SEE CUBED / Hopf geometry
The Hopf Workshop
Pick a point. See its loop. Explore the mathematics, or try a separate fictional builder rehearsal.
Go to practice controls ↓Point and loop controls · geometry only
Press Try it, or pick a letter.
Geometry lab · optional depth. Explore the drawing and its numerical checks. The plan opens the separate fictional team practice; no review or answer is needed to explore geometry.
Something new happened in the live practice. This past view did not change.
The Bundle map. Circles here are fibres, not people. Moving the drawing does not sign a name.
The idea
This version of the plan
The promise none yet
No one has promised this yet. Checks and yeses are not a promise until Make this agreement.
Who answered
Checks for this plan
What was tried
Nothing has been tried on a promise yet.
What happened
Four-seat rehearsal PLAY
A separate simulated table from the three-person builder rehearsal. Readiness is not consent. Closing a round is not a Hopf commit. RETURN keeps the ledger; it is not a reset. This is not SEE CUBED authority.
Next: each seat can say Ready without agreeing.
Full four-seat history
Fictional builders
Choose any lesson, skip or replay. Navigation never answers for the fictional crew. No and stopping remain valid outcomes; agreement and action keep their own safeguards.
Meet the crew
Maya, Finn and Bea are fictional builders preparing a Cloud 9 entrance walkthrough. Confidence is not permission.
Replay moves to the first lesson and keeps your practice. The demonstration explicitly runs scripted fictional responses; it is separate from lesson navigation.
Geometry lab
Sampled fibres illustrate the Hopf bundle; distinct fibres do not meet. Sliders select an exploratory state, not a camera position. Try these coordinates changes the local mathematical state, never consent.
Two solid tori joined rim to rim on the Clifford torus. Each chart carries a circle. This drawing is not a grant.
Angles are radians internally; readouts show degrees. One positive latitude circuit at 60° has phase +90° modulo 360° for this connection, starting at φ=γ=0. The signed normalized curvature integral uses 4,000 midpoint samples. Linking is a bounded approximation, not a proof or permission score.
Coordinates use a unit sphere and dimensionless projected lengths. The torus residual checks one point, in squared coordinate units. Close fibres and near-pole linking may be unsupported. Drawing gaps omit projection-pole or camera-plane regions; they do not break the mathematical fibres.
Choose Recompute linking for the two selected-angle fibres, separated by 120° in azimuth. This check does not use the letter-picker selection.
Fictional builders: Maya, Finn, and Bea no agreement
Current proposal
Active agreement
None. Act will stay blocked until a version is committed.
Tick the three boxes, then Check the proposed plan. Ticks are drafts until that press.
Full builder rehearsal history
Start here
Rehearse how fictional builders prepare a Cloud World walkthrough. Try an idea, check it, ask each person, and see what happens when someone needs to stop. Then explore the geometry behind the workshop.
You control fictional practice characters. Their choices do not record anyone's real consent.
How this model works
Cloud World fictional practice. The reference model supplies the rules; this page uses Cloud World example text. Topology does not authorize. Ready is not Yes. A suggestion is not a grant. Withdrawal stops action; repair records consequences and does not restore consent. RETURN keeps the ledger and is not a reset.
Example: after a committed Cloud 9 entrance agreement, Try the agreed action uses that agreement even if a later Cloud 6 workshop draft exists. That rule is tested in test_act_records_live_agreement_version.
The first screen is Shapes — a world of loops. Builder rehearsal uses fictional Cloud World builders. The drawing still opens on the Bundle map. The hourglass remains a labeled process metaphor, not the bundle. History is a past look, not a third permission model.
Numerical checks are checks, not proofs. Public notes: discipline invariants, practice packet rules, current candidate handoff, visualizer inventory.