1.733A / C
A 0.95 · C 0.55TWO TETRADS. ONE EMERGING IDENTITY.
The geometry of coming into balance.
The active inside-out seed runs Order 2. Its enclosing, lobed connective envelope runs Order 4—meeting at complementary phases.
AA / CC
Order 2 seed / Order 4 envelope0/ 100
Finding balanceAA⁺ 00
Without feedback: 000 / 5layers
Awaiting first AC pass01 / COUPLED GEOMETRY
An active seed in a lobed envelope.
LIVE
Orientation held · circulation unaffected
Geometry only · follows phase and balance
Coupled fieldaz 45.0° · planes 0.0°f 2.00
DRAG TO ORBIT · RIGHT / MIDDLE DRAG: PAN · SHIFT LOCKS X / OPTION LOCKS Y / CTRL LOCKS Z
AA seed ↔ CC envelopeStage 1 / 4
SEED · ORDER 2
ENVELOPE · ORDER 4
Γ₁ · AA → CC → CA → AC → AA⁺
03 / AC SEPARATION
Three simultaneous streams.
Each tetrad produces its own three streams at AC.
Closure
Spectra
Remainder
Each pass can contribute to all three streams.
04 / RETAINED HISTORY
Memory changes the next pass.
Each tetrad contributes its own AC observations.
05 / RESIDUAL MODES
Recurrence has a signature.
Collecting a uniformly sampled residual signal…
06 / DEVELOPMENT
Recurrence and ascent are distinct.
Closure · ascentSpectra · recurrenceRemainder · resistance
07 / COUNTERFACTUAL
What does memory change?
Current experimentNo-feedback baselineDashed line · Unity
Inside the modelEquations, mapping controls & reproducibility ＋
Active seed, connective envelope. The inside-out tetrad runs your Order 2: AA → CC → CA → AC. The outside-in tetrad runs your Order 4: CC → AA → AC → CA. These are complementary whole-tetrad roles; each still contains all four phases. Geometry and dynamics remain exploratory simulation choices, not an ORIGAMI replication or an atomic solver.
Complementary phase matching
AAseed ↔ CCenvelope
CCseed ↔ AAenvelope
CAseed ↔ ACenvelope
ACseed ↔ CAenvelopeMatching is implemented with paired stage boundaries: readiness advances at each side’s natural rate, and the next pair begins when both are ready. A faster side can wait at a boundary while its circulation continues. This gate is our explicit simulation mechanism, not a derived E1P kinetic law. Disorder changes forcing and pruning; these two configured Orders remain fixed.
Circulation, balance & memory
φ̇seed = 2π / Tseed; φ̇envelope = −2π / Tenvelope
ℓd = ln(Ad / Cd); Ad + Cd = 0.75
ℓ̇d = drive + Fd(t) − 0.72ℓd
+ 0.35·coupling·(ℓother − ℓd) − gain·m̄dCirculation remains separately paced; its angle is distinct from readiness to change phase. Each AC pass deposits a tagged layer. Feedback uses that tetrad’s retained observations with weights 0.75^age. Both contribute to the tower. High disorder prunes to the newest two layers. The baseline omits memory feedback; exact deterministic forcing coefficients are in model.js.
A complete matched octave
Eoct = (Āseed + Āenvelope) / (C̄seed + C̄envelope)
Koct = exp[−(ln Eoct / 0.38)²]
AA⁺ advances when Koct ≥ 0.62Four complementary pairs complete both tetrads: the seed returns to AA and the envelope to CC. Shared closure uses their completed-cycle averages. The live shared-balance card uses the instantaneous aggregate. The closure score and threshold are illustrative choices; phase complementarity is maintained by the stage gates.
AC streams, spectra & nested geometry
Kd = exp[−(ℓd / 0.38)²]
Sd = (1 − Kd)·sigmoid(ℓd / 0.16)
Rd = (1 − Kd)·[1 − sigmoid(ℓd / 0.16)]The envelope enters AC while the seed is in CA; the seed enters AC while the envelope is in CA. Each has its own three streams. The residual combines both circulation signals; a 20 Hz Hann-window DFT reports model Hz, without atomic wavelength calibration. Both whole tetrads have four curved lobes: a warm inner seed and a larger blue enclosing envelope. These are prescribed geometry, not reconstructed atomic fields.
Lobes and balance
r = r₀ + D·[a·sin⁴(v)·cos(4u)
+ b·sin²(v)·cos(2u)] + rippleThe four-lobe term forms two opposing pairs. Local imbalance, phase and retained feedback set the pair-transfer coefficient b; coupling and the Lobe depth control set D. One pair grows as its perpendicular pair contracts. Each tetrad tilts and circulates independently. Phase markers lie on its lobe tips. A conservative radius bound keeps the entire seed inside the envelope at every allowed setting. These surfaces read the solver state; they do not feed forces back into it. A stabilizing role for lobes remains a hypothesis to test with a specified feedback law. Exact coefficients are in geometry.js.
Relative orientation is a visual parameter
Default aligns the envelope exactly with AA/W left, CC/E right, CA/N top and AC/S bottom. The seed is rotated −45° in the same plane: AA/SW, CC/NE, CA/NW and AC/SE. These are a geographic reference convention, not an angle derived from E1P. Default also recentres the camera and pauses swing without resetting the experiment. Uncheck Pause swing to resume the independently paced azimuth (±0.12 rad) and tilt (±0.08 rad) oscillations; recheck it to hold the current pose. Phase circulation, shape response and memory continue while swing is paused. Upright scientific serif N/E/S/W letters follow the envelope phase points when you orbit; the diagonal seed retains only its phase labels. The viewer reports the current azimuth offset and acute angle between equatorial planes.
The coupled field is always the base view. Density projection adds a sampled-density layer, and Phase architecture adds labelled phase pathways and arrows; these independent overlays can be enabled together or separately. The Phase guides checkbox controls the faint basic guides when the detailed architecture overlay is off. Overlay settings are included in JSON exports. Camera, overlays, lobe depth, tessellation, theme, fullscreen, and display settings never affect the model. Tessellation spans 40 × 20 to 384 × 192 cells per tetrad, or 147,456 surface cells across both at maximum. The same analytic surfaces are sampled more finely; the geometry coefficients and integration step stay fixed. WebGL accelerates the mesh; a canvas renderer is available when acceleration is unavailable. High detail may reduce playback frame rate. Opacity and point size adjust with resolution to keep overlapping surfaces legible. Tessellation is recorded in JSON exports and is also available within fullscreen. Left drag or the arrow keys orbit; select Pan for left-drag/arrow panning. Right or middle drag always pans. Hold Shift to lock world X, Option/Alt to lock world Y, or Control to lock world Z. Locks combine: Shift + Option leaves only Z free; Shift + Control leaves only Y free; Option + Control leaves only X free. Holding all three blocks orbiting and panning completely. A single key locks its axis and permits motion about or along the other two. Modifier changes take effect during a drag without a jump. Locks work for both mouse and arrow-key navigation; an axis along the sightline produces depth motion, which is invisible in orthographic projection. Default restores the compass cross, diagonal seed and paused swing. Fit restores zoom and centre. Orbit and pan freely, then select Default to return to the compass alignment. F toggles fullscreen and Esc returns. If native fullscreen is unavailable, the viewer fills the browser viewport. Themes are remembered in this browser. Integration: 1/120 model second. PNG exports the current field; CSV and JSON include both tetrads; JSON is an inspection export. Space = play/pause · P = next complementary pair · N = next complete octave · R = reset.