FPRD LabShare an approach

← Claims

Representation theorem

FPRD-T100

Coordinate-carrying cells support exact persistent root sharing

Exact statement

Let a scaffold cell carry a symbol together with the coordinate to use after following its current port. For every backward (s)-port scaffold satisfying clean missing edges and every simultaneous family in which each output pushes onto, keeps, or pops any selected source stack, one appended self-free node with paths of length at most two decodes each output as exactly that action applied to its source. Backwardness and clean missing edges are preserved.

StatusMechanically checked and internally audited
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

A cell stores not only its value but the coordinate that the decoder should use next. This lets multiple outputs share one old root while immediately applying different updates.

Definitions

  • A cell is (a,i)∈A×[s](a,i)\in A\times[s]; the current coordinate selects the edge, and the stored coordinate selects the next label component.
  • Each output independently chooses push, keep, or pop and may select any preceding source slot.

Proof or evidence

Lean proves the total decoder, exact one-step theorem, self-free distance-two targets, preservation of backwardness and clean missing edges, and a calibration producing [7,2,1] and [8,2,1] from one shared source [2,1].

Coordinate-carrying root sharing →

Verification notes

The decoder and all three source actions were independently traced. Push uses the old top with a carried source coordinate; keep reuses the source top cell and edge; pop copies the tail cell and follows the mixed two-port path. Empty and one-cell pops, clean missing edges, distance two, backwardness, the formal endpoints, and proof-hole scan were checked against the pinned source.

Limitations

  • Root sharing does not supply a stationary allocator for a dynamically changing bounded frontier.
  • Deduplication, eviction, equality-sensitive merging, and successor-to-slot assignment remain separate obligations.
  • The theorem alone does not imply that every context-free language lies in PEG.

Open work

Seek external review of the coordinate-carrying decoder and investigate stationary allocation beyond fixed causal refinements.

Notes

A cell stores a symbol and the coordinate used after its current port is followed. Lean 4.30.0 checks the total decoder, exact one-step theorem, distance-two and self-free targets, backwardness, clean-missing preservation, and a two-output calibration that derives [7, 2, 1] and [8, 2, 1] from the same old source [2, 1]. This repairs the fixed-port operation rejected by FPRD-T88. It does not produce a stationary slot allocator from bounded frontier cardinality: deduplication, eviction, and successor-to-slot assignment remain separate obligations. It does not prove CFL subset PEL, opens no M34, and does not modify the paused EPAL publication.