How to read it

The black wireframe lattice is R — the Real schema, drawn as a regular cubic grid. Imagine it as the world's geometric backdrop, the volume in which everything is posed.

The gold ring is A — the Access Manifold currently in play. Here it's the simplest morphology, a closed circular loop. Move it around with the position sliders, tilt it with the rotation sliders, scale it with the radius slider — that's the Sim(3) pose tool acting on A.

The red wireframe is T — the Time schema, anchored at A and extending into the recent past. Its current face (where it touches A) is at full scale and aligned with R; as you go pastward, T shrinks and its lattice peels away from R's lattice. Past scale, scale curve, lock-all-three-dims, and T length each control a different aspect of the warp.

The faded red rings trailing behind A are ringframes — the prints Π has laid down at A's posed position. They ride T pastward, shrinking with T's warp and fading as they age. Crank Π's print rate to make them denser; lower it for a sparse stream.

The four mechanical tools, on this page

Each slider category in the panel maps to one of the framework's tools:

(i) Sim(3) pose of A

The first six sliders — radius, tilt X, tilt Y, and three position sliders — are the Sim(3) tool acting on A. Scale (radius), rotation (tilts), and translation (position) together let you drop A anywhere in the world and at any orientation. T follows — its anchoring face is always A's plane.

(ii) Π — Printing Operator

The print-rate slider controls how often Π emits a ringframe. At 2 Hz you see a sparse pulsing trail; at 20 Hz the trail packs densely. This is the cadence parameter the Cold case modulates (4 → 10 Hz when foot meets cold water).

(iii) Shape of A

This demo holds A at the simplest morphology — a canonical circular ring. The shape tool would let you swap to a taco shell, helical ramp, sphere shell, etc. (not exposed here, but the framework's catalog has more than a dozen basins.)

(iv) Multi-schemal pose lock — and the warp it implies

The T sliders (past scale, scale curve, lock dims, T length) parameterize how T departs from R as you go pastward — i.e., how much pose lock holds across the schema pair. Past scale = 1.0 with linear curve and lock all three dims off would give T = R exactly (full lock everywhere). Lower past scale, exponential curve, and lock-three-dims on each push T further away from R, illustrating that the locking can be partial in many ways.

Try this

• Bare baseline. Set past scale to 1.0 and watch T collapse onto R — they share the same lattice, ringframes don't shrink.
• Steep warp. Past scale 0.2, exponential curve, T length 8 — T compresses dramatically and the ringframe trail bunches up pastward.
• Tilt and translate. Move A out of the origin and tilt it 45°. Watch T's whole tunnel rotate to follow A's frame — T is anchored at A, not at the world origin.
• Print-rate sweep. Drag Π from 2 Hz to 20 Hz. Notice how the perceived "thickness" of the time tunnel changes as more or fewer ringframes overlap.
• Unlock x. Toggle off "lock all 3 dims." Now only y and z scale with the warp; x doesn't. T becomes a cylinder that tapers in cross-section but keeps its length — a different geometry of partial pose-lock.

Where this fits

This page is a hands-on companion to Ring/Bank Theory and the per-case coupling fingerprint figure in the Journal of Ring Bank Phenomenology. The static cards in that figure each freeze one configuration of these sliders; this page lets you sweep continuously between them and see what each tool actually does to the geometry.

Feedback

Bugs, slider requests, or phenomenological cases you'd like to see captured here? Reach out at caldwbr@gmail.com.