Zero-Point Tri-Engine Zero Point Calculations · the eight-step cycle inside the 720-frame register

The Tri-Engine Convergence calculator, rebuilt on the zero-point cycle of The Geometric Engine of Time: The Zero-Point Eight-Step Cycle. Every frame of the 720-frame outer gear is one zero-point step: spinor step k = F mod 8, branch j = F mod 3, joint frame n = F mod 24. So one register holds 90 spinor cycles and 30 joint cycles (Proposition 3.7), not one stretched cycle. The three engines are the three 120° branches. Each carries one instruction of its calculation per joint cycle: onloaded at its k = 2 frame, lifted, projected, inverted and folded back exactly, then offloaded at its k = 6 frame twelve frames later. Calculations of different lengths finish at different times. The three results pair at the zero point, and every register closes with the 720 → 72 → 10 pump and the open memory test. Part 2 · Part 2 manual · Guide · The paper, explained interactively

Speed0.05×18 frames/s

Tension0°

Torsion0°π/6 gate

Coupling κ1.00

Calculations · three branches, one zero-point clock DEFINITION

One expression per branch. Digits, decimals, fractions, + − × ÷, ^ (whole-number powers), brackets and unary minus are exact. sqrt, sin, cos and π are exact where the answer is rational; otherwise they are rationalized at 2⁻⁴⁸ and marked ≈. A job takes as many joint cycles as it has instructions, so longer calculations land later.

A → Engine I · branch 0 (0°)idle

B → Engine II · branch 1 (120°)idle

C → Engine III · branch 2 (240°)idle

Presets: Clutch

Z · The zero-point cycle at frame resolution Props 2.2–3.9

The dial is the eight-step cycle, advanced once per frame. The strip is one joint cycle of 24 frames: each branch onloads at its k = 2 frame (filled) and offloads at its k = 6 frame twelve frames later (outlined). A register of 720 frames holds 30 strips and 90 turns of the dial. On this page a frame is engine v10's 1/720 s (12 per pulse), so a register is one second. The paper takes a frame to be a pulse of 1/60 s.

Joint 24-frame schedule Prop 3.7

Register

The zero point: three closure tests Def 3.12

The eight stages Table 4

k	stage	spinor	reduced	spatial	spread	operation

Four tracks of the spinor clock §8.10

Branch packets Prop 3.3

branch	packet now	exact round trips

A · Three engines, three branches DEFINITION

Each calculation's head A B C leaves a trail frame by frame. It descends a tier each time a fifth of its instructions has been offloaded, and a marker shows where each tier begins. At the zero point the landing triangle appears with its exact closure P₄* (white) and the inferred fourth P₄ (diamond). Memory beads show each value on its engine's outer manifold and the parity Y (gold) on the inner manifolds. The inset dial now turns once every 8 frames.

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B · Convergence core §7.5 · Lemma 8

Each TwistorPair is one branch. It starts outside the lattice and its two streams merge as the branch's instructions are offloaded. The core appears at the zero point where the three pair, placed by the C₃ split of Proposition 3.4: on the axis when the results agree, off it when they differ. If memory parity fails, the trefoils shear.

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IDLE

FRAME 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

Pairing gauge, Propositions 3.4 and 7.14 Prop 3.4

C · Quadrance out, pump and memory exact

Quadrance out: the triangle at the zero point Lemma 5 · 4

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

The 720 → 72 → 10 pump and the memory test Prop 3.9

engine	engaged so far	P, last register	Q⁽¹⁰⁾	Q⁽⁸⁾	H	memory test

Timing clutch and the orthogonal membrane clutch

engine	clutch	own clock	own gear	spin since landing

Memory: outer and inner manifolds 3.10 · G1 · 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 · Compliance with the zero-point paper and the Fifteen Lemmas live

How the zero-point tri-engine uses the paper and the monograph, and which of its choices are definitions.

result	what it governs on this page	live check	result

Telemetry log

What changes from the convergence calculator. There, the eight-step cycle was read off the outer gear as one step per 90 frames, so one 720-frame turn was one spinor cycle. The paper supersedes that reading (Errata 10.2, item 2): 720 is a frame count, and under the exact generator 1 + i the spinor returns every 8 frames, 90 times per register (Proposition 3.7(4)). Here every frame is a zero-point step, and everything that was gated by the old windows is now gated by the frame schedule.
Branches are engines. The nine-phase wheel splits into three 120° triads (Proposition 2.1). The a = 0 triad, in the corrected frame, is three cube vertices, and σ, the 120° turn that relates the three engines, carries each branch to the next. So engine s is branch s. A branch onloads at its k = 2 frame and offloads 12 frames later at k = 6 (Proposition 3.7), once per joint cycle. A calculation therefore runs one instruction per joint cycle, and calculations of different lengths finish at different frames.
Pairing at the zero point. When all three have latched, they pair at the next zero point of the joint cycle (joint frame 0, a Snap). Their exact total is the fourth of the triple quad, the C₃ split gives s and z, and the landing triangle is read out by the TQF. The zero point is a closure state with three tests (Definition 3.12). The spinor test is the clock itself. The geometric test is every packet's exact round trip. The memory test is the open holonomy of each engine's gear over the register, which the 720 → 72 → 10 pump evaluates (Proposition 3.9). With the clutch holding a finished engine, that engine's gear falls behind and the register closes with a recorded residual. That is the case Definition 3.12 allows for: a residual P ≠ 1 that a compensator (H = P⁻¹) removes.
Four tracks. The spinor clock is computed three ways (§8.10). Floating point (track A) drifts slowly. The exact reduced state (track B) cannot drift. Residues modulo 881 (track R) fingerprint B. The page accepts A only within tolerance of B.
Frame convention. This page keeps engine v10's frame, 12 per pulse, so the register is one second. The paper takes a frame to be one pulse of 1/60 s, so its register is 12 s. Its zero-point identities (Propositions 3.7, 3.9, 7.1) count frames and hold under either convention. Its clock-window table (Proposition 3.8) is stated for its own frame and is not used here DEFINITION.
What it does not claim. The lifts into the null cone and the hyperboloid are embeddings that change how a point is represented (Definition 1.1). The value of each calculation comes from the exact evaluation, and nothing here bears on P versus NP, which the paper leaves open (Theorem 5.11).