Quintropy

A causal Bayesian solver for five-letter word puzzles.

Model answer selection, search the complete action space and replay every decision from versioned research artifacts.

Overview · Web solver · Published result · Architecture · Local development · Quality

Overview

Quintropy separates answer modeling from guess selection. A causal prior estimates which words are plausible answers using only information available before each puzzle date. The policy then searches all 12,972 permitted actions using Shannon information gain, direct-hit utility and exact small-state search where configured.

Experiments are stored with their priors, complete action paths, configuration, dependency versions and input hashes. The independent auditor reconstructs the policy and verifies every decision and reported metric.

Web solver

Open the static Quintropy solver to enter the feedback from a live board and receive the selected model's next recommendation. The interface loads a frozen causal snapshot, filters candidates with exact duplicate-letter semantics and searches all 12,972 permitted actions in a Web Worker. Board data remains on the device; the site has no application server, analytics or external runtime dependencies.

The deployable site lives entirely in web/. Regenerate its model snapshot after an intentional training-data or selected-model update:

quintropy export-web --output web/model.json

Published result

The repository contains one immutable evaluation of the selected architecture:

Period	Games	Mean tries	Accuracy@6	Worst case
2026-05-01–2026-08-12	104	3.077	100%	6

The complete, schema-v2 artifact is available under results/baselines/editorial_regime_linguistic_tail_2026-05-01_2026-08-12. It binds the corrected 8,926-word answer universe, the chronological history, dependency versions and the implementation hash. The period was inspected during development, so this is a reproducible retrospective evaluation, not independent prospective evidence.

Capabilities

• Causal prior generation — fit each daily distribution exclusively from earlier answers.
• Separate answer and action spaces — assign probability only to supported answers while retaining every permitted word as an informative action.
• Editorial-regime modeling — estimate interpretable mass across classic, expanded, unseen and repeated-answer regimes.
• Linguistic tail resolution — use a separately stored orthographic and pronunciation model inside a narrow, explicit late-game confidence band.
• Information-theoretic policy — combine feedback entropy, direct-hit utility and optional exact Bellman search.
• Independent experiment replay — verify hashes, manifests, paths, policy decisions and metrics from the published artifacts.

Architecture

flowchart LR
    History["Chronological answer history"] --> Editorial["Causal editorial-regime prior"]
    Lexical["Frequency, spelling and pronunciation"] --> Linguistic["Causal linguistic tail prior"]
    Editorial --> Policy["Entropy and direct-hit policy"]
    Linguistic --> Policy
    Actions["12,972 permitted actions"] --> Feedback["Deterministic feedback table"]
    Feedback --> Policy
    Policy --> Paths["Complete game paths"]
    Editorial --> Artifacts["Versioned prior artifacts"]
    Linguistic --> Artifacts
    Paths --> Audit["Independent replay audit"]
    Artifacts --> Audit

Loading

Answer and action universes

Let A be the answer universe and G the permitted actions. G contains all 12,972 classic actions. A contains the 2,315 classic solutions plus actions with positive English frequency under wordfreq==3.1.1. Priors assign zero mass outside A; informative guesses may still use any action in G.

Causal editorial model

For a puzzle on date t, the model may use only history with date < t. It assigns recency-weighted mass to four regimes:

                         classic vocabulary   expanded vocabulary
previously unseen word           C0                    E0
repeated word                    C1                    E1

Within each regime, the score combines tempered lexical frequency, positional letters, bigrams, vowel structure and repeated-letter structure. Generated artifacts bind the configuration, answer universe, dependency versions, input hashes and generator implementation.

Linguistic tail model

A logistic density-ratio model captures English orthographic and pronunciation evidence. It is trained only on historical prefixes and consulted with 3–20 remaining candidates under explicit editorial and linguistic confidence bounds. It remains a separate artifact and never silently replaces the primary prior.

Model selection uses four contiguous forward folds rather than shuffled K-fold. Every fold has an 84-game tuning window, a seven-game embargo and a later validation block. All learned transforms and priors are fitted from chronological prefixes, and validation targets never enter their own features or distributions.

Decision policy

The policy scores each action with:

score(g) = H_bits(feedback | g) + 3 × expanded_factor(g) × p(g)

where expanded_factor=1.5 for expanded-vocabulary answers. A concentrated posterior triggers a direct MAP guess; otherwise the policy evaluates every permitted action. Endgames with at most three candidates use exact Bellman search over the complete action space.

Local development

Requirements

• Python 3.10 or newer
• pip

Setup

git clone https://github.com/jorgeflmendes/quintropy.git
cd quintropy
python -m venv .venv
# Windows: .venv\Scripts\activate
# POSIX: source .venv/bin/activate
python -m pip install -e ".[dev]"
quintropy --help

Run an experiment

quintropy evaluate \
  --start 2026-05-01 --end 2026-08-12 \
  --prior-family editorial-regime \
  --expanded-language-override \
  --output results/experiments/local

python benchmarks/audit_experiment.py results/experiments/local

Use generate-priors followed by evaluate-priors to inspect and freeze priors before policy evaluation. Local experiment output is ignored by Git.

Quality

python -m ruff format --check src benchmarks tests
python -m ruff check src benchmarks tests
python benchmarks/verify_wordlists.py
python benchmarks/verify_checksums.py
python benchmarks/audit_experiment.py results/baselines/editorial_regime_linguistic_tail_2026-05-01_2026-08-12
python -m pytest
python -m quintropy export-web --output web/model.json --check
node --test tests/web/*.test.mjs

The quality pipeline covers static checks, causal-boundary regression tests, word-list and artifact integrity, complete policy replay and independent metric recomputation.

Repository layout

.
├── benchmarks/  Integrity checks and experiment replay
├── data/        Versioned source inputs
├── results/     Selected immutable evaluation
├── src/         Quintropy package
├── tests/       Logic, causal, regression and audit tests
└── web/         Static local-inference solver for GitHub Pages

Data provenance

Source	Use	Rights note
Laurent Lessard's wordlesolver	Classic answer and action lists	No explicit upstream license was found; confirm redistribution rights
english-word-frequency	Local English-frequency data	No explicit upstream license was found; confirm redistribution rights
nyt-wordle-played and the official daily endpoint	Chronological history verified through 2026-09-04	CC0 upstream archive; factual daily puzzle metadata

Current limitations

• The published period is retrospective and was inspected during development.
• Editorial behavior may drift beyond the frozen history window.
• Open-world coverage depends on the declared answer universe.
• The bundled third-party word lists require an independent redistribution-rights review.

Legal and citation

Quintropy is independent of and unaffiliated with The New York Times Company. No project-wide software license is currently declared. See NOTICE.md and CITATION.cff for legal and citation metadata.