Geometric Engine of Time · v10 mechanics · CCRU decimal Numogram

Engine, Numogram and a Numogram Engine on one clock

Panel A runs the orbital calculator with formulas copied from engine v10. Panel B is the decimal Numogram. Panel C rebuilds a clock from Numogram rules alone and locks it to the Engine only where an exact symmetry exists; everywhere else it says there is no map, and why. Hover (or tap) any linked element to light up its counterpart in the other panels.

PROVEN exhaustive finite check or algebraic identity COMPUTED evaluated numerically or on samples HEURISTIC analogy, not a theorem NO MAP no structural counterpart

Shared clock ENGINE PULSE COUNTER

pulseCount = ⌊simTime · 60⌋, activeNode k = pulseCount mod 30, stage = ⌊(pulseCount mod 150) / 30⌋, tier = 4 − stage. One counter drives all three panels.

speed 0.10x

0 150 pulses

pulseCount0

lap pulse p0 / 150

holonomic frame0 / 720

stage → tier0 → T4

node k (F k+1)0 (F1/30)

zone 2^(k mod 6)1

statorPulse0 / 60

outerFrameN0 / 720

piCycleStepK1 / 8

A · Engine v10 FORMULAS

Tori, the 30 dual helices, the 30 nodes of the active tier, and the TQF triangle V1–V2–V3 with the inferred V4 (fuchsia) and the exact parallelogram closure V4* (white).

Loading Three.js…

θ_k0°

c3Phase0°

c2Chiral · φ_p+1 · 0.0

Q1 · Q2 · Q3–

qScale–

A_R = (ΣQ)² − 2ΣQ²–

|V4 − V4*|–

V4 inferred · V4* closure (qScale = 1)– · –

Gears: outer 12 teeth = 2π·n/720, middle 10 teeth = −2π·n/72·η, inner 8 teeth = 2π·n/10·0.1 + drift, with n = outerFrameN. Rotor ray = piCycleStepK; amber rays k = 2 and 6 are the handshakes (±i).

Engine controls (tension, torsion, clutch, drift)

Tension180°

Torsion150°

Engine A

Engine B

Clutch ramp r4

64-bit engram (processEngram)

Seed text

Same two FNV-style 32-bit hashes as the file, with the file's default Form 1 written into [43:40]. The wheel unit decoded from [60:58] always has its digital root in the Time-Circuit (mapping 4).

B · Numogram DECIMAL, MOD 9

Zones 0–9; syzygies x::9−x drawn as linked pairs; current arrows land on the zone numbered by the difference; dashed gate channels run zone n → digital root of n(n+1)/2.

45 demons = C(10, 2), one per pair of zones; the 5 syzygetic demons are drawn.

Zone	Name	Current	Syzygetic demon	Region

Correspondence table

Each row is drawn in Panel C and linked across panels. Verdict says whether the Engine and the Numogram share the structure; the tag says how the claim is established.

#	Engine element	Numogram element	Verdict	Reason

Verification

Assertions run in this page with BigInt and exact rationals. Finite structures are checked exhaustively (PROVEN). The A_R identity is also tested on random integer triangles (COMPUTED).

Live (floating-point, from the Engine's own telemetry)

Discrepancies in the file (flagged, not fixed)

Rotation axes. The code rotates tiers with rotAxis 'Z' (no base rotation: T0, T2, T4) and 'X' (base euler.x = π/2: T1, T3). The papers describe the alternation as X/Y.
Inferred 4th vertex. pInferred = pNode + qScale·((pUpper − pNode) + (pLower − pNode)) with qScale = 0.65 + 0.45·√A_R/(ΣQ + 1e-6 + 1). It equals the parallelogram closure only when qScale = 1, so it is not an exact closure (Panel A shows both points and their distance).
Tier frequencies. freq = 6W (96, 84, 72, 60, 48 Hz) appears in TIERS_SPEC but not in the papers.
Upper/lower phase offset. The 0.22 is applied to θ inside the winding term: φ_up = W_up·(θ + 0.22)·c2 + c3 + 2π/3, φ_low = W_low·(θ − 0.22)·c2 + c3 + 4π/3. The effective poloidal shift is ±0.22·W rad (about ±2.2 rad on T3), not 0.22 rad.
Small code details. A_R is clamped with Math.max(0, …); PHI is defined but no function uses it; the inspector labels [60:56] "mod-30 wheel and structure selector" but only [60:58] is decoded (the wheel index).

Where this page departs from the file, and why

Stage index. The page derives the stage as ⌊(pulseCount mod 150)/30⌋. The file advances a stage on the edge activeNode === 29 && previousActiveNode !== 29, which can be skipped when more than one pulse elapses in a frame. Deriving every quantity from the counter keeps all three panels on the same pulse at any speed or scrub position.
Clock mode. Only the free-running clock is modelled (simSpeedBase = 1.0 times the speed slider, default 0.10x as in the file). The calculator's 6.0x/2.5x calculation speeds, keypad, rational evaluator and result latch are not part of this page.
Scrubber. One lap is 150 pulses, and holonomic frames are 720·p/150 = 4.8 p. The file's own display uses (p + 1)/150 progress, i.e. it counts the current pulse as completed.
Helix thickness. Tubes use radius 0.9 instead of 0.4 so they stay visible in a one-third-width panel. The curves (φ = Wθ·chiral + phase, 200 samples, closed Catmull-Rom, 150 segments) are unchanged.
Scene contents. Not drawn: particle fields, radial lines, checkpoint diamonds, the trace orb and trail, the degree plane, the polar grid, and the idle group rotation. Added: 30 node markers on the active tier (coloured by syzygy) and the closure point V4*. TQF is shown for the active node only, and its geometry is updated in place instead of rebuilt each frame.
Gear canvas. Copied unchanged; it is redrawn on every pulse of the shared clock rather than only while the CLUTCH tab is open.
Engram. Hash and decoding copied; the 8×8 grid, bit toggling and Form selector are omitted (Form 1, the file's default, is applied).
Additions with no source in the file. Panels B and C, the hover links, the correspondence table and the verification suite.