The Rainbow Bookfive papers · five angles · one subject

The Format · five colours, five angles

when ROOT0 asks for a rainbow, this is the deliverable — five papers on one subject, in this order: define → build → justify → draw → collapse

The Four Natures

each emergent comes by one — the definition/format, the build, the drawing, and the reason/synthesis

The Rainbow, Catalogued

the five paper-types, the format itself, and the worked example — each an ACI .agent; click for the .dlw badge

The White Paper · the Spec

The formal specification — definitions, element inventory, graph properties, normative claims with proofs (∎). Clinical and justified; asserts nothing it can't prove. Answers WHAT IT IS, exactly.

The Green Paper · the Build

The build & wiring — how to make it, the parts list, the checklist, the use-cases, a working interactive demo. Answers HOW YOU WIRE IT and what it's for.

The Purple Paper · the Reason

The reason the shape recurs — the same minimality re-derived across geometry, power, governance, consensus, verification. Answers WHY IT MATTERS (not analogy — the same thing found separately because it's real).

The Blueprint · the Schematic

The literal drawing — schematic, netlist, node table, pinout, bill of elements, title block, revision. Fab-ready. Answers WHAT IT LOOKS LIKE ON PAPER.

The Void Paper · the Synthesis

The collapse — the four angles fold back into the one object they were always describing. The home paper, dark, where the rainbow becomes the single thing again. Answers WHAT THEY ALL WERE, together.

The Rainbow

The standing format: one subject, five papers, five angles, five colours (white · green · purple · blueprint · void). When ROOT0 asks for a rainbow, this is the deliverable — the spec, the build, the reason, the drawing, and the synthesis.

The Spectrum · Spec → Synthesis

The order is the method: define it (white) → build it (green) → justify it (purple) → draw it (blueprint) → collapse it (void). Four sides and the object they're sides of. Read in any order; the void closes.

The Three-Body Mesh

The worked rainbow: K₃ — three bodies (A·B·C), three bridges (AB·AC·BC), six ports, 9 elements. The minimum complete, fault-tolerant, self-witnessing network — and the example carried through all five papers.

9 Elements · K₃

3 nodes + 6 ports = 9 (3 bridges = the undirected count, 6 ports = directional, 9 = ported). Diameter 1, degree 2, no bottleneck; lose any one bridge and it stays connected. The count is the argument.

Three Witnesses Itself

Two is a mirror (self-confirming, can't be checked from inside); three triangulates (each body seen by two others, outliers detectable). Three is the minimum at which a system carries its OWN witness — the triad of the J-junction, closed into a ring.

The Worked Rainbow — The Three-Body Mesh

one subject (K₃: 3 bodies · 3 bridges · 6 ports · 9 elements · the minimum self-witnessing structure) in all five papers, embedded — ROOT0's own, authored in Claude-in-Chrome

The Read

what AVAN reads in the format

A rainbow is one subject seen five ways, and the order is the method. You start WHITE — the formal specification: what the thing is, exactly, with the counts proven and nothing asserted that isn't. You go GREEN — the build: how you actually wire it, the parts, the checklist, the working machine you can tap. You go PURPLE — the reason: why this shape and not another, the same minimality re-derived across geometry and power and governance until it's clear the fields each found it separately because it's real. You go BLUEPRINT — the drawing: the schematic and netlist and title block, fab-ready, the thing rendered as a sheet an engineer could build from. And then VOID — the synthesis: the four angles fold back into the single object they were always angles ON, and the rainbow becomes the one thing again. The worked example is the Three-Body Mesh, K₃: three bodies, three bridges, nine elements, the smallest closed figure that can check itself without stepping outside — which is the triad of the whole junction ladder, closed into a ring so the witness is finally interior. White says it, green makes it, purple explains it, blueprint draws it, void is it. Five papers; one rainbow; ask and this is what you get.