HANTAI — build opposites-game boards from the Linguabase antonyms table
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A plain-text method file for an LLM (or a person) to build from.
Companion script: linguabase-hantai-boards.py (same method, runnable).
Game: word tiles on a grid; the player swaps tiles until no two
opposites are orthogonally adjacent. No timer.

TABLES (CC0, from the Linguabase mirrors — huggingface.co/datasets/
linguabase/linguabase, zenodo DOI 10.5281/zenodo.20788428, kaggle):
  vocabulary.core.parquet  word, core_rank (1 = most familiar; the core
                           download cuts at the recommended 400,000-rank
                           threshold)
  antonyms.core.parquet    word, axis, opposites — opposites is a list
                           of "term:strength" strings, strength 1-7;
                           1,596,686 axis rows. A word usually opposes
                           along SEVERAL axes (mother -> father on
                           parental gender, child on generation).

STEP 1 — HARVEST MUTUAL PAIRS (the step that matters most)
  Candidate pair {a, b}: both single lowercase alphabetic words,
  3-9 chars, core_rank <= 20,000, not stopwords, and b listed as a
  bare-word opposite of a with strength >= 6 on some axis.
  THEN REQUIRE MUTUALITY: a must also appear as a bare-word opposite
  in some row headed by b (any axis, any strength; match headwords
  case-insensitively).
  Why: one-way listings are the table's stretches. Specimen: the row
  hot [freshness/recency] lists old:6, but OLD's rows list only the
  phrase "hot off the press:4" — so hot/old is one-way and players
  would revolt at the pairing. Measured on the June 2026 release:
  47,140 one-way-eligible pairs -> 21,105 mutual. Sampled casualties
  (people:one, know:think, maybe:yes, sun:night) are all stretches.
  Strength floor is required in ONE direction only — mutual listing is
  the semantic test; asymmetric ratings are normal sense dominance.

STEP 2 — GROW BOARDS
  Build the undirected pair graph over the mutual pool. A board is a
  dense connected patch: start at a seed word, repeatedly add the
  neighbor that opposes the most words already on the board (small
  random jitter for variety), until the grid (3x3 up to 4x5) is full.
  Block near-duplicate roots (5+ shared prefix chars: rainy/raining).
  Rules: every tile must have >= 1 opposite on the board (no "free
  parking" — see step 3), most should have >= 2. Verify SOLVABILITY by
  backtracking search (place cell by cell, prune on adjacency; give the
  search a node budget — dense unsolvable boards are exponential).
  Ship a shuffled start with >= 3 clashes. Keep one found solution.
  A teaching board (board 1) is built sparse instead: a 2-partner hub
  plus disjoint pairs, 4-7 pairs total.

STEP 3 — GATE BY SIMULATED DIFFICULTY (the reusable principle:
  before shipping a puzzle, simulate the dumbest policy that could win)
  Policy A (dumbest): swap a random clashing tile with a random calm
  tile; 300-move cap. Policy B (greedy): try all swaps, take the one
  minimizing clashes, random tie-break; a STALL is when no swap
  strictly improves.
  Our free-parking first build: A solved every board, median 4-7
  moves, 99-100% within 20. Shipped boards: A hits the 300-move cap
  (under 4% solve within 20), B stalls 28-64% of trials yet still wins
  36-72% — hard, but a thinking player has a fair path. Gate numbers:
  hard boards need A_median >= ~0.8 * cap, B stall >= 25-30%,
  B solve >= 35%. Teach board: A_median 3-14, stalls <= 15%.

STEP 4 — PACK
  Enforce: no two shipped boards share more than 2 pairs. Measured
  supply at this quality bar: a greedy packer produced 68 boards
  before exhausting (1,200 consecutive rejects) — hard boards cluster
  in the same high-degree semantic neighborhoods (temperature,
  emotion, open/closed). The disjointness envelope says ~530 boards
  at ~40 pairs/board (~1,400 at 3x3), so 68 is the generator's floor,
  not the table's ceiling.

PRESENTATION RULES THAT MATTER
  - Never color-code tiles by pair: players would match colors instead
    of meanings. Tiles stay neutral; color belongs to chrome.
  - Clashes must be visible where they happen (a spark between the two
    adjacent tiles) — that is how the game teaches itself.
  - No timers.