Joint Notation Grammar — Draft Review

Layer 2, Pass 1. Hand-drafted visual grammar for compound (shape × shape) notation. These three SVGs use the same pair of shapes (tetrahedron × tetrahedron at {3}-face) at three discrete orientations k=0, 1, 2. Each orientation produces a different alignment of internal markers at the joint vertices, and is therefore a distinct entry in the catalogue.

Interface mark vocabulary

• ◆ filled diamond — peak meets peak. Compounded concentration at this interface vertex.
• ▶ gradient arrow through band — propagation arrow on A continues through the joint into B. Information flows across.
• ✕ yellow X — peak meets void. Transfer: energy moves from one cavity into the other through this point.
• ◇ dashed open circle — void meets void. Silent interface. No information crosses here.

Twist / chirality continuity (↺ / ↻) is reserved for joints whose monomers carry rotational propagation; not shown in these orientations because both monomers' arrows are linear, not rotational.

v3 — Combined-body style (current)

Two shapes drawn as a single combined diagram, joined at the shared face. The shared face appears as a vertical dotted line down the center. The internal markers from each shape's atlas notation are kept on their respective halves, so the compound reads as one continuous body. A single interface symbol sits on the join line — one mark per orientation, indicating what happens at the connection (peak⊕peak, peak⤳void, flow continuous, or silent).

v3, k=0 — interface mark ◆ peak⊕peak. Compounded concentration at the join.

v3, k=1 — interface mark ✕ peak⤳void. Energy transfers from one cavity into the other at the join.

v3, k=2 — interface mark ▶ flow continuous. Propagation crosses the join cleanly.

v2 — Side-by-side style (deprecated)

This second draft matches the style of the existing pair schematics (e.g. spinel, perovskite, fullerene). Each shape is rendered as its own circuit-language notation symbol from the atlas, side-by-side, with the connection point in the center carrying the {n}-fold symmetry silhouette and the four interface marks at its vertices. Three orientations of the same pair shown — same monomers, same decoherence step, but the marks rotate around the shared face.

v2, k=0 — using actual atlas notation for tetrahedron (id=016) and octahedron (id=066). Joint marks: ◆ peak⊕peak top, ▶ flow continuous bottom-right, ✕ peak⤳void bottom-left.

v2, k=1 — same pair, B rotated 120°. Marks shift one vertex around the {3}-fold triangle.

v2, k=2 — B rotated 240°. Each orientation is a distinct catalogue entry because the interface mark profile changes with rotation.

v1 (deprecated) — symbolic-cavity style

Earlier draft, kept for reference. Used abstract triangle outlines rather than the actual notation symbols.

v1 Orientation k=0

Top vertex: peak⊕peak. Middle: flow continuous. Bottom: peak⤳void. This is the maximum-coupling alignment — energy compounds at one vertex and transfers through another.

v1 Orientation k=1

Same pair, B rotated 120° around the joint normal. Marks shift one position. Now top is peak⤳void, middle is peak⊕peak, bottom is silent. Different compound behavior; different catalogue entry.

v1 Orientation k=2

B rotated 240°. Top is silent, middle is peak⤳void, bottom is peak⊕peak. Yet another distinct compound profile from the same monomer pair.

What you're reviewing

• Does the visual read at a glance? Can you tell what's happening at the joint without reading the captions?
• Are the four interface marks distinguishable enough to scan?
• Is the interface band's symmetry-silhouette useful, or noise?
• Should the bottom address strip be more or less prominent?
• Do you want orientation labels (k=0,1,2) more visually distinct between rotations?

Tell me what to adjust before we generate this notation at scale across the handshake matrix.