Context
An occurrence record and the final cell of its new receipt rope point to one another. A sequential allocate-then-link model cannot express that same-step cycle, although a scaffold node can encode it with SELF.
Definitions
- The constants are the number s of roots, fresh-slot bound A, pointer-field bound q, and old dereference radius r.
- A logical pointer is missing or a pair (time, slot); a transition chooses a complete finite adjacency table from old observations.
Proof or evidence
The definition is stated in the paper, theorem inventory, and proof audit, with explicit self-loop, forward-reference, and mutual-cycle examples.
Verification notes
The imported topologically ordered allocator was rejected because it excluded the construction's owner-to-rope-to-owner cycle. Draft 2 uses simultaneous allocation explicitly and forbids same-step inspection of fresh payloads.
Limitations
- Simultaneous allocation is a finite graph specification, not a domain-theoretic fixed point.
- The definition alone does not show that a particular persistent program has bounded observation or allocation.
Notes
This corrects the imported PC-83 source model, which allowed only already-constructed fresh targets even though its receipt equation created a same-step semantic cycle. Simultaneous allocation is a finite graph specification, not a domain-theoretic fixed point or permission to inspect a newly allocated record during the same transition.