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The parity vectors (even/odd sequences of the first k steps) of the 3n+1 (Collatz) map and the induced map from residue classes modulo 2^k to parity patterns, including its well-definedness, bijectivity, stopping-time/parity results, and the associated 2-adic encoding of Collatz dynamics. Density or probabilistic claims about the map go under their own tags.

The map assigning to each residue class modulo 2^k its first k Collatz parities is a well-defined bijection onto the 2^k parity patterns.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Number theory Collatz conjectureimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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