse, liquidity fragmentation, and instability under self-induced market adaptation.
• Implicit liquidity modeling: treats liquidity as a latent dynamical field induced by interaction, not an observed variable.
• Machine-checked theory: every load-bearing identity of the six closed-form results is re-derived numerically (66 proof certificates), with the logical skeletons formalised in Lean 4.

Model lineage

Five generations of the same idea, an endogenous market whose stability is governed by a single feedback parameter, each more structural than the last:

flowchart LR
    A["edl_simulator_v1<br/>(HTML/JS mockup)<br/>analytical LQ model"]
      --> B["endo_market_v1<br/>(Python / PyTorch)<br/>learned operator + RRM"]
      --> C["endo_market_v2<br/>(Python / PyTorch)<br/>refined, result reproduced"]
      --> D["endo_market_v3<br/>(+ real data)<br/>un-blinded ML + closed-form theory"]
      --> E["endo_market_v4 / reflex<br/>(FINAL)<br/>structural PerfGD + theory 1.6 + tuning + verification"]

Loading

	edl_simulator_v1	endo_market_v1	endo_market_v2	endo_market_v3	endo_market_v4 (reflex)
Role	Earliest prototype	Legacy iteration	Superseded	Superseded (produced the 07-10-2026 run)	Current — FINAL
Implementation	HTML/JS browser mockup	Python (PyTorch, CPU)	Python (PyTorch, CPU)	Python (PyTorch + pandas, CPU), real-data calibrated	Same, + verification layer (numerical certificates + Lean 4 skeletons)
Market model	Analytical linear-quadratic OTC bond	Structural multi-bond simulator (uninformed + toxic flow)	Structural OTC simulator + latent liquidity field	Same + genuine N-dealer shared informed pool	Same
Learner	Closed-form fixed point	Learned operator T_θ + RRM loop	Same, refined	Un-blinded T_θ (windowed fit learns dD/dφ) + PerfGD-corrected loops (analytic & free-form learned)	+ perfgd_structural: GLFT-anchored fits of the loop's own data; the learned loop that stabilises beyond the boundary
Control parameter	Adversarialness α	Adversariality α ∈ [0,1]	Feedback gain ε (α found to be confounded)	ε, dealer count N, universe size d, market regime	+ inner steps per deployment K (lazy deployment, theory 1.6)
Stability law	Stable iff α < α_c = 1; rate α^t	m = K·α, boundary α* = 1/K	m ≈ εβ/γ, boundary ε < γ/β	Closed-form ε < γ/β, ε < γ/(N_eff·β), ρ(M) < 1 - predicted a-priori, then verified	+ mu(K) = −m + c^K(1+m) (deadbeat / max-stable K; two-branch γ_eff)
Headline status	Validated at α = 0.45	Scaffolding done; α* result not reproduced	Result reproduced (measured crossing later shown protocol-inflated; see its README)	Theory+ML+data unified; real-data fragility index; loop-level gap honestly documented	The gap closed: the structural learned loop settles at the realized performative optimum where blind RRM diverges; estimators tuned; theory machine-verified
Tests / artifacts	Sample run screenshot	18 unit tests	63 tests + phase-diagram PNG & sweep CSV	110 tests + 9 experiments, full-profile verified 8/8 (curated in research/results/07-10-2026/)	152 tests + 12 experiment entry points, full-profile verified 11/11 (curated in research/results/07-12-2026/)

The progression: edl_simulator_v1 proved the concept (one parameter flips a market between convergence and chaos) analytically; endo_market_v1 rebuilt it as a learned-operator performative-prediction loop but couldn't cleanly tune the transition; endo_market_v2 identified ε (not α) as the clean control and reproduced the ε < γ/β stability boundary; endo_market_v3 unified the ML, the closed-form theory and the real-data calibration and un-blinded the learned operator - leaving one honestly-documented gap: the corrected learned loop did not stabilise. endo_market_v4 closes that gap by anchoring the learned response to the GLFT structural form (fit the theory's own response families to the loop's deployment history, ascend the estimated corrected gradient), adds the lazy-deployment theory (1.6), tunes the estimators, and wraps the whole theory in a verification layer. The four prior generations are frozen in archive/.

Repository layout

REFLEX/
|- README.md                    <- this file
|- CLAUDE.md                    <- orientation and conventions for AI coding agents
|- LICENSE                      <- Apache License 2.0
|- endo_market_v4/              <- CURRENT (FINAL): the self-contained `reflex` package
|  |- README.md                 <- methodology, the six pillars, quickstart, honest caveats
|  |- theory/                   <- the six derivations (shipped copies) + code map
|  |- lean/                     <- Lean 4 formal skeletons of 1.1-1.6 (+ honest status)
|  |- data/                     <- calibration CSVs + daily master panel (provenance notes)
|  |- configs/                  <- default | smoke | sweep specs
|  |- reflex/                   <- the package: env (incl. N-dealer), policy (+GLFT baseline),
|  |                              operator (un-blinded T_θ), theory (1.1–1.6), equilibrium
|  |                              (4-mode loops incl. perfgd_structural + joint loop),
|  |                              estimators (tuned ε triangulation + K-step probe),
|  |                              calibration, objective, analysis (incl. fragility),
|  |                              verification (proof certificates), utils
|  |- experiments/              <- 12 entry points incl. run_all --profile smoke|full
|  |- outputs/                  <- CSVs + PNGs from the latest full-profile run
|  \- tests/                    <- 152 tests (142 fast + 10 slow)
|- literature/                  <- two curated literature collections
|  |- literature-vignesh/       <- 10 foundational papers + reading map (PDFs downloaded)
|  \- literature-raghav/        <- same core + 8 extension papers + research roadmap
|- research/                    <- the research program around endo_market_v4: theory, data, runs, analyses, paper
|  |- README.md                 <- full methodology write-up and the To-Do checklist
|  |- math-theory/              <- canonical derivations 1.1–1.6 (.md + .tex + PDFs)
|  |- data_collection/          <- real macro + bond-factor dataset (raw/processed/master) + verification
|  |- preprocessing/            <- cleaning, calibration fit (A,k), episode splits
|  |- results/                  <- executed paper-grade runs (07-10-2026 v3; 07-12-2026 v4)
|  |- analysis/                 <- written analyses of those runs (tables, figures, breakdowns)
|  \- paper/                    <- the ICAIF 2026 submission draft (ACM sigconf, double-blind)
\- archive/                     <- the four frozen prior generations (see archive/README.md)
   |- edl_simulator_v1/         <- earliest prototype (HTML/JS mockup)
   |- endo_market_v1/           <- earliest Python iteration
   |- endo_market_v2/           <- second generation (result absorbed into v3)
   \- endo_market_v3/           <- third generation (produced the 07-10-2026 run)

Experiments

A dealer's quoting policy φ induces the data distribution D(φ): tighter quotes summon more informed ("toxic") flow that picks the dealer off. Under repeated retraining (RRM), when does the policy↔distribution loop converge vs. diverge - and can the loop be stabilised by un-blinding it, analytically (closed-form PerfGD) or by learning (the v4 structural mode)?

Executive summary of the v3 paper-grade results (July 10, 2026)

The full-profile suite ran 8/8 in ~10 min CPU after a measurement-layer audit fixed six probe/protocol defects; every number below is from the curated run in research/results/07-10-2026/ (complete illustrated report: REPORT.md).

• Real-data fragility (1.1 on 36 years of data): the closed-form stability headroom ε* = γ/β collapses ~4.4× (IG) / ~4.3× (HY) from calm to crisis, HY sits >10× below IG in every regime, and the modulus at observed spreads falls into crisis (0.85 → 0.14): defensive widening, live on real data. The index saturates at a crisis plateau through the GFC and the COVID freeze (degenerate crisis fit, flagged).
• Predict-then-verify (1.1 + 1.4): under the clean probe protocol the measured modulus tracks the closed form within ~10–25% in the contracting regime (0.39 vs 0.43 at ε = 2), and the measured boundary crossing (ε* ≈ 3.17) sits left of the a-priori prediction (4.70) by almost exactly the realized-state correction (~2.8–3.0) that the triangulation measures independently. The robust certificates grade the grid stable → undecided → unstable exactly as the seed bands warrant.
• Systemic risk on a genuine multi-dealer market (1.3): common-mode amplification 1.74× / 3.16× vs the predicted N_eff = 2 / 3, with the differential mode dead at full spillover: competition destabilises the market a factor N_eff before any single dealer would.
• Three-way ε triangulation (1.1 §9): the Sinkhorn and CKS legs agree with each other within 14% and bracket the realized-state closed form at 2.3–2.7×, with the liquidity-inflation channel (realized ρ ≈ 2.3 vs the a-priori 1.0) identified as the dominant correction.
• Factor scaling (1.5): ρ(M) ≈ 0.50 flat from 8 to 128 bonds on data-calibrated per-bond dispersion; the truncation bound holds with orders of magnitude of slack; 0.07 s at d = 128 via Woodbury.
• The α confound (appendix): the adversariality sweep shows its full non-monotone hump (0.08 → 1.83 → 0.67), the quantitative case for the feedback gain ε as the headline control variable.

What v4 adds (paper-grade run, July 12, 2026; research/results/07-12-2026/)

• The loop-level gap is closed (1.2, v4): in the genuinely RRM-unstable regime the blind loop fails to converge while perfgd_structural - the learned loop with its response anchored to the GLFT structural families and fitted to its own deployment history - settles at the realized performative optimum, verified against independent structural fits (and strictly inside their blind stable point: the realized echo-chamber gap, closed). The free-form learned mode remains a documented negative result - anchoring, not capacity, is what closes the gap.
• Lazy deployment (1.6): the K-step outer map mu(K) = −m + c^K(1+m) fits the measured signed CRN K-probe curve with one parameter; laziness reads as a two-branch effective curvature γ_eff(K) (inertia below the equal-modulus count, stiffness above), with deadbeat and max-stable step counts in closed form.
• Estimator tuning: the Sinkhorn blur is tuned scale-relatively against the exact 1-D quantile W1 (U-shaped bias curve, minimum at 0.02 × sample std, baked in as reg="auto"); the robust ambiguity radius gets a distribution-free coverage calibration (z*s measured conservative; the quantile radius matters for contaminated/railed-probe patterns).
• Machine-checked theory: 66 numerical proof certificates re-derive every load-bearing identity of 1.1–1.6 on raw and calibrated real-unit configs (catching, en route, a real λ_q bookkeeping subtlety in the 1-D helpers); the logical skeletons are formalised in Lean 4 (endo_market_v4/lean/; reviewed statements, compile pending a toolchain - honest status in its README).

The real-data headline: daily stability headroom on 36 years of market data, plateauing through the GFC and COVID	Predict then verify: measured modulus (median + IQR + robust bands) vs the closed form at the probe spread
The v4 gap closure: blind RRM vs analytic vs free-form learned vs the structural learned loop, with the three-way seam	Theory 1.6: the measured K-step map vs the one-parameter closed form, and the two-branch effective curvature

The experiment suite (11 experiments + the run_all driver)

Run everything with python -m experiments.run_all --profile smoke|full (full profile: ~15-25 min CPU, deterministic from (config, seed)):

Experiment	What it shows	Theory
run_certificates	66 numerical proof checks of every 1.1–1.6 identity (raw + calibrated)	all
run_fragility	The daily 1990–2026 fragility index on real data	1.1 on data
run_calibrated	A-priori boundary per (rating × regime) from fitted (A, k, σ, h)	1.1 + data
run_sweep	Predict-then-verify phase diagram: analytic overlay + measured median/IQR + robust bands	1.1 + 1.4
run_perfgd	Closed-form beyond-boundary demo + echo-chamber gaps + the four-mode ML loops (incl. the structural gap closure)	1.2
run_dealers	(N, ε) systemic surface m_N = N_eff·m₁; genuine shared-pool market probes	1.3
run_universe	ρ(M) at 128 correlated bonds via O(d·k²) Woodbury; truncation bound verified	1.5
run_triangulation	Three independent ε estimators (BR-slope / Sinkhorn / CKS) vs the closed form	1.1
run_lazy_deploy	The signed K-step map vs mu(K) = −m + c^K(1+m); γ_eff(K)	1.6
run_tuning	Sinkhorn blur bias curve + robust-radius coverage calibration	1.1 + 1.4
run_single	One outer loop in any mode with seam diagnostics	-

See endo_market_v4/README.md for methodology, layout, install/run and honest caveats. Prior generations: archive/README.md; endo_market_v2's historical headline result (and its post-audit correction) lives in archive/endo_market_v2/README.md.

Literature

REFLEX/literature/ holds two curated collections at the intersection of performative prediction / decision-dependent stochastic optimization and optimal OTC market making. Each paper maps to a specific component of the codebase and points at a concrete extension.

• literature-vignesh/: the original 10 foundational papers and the reading map that ties each one to a piece of the codebase (the RRM loop, the operator T_θ, the BR-slope modulus, the toxic-flow gate, inventory state, the scale-up caveats). PDFs are already downloaded under pdfs/.
• literature-raghav/: the same foundational core, expanded with deeper per-paper "critical reading notes" and a more opinionated research roadmap (specific theorems to prove, experiments to run, venues to target). Run its download_pdfs.sh to fetch the PDFs.

The throughline: Perdomo et al.'s performative-prediction theorem says repeated retraining converges iff ε < γ/β. The optimization literature sharpens that loop, makes it stateful, and makes ε explorable; the market-microstructure control theory (Guéant-Lehalle-Fernández-Tapia, Bergault-Guéant, Barzykin et al.) supplies the structure that lets γ, β, and the toxic slope be derived from first principles rather than tuned. REFLEX is the bridge that realizes the theorem structurally inside an OTC bond market. Full per-paper notes and BibTeX live in each collection's README.md and references.bib.

Analytic stability theory (research/)

Where the simulator measures the stability boundary by sweeping, the research/math-theory/ program derives it in closed form from the simulator's own microstructure primitives - then verifies each derivation against the code. All six results are derived and implemented as dependency-light closed-form modules - authoritative versions in endo_market_v4/reflex/theory/ (originals frozen in archive/endo_market_v2), each with tests and numerical proof certificates:

#	Result	Key object	Novelty
1.1	Analytic boundary	m = εβ/γ, stable iff ε < γ/β	γ, β, ε are computed from GLFT fill-curve curvature + the toxic-flow slope dτ/dh, not treated as tuned Lipschitz constants - an a-priori boundary you can evaluate before running the loop.
1.2	PerfGD un-blinding	Δ = −β(h−ψ)ε(h), γ_PO	The distribution response dD/dφ is supplied in closed form (no estimation), so the corrected loop is governed by the objective curvature γ_PO and converges where blind RRM diverges - past the boundary ε*. v4 addendum: the same correction with every ingredient estimated from deployment data (perfgd_structural) stabilises the actual learned loop.
1.3	Multi-dealer systemic risk	ε < γ/(N_eff·β), N_c = 1/m₁	A shared toxic pool makes competition a synchronised common-mode cobweb: the market destabilises a factor N_eff before any single dealer would - competition manufactures systemic fragility.
1.4	Robust boundary	ε̂_n + δ_n < γ/β, δ_n = O(1/√n)	The parametric 1/√n radius is bought by the common-random-numbers probe (a naive difference gives only n^{−1/3}); the crossing is statistically hard to pin (n_req = O(Δ^{−2})), separating statistical from structural uncertainty. v4 addendum: a distribution-free coverage calibration of the radius.
1.5	Factor-model scaling	modulus matrix M = βΓ⁻¹E, ρ(M)<1	The curse of dimensionality is defused by the same factor structure that causes it - Γ is diagonal-plus-low-rank, so ρ(M) is O(d·k²) via Woodbury with a truncation error linear in the residual factor variance λ_{k+1}(C).
1.6	Lazy deployment (v4)	mu(K) = −m + c^K(1+m), γ_eff(K)	The outer loop between the greedy-RGD and exact-RRM idealisations in one closed form: laziness interpolates the cobweb, can deadbeat it at finite K, keeps an m > 1 market stable up to K_max, and masquerades as a two-branch effective curvature.

The novelty in one line. Performative-prediction theory (Perdomo et al., ICML 2020) proves repeated retraining converges iff ε < γ/β but treats γ, β, ε as abstract constants of an unspecified loss. REFLEX pins them to a structural OTC market-making model and turns that single point boundary into a predictive, un-blindable, multi-dealer, statistically-robust, 100+-bond, lazily-deployed one - every claim stated as a closed form, made falsifiable against the simulator, and machine-checked by the verification layer. See research/README.md for the full methodology and research/math-theory/ for the derivations (each with a compilable LaTeX companion) and the module-by-module code map.

Data (real-market calibration)

research/data_collection/ and research/preprocessing/ hold a real, public, verified dataset used to calibrate the simulator's microstructure regime - ~36 years of daily and ~70 years of monthly series joined into REFLEX_MASTER_DATASET.csv:

• Macro / regime: CBOE VIX (σ proxy, regime classifier), EIA WTI crude, Fed H.15 10-year Treasury (DV01), Shiller S&P 500 / CAPE, gold + BLS CPI.
• Bond microstructure: Dickerson–Mueller–Robotti (2023 JFE) TRACE-derived bond factors - the liquidity risk factor is the primary ε proxy - and monthly returns for 212 real-CUSIP corporate bonds (the D(φ) proxy).
• Preprocessing: cleaning/winsorisation/ADF, reconstructed (h, q, τ) proxies, an exponential-intensity λ(h)=A·e^{−k·h} fit per rating×regime, and lookahead-safe calibration / validation / held-out episode splits.

Honest provenance (stated in the paper, not a footnote): this is not trade-level TRACE - dealer-side prints, per-dealer inventory q, and per-bond A/k require WRDS TRACE Enhanced (access pending), so those quantities are proxied from the closest free sources. See data_collection/docs/REJECTED_SOURCES.md.

endo_market_v4 ships copies of the artifacts it consumes (endo_market_v4/data/) so the package is self-contained; regenerate everything from public sources with the pipeline's four scripts.

Docs

Every document in the project and where it lives:

Document	What it covers
README.md	This file: the project overview
CLAUDE.md	Orientation and conventions for AI coding agents (layout, gotchas, build/test/run)
endo_market_v4/README.md	The current package: methodology, the six pillars, quickstart, honest caveats
endo_market_v4/theory/README.md	Code map from the six derivations to reflex.theory (+ shipped derivation copies)
endo_market_v4/lean/README.md	The Lean 4 formal skeletons: scope, build instructions, honest compile status
endo_market_v4/data/README.md	Provenance of the shipped calibration artifacts
research/README.md	The full research-program methodology and the To-Do checklist (incl. ICAIF requirements)
research/math-theory/README.md	The six canonical derivations 1.1–1.6 (each .md + compilable .tex; PDFs for 1.1–1.5)
research/data_collection/README.md	Dataset sources and construction; docs/ holds DATA_CATALOGUE.md, VERIFICATION_LOG.md, REJECTED_SOURCES.md
research/preprocessing/README.md	Cleaning, enrichment, intensity fits, episode splits
research/results/README.md	Conventions for the dated run folders
research/results/07-10-2026/REPORT.md	The complete illustrated report of the v3 paper-grade run
research/results/07-12-2026/REPORT.md	The illustrated report of the v4 paper-grade run (11 experiments, incl. the gap closure)
research/analysis/README.md	Index of the analysis layer
research/analysis/ANALYSIS-full-2026-07.md	The master per-experiment analysis of the v3 run: tables, breakdowns, limitations
research/analysis/pre-run-audit-2026-07.md	The measurement-layer audit: six defects, root causes, fixes, reframings
research/paper/README.md	The ICAIF 2026 submission draft: contents, Overleaf build, ICAIF checklist mapping, camera-ready TODOs
literature/literature-vignesh/README.md	10 foundational papers, reading map, per-paper notes (+ references.bib)
literature/literature-raghav/README.md	18 papers with critical reading notes + research roadmap (+ references.bib)
archive/README.md	The four frozen prior generations: what each was, why superseded, provenance notes
archive/endo_market_v3/README.md	The superseded third generation (produced the 07-10-2026 run)
archive/endo_market_v2/README.md	The superseded second generation: mechanism, historical headline result + post-audit note
archive/endo_market_v1/README.md	The legacy first Python iteration
archive/edl_simulator_v1/README.md	The earliest analytical prototype (HTML/JS)

Status and next steps

The research program targets one novelty claim: derive the performativity stability boundary analytically from microstructure primitives instead of sweeping it by hand.

Where things stand (July 2026, v4 - the repo side is complete): theory (1.1–1.6) derived + coded; the ML un-blinded and the loop-level gap closed by the structural mode; the estimators tuned; the theory machine-verified (66 numerical certificates + Lean 4 skeletons); real-data calibration wired in; the measurement layer audited (six probe/protocol defects found and fixed; 152/152 tests); paper-grade full-profile suites executed and curated (research/results/07-10-2026/ for v3, research/results/07-12-2026/ for v4).

• Analytic boundary (P1): γ, β, dτ/dh in closed form (reflex/theory/analytic_boundary.py); the three-way ε triangulation built, tuned and verified against the realized-state closed form (reflex/estimators/).
• Un-blind the operator (P2): PerfGD-corrected loops with the analytic, free-form learned and structural dD/dφ (reflex/theory/perfgd.py, reflex/equilibrium/loops.py, reflex/equilibrium/structural_response.py); closed form verified and the loop-level stabilisation demonstrated (the structural mode settles at the realized optimum beyond the boundary; the free-form mode remains the documented negative result).
• Multi-dealer / systemic risk (P3): PSNE boundary ε < γ/(N_eff·β), mean-field limit, and a genuine N-dealer market with amplification verified (reflex/theory/multi_dealer.py, reflex/env/multi_dealer.py).
• Robust uncertainty (P4): robust ε* with O(1/√n) radius; bands + certificates on every sweep; the v4 coverage-calibrated radius (reflex/theory/robust.py).
• Scale and calibrate (P5): 128 correlated bonds via O(d·k²) Woodbury with data-calibrated per-bond σ; regime-calibrated microstructure (reflex/theory/factor_scaling.py, reflex/calibration/); trade-level TRACE calibration pending WRDS access.
• Lazy deployment (1.6, v4): the K-step map, γ_eff, and the swept verification (reflex/theory/lazy_deploy.py, experiments/run_lazy_deploy.py).
• Estimator tuning (v4): the Sinkhorn blur (scale-relative, 0.02×std) and the robust ambiguity radius (coverage-calibrated) (experiments/run_tuning.py).
• Verification layer (v4): 66 numerical proof certificates (raw + calibrated configs) + the Lean 4 skeletons (reflex/verification/, lean/; Lean compile pending a toolchain — honest status in its README).
• Paper-grade full-profile runs → curated results: v3 (July 10, 8/8) and v4 (July 12, 11/11) in research/results/.
• Draft the ICAIF 2026 paper (ACM sigconf, 8 pages, double-blind; deadline Aug 2, 2026) - the submission draft lives in research/paper/, scoped as settled in the analysis: closed forms + real-data fragility + probe-level verifications are the headline; the v4 structural stabilisation is reported against the realized-market benchmark with the A2-gap channels named. Compiled on Overleaf at exactly 8 pages (research/paper/REFLEX_Research_Paper.pdf). Remaining: the double-blind re-toggle + anonymized repo mirror, CMT submission.
• Secure a research placement at a top AI lab (with affiliation).
• Vignesh will submit to ICAIF 2026 (ACM Intl. Conference on AI in Finance) or another main-track venue.

Full task breakdown across math, data, preprocessing, architecture, training, and ICAIF submission requirements: the To-Do section of research/README.md.

License

Licensed under the Apache License 2.0: free to use, modify, and distribute with attribution and notice of changes.