Tri-Engine Convergence Galactic Lensing Hierarchy · Part 2, reversed

The Tri-Engine Soliton run backwards. Part 2 takes one set of measurements, splits it across three engines and reads what they leave over as the emergent fourth. Here three separate calculations run on the three engines at once. Each job starts on its own schedule but all three share one geometric clock. A job enters on the outer manifold (T4), winds inward one tier per turn of the wheel leaving a trail, and latches on the inner manifold (T0). When all three have landed they converge. Their exact sum becomes the fourth of a triple quad, the three landing nodes are read out as a Triple-Quad triangle (the quadrance-out), and the word is held in memory on both manifolds, where any one lost value is rebuilt from the other three. Part 2 · Part 2 manual · Guide

Speed1.0×

Tension0°

Torsion0°π/6 gate

Coupling κ1.00

Calculations · three engines, one clock DEFINITION

One expression per engine. Digits, decimals, fractions, + − × ÷, ^ (whole-number powers), brackets and unary minus are exact. sqrt, sin, cos and π are exact where the answer is rational (sqrt(16/9) = 4/3, cos(0) = 1); otherwise they are rationalized at 2⁻⁴⁸ and marked ≈.

A → Engine Iidle

B → Engine IIidle

C → Engine IIIidle

Presets: Clutch

A · Three engines, three calculations DEFINITION

Each calculation's head A B C winds from T4 to T0 of its engine and leaves a trail, with a marker where each tier begins. The faint line joins the heads, which always sit on the same node. On convergence the landing triangle appears with its exact closure P₄* (white) and the inferred fourth P₄ (diamond), which slides into the core. Memory beads: each value on its engine's outer manifold, the parity Y (gold) on the inner manifolds.

Loading Three.js r158…

B · Convergence core §7.5 · Lemma 8

The Part 2 crystal with its roles reversed. Each TwistorPair is one calculation. It starts outside the lattice and its two streams converge as the job winds inward, becoming one stream when the result latches. The core appears when all three have converged, placed by the Proposition 7.14 gauge of the three results: on the axis when they agree, off it when they differ. If memory parity fails, the trefoils shear.

Loading…

IDLE

STEP 000/720

Micro-twist 2.50 Buckle radius 3.0 Inverse sep 0.8 Torus radius 20.2 Z-scale 10.0 Pole height 34.6

The 4 × 4 memory layer, §7.7 §7.7

Convergence gauge, Proposition 7.14 Prop 7.14

C · Quadrance out and memory exact

Quadrance out: the landing triangle Lemma 5 · 4

word	Q₁	Q₂	Q₃	A_R poly = Gram	χ (≤ 1/√3)	Δφ A · B · C (mrad)	state

Timing clutch and the orthogonal membrane clutch

engine	clutch	own clock	own gear	spin since landing

Memory: outer and inner manifolds G1 · 7.11 · 15

addr	A · T4 I	B · T4 II	C · T4 III	Y · T0	parity	chain	word

Tiles and the memory root §6.1 · 15

newest word	A	B	C	Y

D · Fifteen-Lemma compliance, Part 2 reversed live

How the convergence calculator uses the monograph, and which of its choices are definitions.

result	what it governs on this page	live check	result

Telemetry log

What is reversed. Part 2 analyses: one measured total per class is split into three systems' models and the residual, the emergent fourth. This page composes: three independent results go in, and their exact total is the fourth. In both, the four make a group whose any one member is fixed by the other three (Proposition G1). Part 2's lock means the three engines agree about the data; here it means the three calculations agree with each other.
One clock, three schedules. All three engines run on engine v10's master clock (pulse p, node k = p mod 30). A job may be submitted at any moment, but it waits on the outer manifold until the wheel reaches node 0. It then spends one full wheel turn on each tier: T4 ingest, T3 compile, T2 and T1 evaluate, T0 reduce and latch, landing on node 29 after 150 pulses. Jobs started on different turns are at different depths, yet every engine always samples the same node, so their results can be combined with no clock conversion. A job that lands first is held in memory until the others arrive DEFINITION.
Quadrance out. On convergence the page reads out, with no further input, the Triple-Quad Formula of the three landing nodes: three quadrances, the quadrea in two exact forms, the ratio χ and the exact closure P₄*. The triangle encodes agreement, not the values themselves. Values are kept exactly in memory, which is why the readout and the memory are separate.
Memory on both manifolds. A, B, C are written to the outer manifolds and Y to the inner manifold, at the word's address on the wheel. Erase any one cell of a word (click it) and it is rebuilt from the other three. "Alter one cell" changes a stored value by 2⁻²⁴ without updating the others. Parity then detects it, the Merkle chain locates it (the deepest layer that differs is the altered leaf), and the parity rebuilds it.
Timing clutch. Each engine has its own clock, the pulses during which its clutch is engaged, and its helices turn only then. With hold finished engines an engine that has latched disengages: its gear stops and its result stays where it landed while the others catch up. With free-run every engine keeps turning, so a held result rides its helix away from where it landed. The engines counter-rotate, so equal results then land on a sheared triangle: the asynchronous frustration. With free-run + membrane the three carried spins split as in Proposition 7.14 into a common rotation s, which leaves the three congruent, and an orthogonal differential z, which is the shear. The membrane takes z in at the step-2 window and removes it exactly at the step-6 window, 180° of spinor phase later, where the three pair DEFINITION.
Shared with Part 2. The engines, the exact frames, the cross-engine TQF, the crystal, the gauge, the §7.7 layer and the tiles are Part 2's code, built from the same source.