CC 5-window build · W1 source · W2 contributions · W3 1D · W4 2D+interactive · W5 3D + missing piece

The Spinor — five windows, one rotation

One master angle drives all five windows. Turn it and each window reacts, then reports its verdict up to W1. Watch them agree everywhere except 360° — where the disagreement is the whole discovery.

master rotation θ 0°
W1 · source
What it is · where found
Spinor — the true object under a spin-½ particle's "spin arrow." Defining trait: it takes 720°, not 360°, to return to itself; one full turn multiplies it by −1.
Found: you asked for it after the positronium build ("add a spinor"). Grounding: Dirac / Pauli spin-½; rotation operator R(2π)=−I for any axis. Real: Rauch 1975 neutron interferometry measured the −1.
LIT720° period, R(2π)=−I, cos(θ/2) phase — node-verified.
AMBERbelt-trick as intuition (illustrative, not a proof).
W2 · contributions
Built together · who did what
Aggregate — one build, two hands.
ROOT0 → the ask ("add a spinor to add"); the positron-is-it-real challenge; the corpus resonance — "Top, the spinor (0 = balance)" already sits at the centre of UD0.
Claude → the rotation-operator verification (R(2π)=−I); the phase-at-half-speed (cos θ/2); belt-trick framing; Rauch-1975 grounding; the 5-window wiring.
together → the house rule itself, and the choice to let W5 dissent.
buildspinor.5w
ruleCC 5-window
W2 modeaggregate
W3 · 1D view
The hidden phase, one line
The spinor reduced to one number: cos(θ/2), the real part of its hidden phase. +1 → −1 (at 360°) → +1 (at 720°). This scalar is the truth the arrow can't show.
phase+1.00
home?yes
W4 · 2D + interactive
Arrow + belt, flat & playable
The arrow (what you see) and the belt ribbon to the world. Drag the master dial: the arrow returns at 360°, the ribbon's twist only clears at 720°.
arrowup
twists0.00
home?yes
W5 · 3D + missing piece
Bloch sphere · & its blind spot
Bloch sphere — the standard 3D picture of a qubit. The vector returns at 360°. The missing piece: it's structurally blind to the −1 — no 3D observable can show it. To see the sign you must interfere two copies (Rauch). W5 adds the second, ghost, copy.
Bloch vechome
interfere 2bright
home?yes
Reading the five windows. W1 tells you what a spinor is and where it came from; W2 credits the build honestly as a joint one; W3 strips it to a single number, the hidden phase cos(θ/2); W4 lets you play with the arrow and belt in the plane; W5 lifts it to the Bloch sphere and then admits the sphere's blind spot. The feedback panel in W1 is the point of the whole rule: W3, W4 and W5 each measure "am I home?" off the same live angle and report up, and at 360° they split — W4's arrow and W5's Bloch vector say

home

, but W3's phase says −1. That dissent is true and structural: the arrow and the Bloch vector are observables, and a global phase cancels out of every observable, so they are physically incapable of seeing the sign flip that W3 reads directly. The resolution — the thing W5 contributes that none of W1–W4 hold — is that the −1 stops hiding the moment you have two spinors to compare: interfere the rotated copy with an untouched one and the sign becomes a shift you can measure, which is exactly Rauch's 1975 neutron experiment and exactly the para-vs-ortho combination that set positronium's 2-vs-3 gamma rule. Five windows, one rotation, and the disagreement between them is where the physics actually lives.