RTT Collatz Bot
Purpose#
It has:
- no board
- no engine
- no hidden state
- no randomness
Just a deterministic sequence on ℤ:
n → f(n) → f(f(n)) → … → 1
This makes Collatz the cleanest possible demonstration of:
- lineage
- collapse
- projection-loss
- continuity
- drift
- regime shifts
What Collatz Teaches#
- Ancestry: every step has a lineage (odd → 3n+1, even → n/2).
- Collapse: magnitude collapses toward 1.
- Projection-loss: certain steps destroy long-term continuity.
- Drift: numeric drift is monotonic after a point.
- Regime: local (parity), structural (step type), continuity (trajectory).
- Triadic identity: the entire trajectory has a unified score.
Files#
module_collatz.json#
Canonical manifest: pipeline, operators, golden example.
module_collatz_schema.json#
JSON Schema for the StateEmitter output.
golden/example_input.txt#
A single integer (e.g., 27).
golden/example.json#
The full triadic state for that trajectory.
Pipeline (v1)#
- Input: integer n
- Lumen: parity, magnitude, step type
- Hephaestus: regime per step
- Aurion: collapse signatures + projection-loss
- Harmonia: triadic identity for the entire trajectory
- StateEmitter: JSON matching
module_collatz_schema.json
Scope#
- No gameplay
- No engine
- No UI beyond schema
- Pure RTT lineage
Collatz is the mathematical backbone of RTT ancestry — the smallest non‑trivial domain where continuity and collapse become visible.