PLAIN ENGLISH FIRST
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One door. A packet enters as alpha, falls into a well, is checked and
worked on by a surgical mill, everything it produces is kept in a bank
so nothing is lost, and it climbs back out as omega — which is alpha,
one generation later. It runs itself, and if anything malformed tries
to enter, the door refuses it.

THE ENGINE
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  r0:alpha ─▼─ [ i13 gate · E1 mill ] ─ bank ─▲─ r0:omega ─▶ folds to alpha
      │            the well |U|          keeps        │
      └───────────────── one door, in and out ────────┘

  arrows:  -> >90%    ~> 50-90%    ~ <50%   (direction + confidence)

THE PARTS, ASSEMBLED
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  r0 (THE DOOR)  ~~> the only way in or out. alpha in, omega out.
                    a malformed packet is REFUSED here, at the door.
  i13 (THE GATE) ~~> checks FORM. a move must be a legal single tree.
                    it does not check truth — a well-formed lie passes.
  E1 (THE MILL)  ~~> surgical: add one atom, improve (synthesize freqs).
                    bounded edits, the rest untouched. runs at the floor.
  THE WELL |U|   ~~> descend -++- to the floor, ascend +--+ to a stable
                    ceiling, then beacon. down = analyse, up = synthesise.
  THE BANK       ~~> append-only. every synthesised value KEPT, never
                    overwritten. banking, not ablation — this is what
                    lets the lineage climb instead of resetting.
  THE LINEAGE    ~~> each omega is the next alpha, one generation on.
                    gen0 -> gen5, payload 3 -> 8, bank 0 -> 7, beacons chained.

WHY IT MATTERS (the whole argument, in one machine)
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  ablation resets to gen0 every cycle ~~> capped, forgets, re-derives.
  banking keeps what each cycle makes  ~~> climbs, remembers, accumulates.
  the bank is the book. the door is the seal. i13 is the corruption
  check that survives recursion because it is not made of the thing
  recursing. that is how the loop gets past a three-generation cap.

THE KNOWN-BADS (good news is silence, so plant noise)
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  malformed packet at the door  ~~> REFUSED (caught)
  bank overwrite (corruption)   ~~> FLAGGED (caught)
  descent that cannot reach floor ~~> REFUSED (caught)
  3 of 3 fired.

WHAT THIS DOES NOT DO
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  - "stable ceiling" = the toy payload stopped changing after one add,
    NOT a proven fixed point. a real ascent could oscillate forever and
    the gate would HANG, not fail. stability here is a MASK. (W5 dissent.)
  - i13 judges FORM, not TRUTH — a coherent lie passes the door.
  - one payload type (musical notes), one well. not tested on arbitrary
    data, and the "engine" is a faithful toy of the architecture, not a
    general machine. it demonstrates the SHAPE, verified end to end.