E01 · F02 · SP-002 — Research for F02

Find, read and record the sources of every story of F02 before its implementation (ADR-0020, research protocol §8).

Acceptance criteria

• Given each story of F02, when the spike ends, then every formula, algorithm and behavior it needs has a verified REF-*, a DERIV-* or an open research request.
• Given the sources found, when the spike ends, then the stories' criteria and tasks cite them, and a research note records what was found and what remains open.
• Given the symbols of synoptic views and process diagrams, when the spike ends, then the Product Owner has a sourced proposal for the largest number of corners (Q19), and decides it.

Questions

• Vertices of a regular polygon on its circumscribed circle, its bounding box and its apothem: a readable source for the formulas of DERIV-regular-polygon-fit steps 1–3.
• Placement: centering in the box and the flip to the SVG frame; starting vertex and clockwise order (Q11, Q18).
• Inkscape's Star/Polygon tool (REF-INKSCAPE-POLYGON, [unverified]): read it, record what F02 keeps and what it does not.
• Maximal radius: proof that the fillets of a regular polygon at their maximum form its inscribed circle (apothem as radius).
• Floating vertices: Corner.point says integer coordinates, while a polygon's vertices are derived floats (ADR-0003); does the F01 geometry hold, and with which tolerance (EPSILON)?
• Q19: which regular polygons appear in synoptic and process symbols (ISA-5.1, ISA-101, ISO 10628-2, IEC 60617…) and in their display; what largest n is useful, and what it costs to draw.

Inventory

Story	Needs
EN-008	vertices of a regular polygon on the unit circle; flat base; screen frame; clockwise order; starting vertex (Q11, Q18)
US-005	unit bounding box; uniform scale; centering; refused values, largest number of corners (Q19); derived, fractional vertices
US-006	F01 clamp on fractional vertices; effective radius of a polygon; maximal radius = inscribed circle (inradius, apothem)
US-007	playground behavior only: no formula; Inkscape's tool as functional reference (REF-INKSCAPE-POLYGON)
AUD-002	the sources above, re-verified
VAL-002	the check table of DERIV-regular-polygon-fit

Tasks

One task = one commit, referenced as SP-002.Tn.

• T1 — Inventory the formulas and behaviors of the stories (1 h)
• T2 — Find, read and record the sources; update or write the derivations (3 h)
• T3 — Q19: polygons used in synoptic and process symbols, proposal to the Product Owner (2 h)
• T4 — Write the research note and update the stories (1 h)