3Chess Axioms
The locked axiom systems for 3Chess — game rules, rating, environment, and the systems that govern online play and shared vocabulary.
The axiom systems that hold 3Chess together.
Each system lists axioms, theorems, version history, and a changelog. Axioms are scoped per system — A1–A24 are game rules, R1–R15 are rating, and so on.
How they relate
Game rules (A1–A24) define the board, pieces, turn order, and win conditions. Rating (R1–R15) derives from the match outcomes those rules produce. Environment (E1–E18) sets the surrounding clock, table, and platform. HexPair admission governs the online handshake. The Glossary fixes the language.
Systems
| System | Range | Version | Status |
|---|---|---|---|
| Game rules | A1–A24, T1–T15 | v2.2 | locked |
| Rating | R1–R15 | locked | decided · 0/15 implemented |
| Environment | E1–E18, ET1–ET7 | locked | locked |
| HexPair admission | 26 axioms | rev 4 | locked |
| Glossary | 9+ canonical terms | v0.2 | working · available now |
Additional axiom systems are in development and will be published as the work they govern ships.
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Environment
The clock, the café, and the platform — 18 axioms (E1–E18) plus 7 theorems (ET1–ET7) that wrap the board.
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Game rules
The 24 axioms (A1–A24) and 15 theorems (T1–T15) that define 3Chess — board, pieces, turn order, win conditions.
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HexPair admission
The online handshake — 26 axioms governing how a player joins a table, gets admitted to a seat, and how the server confirms identity.
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Rating
PL-Elo Exact — a custom three-player rating model (Plackett–Luce closed form + per-player σ tracking on the Elo scale).
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Glossary
Canonical terms for 3Chess — definitive definitions of the vocabulary the game introduces.