Sgr A* as the centroid of three nested 6-channel, 5-tier geometric engines (Systems I, II, III) with an emergent fourth, the closure residual. Physics is weak-field general relativity in floating point (Layer A). The engine's bookkeeping, residual parity and frame closure, is exact rational arithmetic in BigInt (Layer B).
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A · Nested torus view DEFINITION
Five tiers per system at the spec's log radii; each tier carries its six channels as helices with Wn = 16 − 2n windings (phase = observable class, chirality = model/data). Drag to orbit, scroll or pinch to zoom, hover a pulsar for its data.
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B · Engine dashboard C3 × C2
Six channels per system. Row = observable class (C3), column = side (C2). The gold cell is the active channel k mod 6 of the 30-node clock.
Einstein radii behind Sgr A* (log radius), the scattered image against the weak-lensing shift, the magnetar's timing budget, and each pulsar's astrometric shift.
D · Fifteen-Lemma compliance live
How the page uses each of the monograph's fifteen lemmas and its §6–§7 system results, with the checks it runs itself. "Not used" rows make no claim. · Companion guide
8-step cycle and handshake windows Lemma 8phases
The triple quad: three groups of four Prop 7.11
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Data. Constants, the seven pulsars and every computed number come from the_galactic_lensing_hierarchy.md and verify_galactic_hierarchy.py. "Run Verification" is a line-by-line port of the script, including Python's Mersenne Twister seeded with 20261026, so the exact-arithmetic checks run on the same random cases; its output is compared with the script's captured output.
Simulated observations. The "model" side of each channel is a forward prediction from simple mass models: Sgr A* as a point mass; the nuclear star cluster as a Hernquist sphere of 2.5 × 10⁷ M☉ with a 4.2 pc half-mass radius HEURISTIC; and System III's observer terms (Gaia drift, Gaia acceleration, solar reflex). The "data" side is model + Gaussian noise + any injected signal. Pulsar position angles on the sky are illustrative; only projected distances are from the table. Line-of-sight depths are unknown (Problem G1) and are set equal to the projected offset, as in §6.2.
Fifteen Lemmas. Panel D maps every lemma of The Geometric Engine of Time: The Fifteen Lemmas onto this page and re-checks the ones it uses: tile fields follow §6.1, each update's twelve streams are chained with SHA-256 as in Lemma 15, frame legs come from the Cayley map of Lemma 9, closure uses Lemma 12's open convention, and Panel A's tier frames follow Lemma 4 (toggle "Lemma 4 frames" for the engine v10 frames). The companion guide explains how one engine becomes this three-system, twelve-stream arrangement.
Part 2.Tri-Engine Soliton turns the three shells into running engines, compares them node by node with an exact Triple-Quad Formula, and draws the emergent fourth as a soliton crystal built from the monograph's §7.5 bipyramid.
Clock. One master clock: pulseCount = ⌊t·60⌋, gears at 2π·n/720, −2π·n/72·η and 2π·n/10·0.1 with n = 12·pulseCount mod 720 (engine v10). One 720-frame cycle is one observation epoch of 0.25 yr. 1× speed advances 0.5 cycle per second; physics uses a fixed 1/60 s step with interpolated rendering.