The output

beloch fold FILE.bel writes one JSON document in the FOLD format ¹, extended with fields under the beloch: prefix as FOLD's custom-property rule allows. FOLD is the exchange format the origami tools read (ADR 0002); the extension carries what the model and the language know and FOLD has no field for. SPECIFICATION.md §7 is the field-level contract; this document explains what the file represents.

The output refers to the model by statement ids and to the kernel by module. Neither refers back.

A file is the path, frame by frame

The model's meaning of a program is the sequence of states it passes through (BELOCH.md, "A program is a path"). The file records that sequence: the top-level dictionary is frame 0, the flat sheet with every crease drawn on it in paper coordinates, and file_frames holds one foldedForm frame per statement that moved the paper, each a flat folded state (def-flat-state) in table coordinates. A reader that wants only the result takes the last frame; a reader that wants the diagram sequence takes them all.

A program with several sheets (the sheet-as-value design) keeps this shape: a frame holds every sheet as its own connected component of the planar graph, and a field beloch:sheets maps faces to sheet names. An assembled body is one frame like any other, since the model treats it as one folded state.

This is where the history lives that the model's state does not carry. The file is a record of the run, and no operation of the language reads it.

Standard fields

Each frame uses the FOLD vocabulary for what FOLD can express:

vertices_coords, edges_vertices, faces_vertices: the planar graph of the faces of the state, vertices deduplicated by coordinate. Frame 0 is in paper coordinates, every other frame in table coordinates.
edges_assignment: B for the sheet boundary, M and V for folded creases with the letter derived from the state, F for a marked crease that has not folded. U never occurs, since a state always knows a crease's disposition.
edges_foldAngle: $0$ or $\pm 180$ , the hinge angles of the state.
faceOrders: the layer relation $\lambda$ as FOLD encodes it, one triple per pair of overlapping faces with the sign taken relative to the second face's normal. Pairs that do not overlap are absent, as in the model.
frame_classes, frame_parent, frame_inherit: FOLD's frame bookkeeping; every folded frame is a child of frame 0 without inheritance.

Exact coordinates are rounded to decimal only at serialisation; the values the kernel computes stay exact (ADR 0008, 0012).

Beloch's fields

What the language knows about a state and FOLD cannot say:

beloch:edges: per crease edge, the statement that scored it as an index into beloch:statements (statement) together with its source span, its construction (which axiom or verb), the names of the points and lines it was built from, and the crease's name if it has one. Consumers join on the index; two statements may share a source line, so the span alone leaves the join ambiguous. This is the attribution the model calls provenance (ADR 0019).
beloch:source_line, on each folded frame: the source line of the statement that produced the frame.
beloch:statements: one entry per top-level statement in source order, a sourcemap from the program to the frames. Each entry carries the kind that says which axis it moves (ADR 0026), its source_line and its span, and the frame_index of the frame it reads against. fold and mark are the writes: the paper moved, or it was scored and stands where it was. bind moves the program alone, which a point, a construction line, a bundle, a definition and an export all do. A reader stepping through the fold sequence walks the writes; a reader of the program walks every entry.
beloch:references: one entry per resolved mention of a crease name in the source, each with the span it occupies and what it names: a crease_id, or edge for a paper boundary. The arguments of a flatten, the operands of a map, a filter: every place the program names a crease. The spans a crease's own entry in beloch:edges carries say where it was defined; these say where it is used, which no consumer can recover by re-reading the text, since one spelling names different creases inside a def body and after a --x! rebinding. Deduplicated by (target, span).
beloch:named_points[].statement and beloch:named_lines[].statement: the statement that binds the name, as an index into beloch:statements. The step beside it counts frames and cannot separate two names bound between the same pair of folds. It is null for a name no statement bound, which the four paper corners are. A FOLD written before every statement was logged reports the next state-changing statement instead, which is what the field meant then.
beloch:vertices_names, beloch:named_points, beloch:named_lines with beloch:named_lines_frame: the names a program gave to points and lines, mapped to vertices and to lines. See issue #82 for the frame the lines are currently reported in.
beloch:marks: reference marks that subdivide no face (mark … at, mark … between ending mid-face), which are creases in the language and no edges in the graph.
beloch:free: every free point (free on … from … at …) with its parameter, so a renderer can offer it as a slider.
beloch:faces_matrix: each face's isometry as a matrix, the restriction of $f$ to that face, so a renderer can interpolate between frames without re-deriving it.
beloch:inspect: an inventory of creases, segments and flaps of the final state keyed by crease id, for the playground's entity inspector.

Everything under beloch: is optional to a FOLD reader that does not know Beloch; the standard fields alone describe each state completely.

What this document will grow into

A worked file for the preliminary base, frame by frame, with the fields called out; and the diagram output, the YR-style folding sequence, once it exists.

Demaine, Erik D., Jason S. Ku, and Robert J. Lang. “FOLD File Format Specification (Version 1.2).” n.d. https://github.com/edemaine/fold. ↑ a

Notes

Erik D. Demaine et al., “FOLD File Format Specification (Version 1.2),” n.d., https://github.com/edemaine/fold.↩