PUM Calculator · step-ratio operations

Work out any ring's value at any sector. Pick a divisor D below and all four modes use it. Start with D = 32, which is what the chart's outer rings use.

(half / default / double resolution)

Orientation

The PUM mandala lays out 24 numerical systems as concentric rings. Each ring has an anchor value, its MAX: 24 for hours, 360 for degrees, 25,920 for the great-year cycle. That value is swept clockwise from 12 o'clock in equal steps, so sector S of a linear ring comes to MAX × S / D.

Reading a ring
  • S runs 0 .. D−1 clockwise from 12 o'clock. S = D/4, D/2, 3D/4 land on the cardinal clock positions.
  • Linear rings: value = MAX × S / D. Clock at D = 32: S = 8 → 6 hrs, S = 16 → 12 hrs.
  • S = 0 is the wrap-around anchor, labelled MAX / 0 (as on the chart): the cycle starts at 0 and closes at MAX in the same cell.
  • Native sector counts on the chart: 16 for §2–§10, 32 for §11–§24. The D toggle re-resolves any ring at 16 / 32 / 64.
  • One ring is not a straight sweep: §24 uses 10S × (36/D).
Modes
  • ① apply S/D to a value V — table of every cell for a hypothetical ring with MAX = V.
  • ② fix S, show the value in every ring.
  • ③ reverse — given a value, the closest sector in each ring.
  • ④ reference table — MAX, step size, formula.
Categories
aether light / 6D / DC sun solar radii, orbital miles time hours, years, cycles matter 64/0 cycle, mileages, plasmoid rotations freq elemental frequencies, sound, RFEU, dimensions degrees compass, language special non-linear (§24)

① Apply step ratio · V × S/32

Treat V as the MAX of a ring and the table lists every cell at the current D. Worth trying: 24 (clock), 360 (compass), 144 (light), 25,920 (great year), 1,296 (RFEU).

② Sector → Values across all rings · cell(S, ring) = maxring × S/32

Fix S and read every ring at that angle. S = D/4, D/2 and 3D/4 land on 3, 6 and 9 o'clock. At S = 16 with D = 32, the bottom of the chart, the clock reads 12 hours, the compass 180°, light 72, dimensions 4.9995.

/ 32 = 0.500 × max

③ Value → which sector?

The other direction: for each ring, which sector sits closest to the number you enter. Sector counts are fractional so you can see whether a value lands on a boundary or between cells. Try 432, 144, 25,920, 1,296, 7,200.

④ Reference · all rings at 32 steps

MAX, the step size at the current D, and the formula. One ring doesn't follow the linear sweep: §24 is exponential, 10S × (36/D), so at D = 32 sector 16 gives 1018 and sector 32 gives 1036.

Per-ring formula strings quote each ring's chart-native D (16 for §8, 32 for §11–§24); the max and one-step values always use the selected D.

§RingMax One step (= max / D)Formula
Glossary — the terms used on this page
Mandala
Sanskrit for "circle". In PUM, the chart is a series of concentric ring-bands around a central core, with each ring representing one numerical system.
Ring
One of the 24 concentric bands. Numbered §1 (centre: Sun/Earth/Moon) outward to §24 (outermost: All Plasmoid Energy).
Sector / Cell
A wedge-shaped slice of a ring. Sectors are numbered 0..D−1 going clockwise from 12 o'clock. A "cell" is the ring × sector intersection.
MAX (anchor value)
Each ring has one characteristic number — its largest meaningful value (e.g. 24 hours, 360°, 25,920 years for the great year). At sector 0 the ring shows MAX as a "wrap-around" anchor; at sector D it would also equal MAX (the cycle closes).
Divisor D
How many equal steps the ring is split into. The chart uses 16 for inner rings, 32 for outer, but any ring can be re-divided by any D. This calculator lets you switch among 16, 32, and 64.
Step ratio (S/D)
The fractional position of sector S within the ring. The value at that sector is MAX × S / D for linear-sweep rings.
Exponential ring
§24 All Plasmoid Energy uses 10S × (36/D). The exponent grows linearly with S while the value grows exponentially.