source: derived from notes/01–03 (PUM poster) purpose: distil the model into computable form before reading the patents status: first pass — to be cross-checked against patent series

PUM as an algorithmic system — first distillation

1. The four cardinal scalars (one per quadrant)

The “dimension constants” are the repeating decimals 3.3̄, 4.4̄, 5.5̄, 6.6̄. As fractions: 3.3̄ = 10/3 ; 4.4̄ = 40/9 ; 5.5̄ = 50/9 ; 6.6̄ = 20/3.

2. The dimensional cascade (verified arithmetic)

Starting from AETHER = 144,000 and dividing by each dimension constant exactly reproduces the four cardinal scalars:

So the four “fundamental” PUM scalars are mutually generated by multiplying / dividing through the dimension constants:

AETHER  = 144,000
GREAT YEAR (A÷5.5̄)        = 25,920
SUN     = 864,000      = 25,920 × 33.333  = AETHER × 6
TIME    = 518,400      = 25,920 × 20      = AETHER × 3.6
MATTER  = 3,456,000    = 25,920 × 133.333 = AETHER × 24

3. The Earth / Moon / Sun anchor numbers

Legend item 1 declares:

• Sun = 864,000 [DC]
• Earth = 7,920 [AC]
• Moon = 2,160 [AC]

Legend item 17: Sun has 864,000 mi diameter, 432,000 mi radius. Legend item 18: “Matter” = 3,456 (3,456,000 mi — ‘Sun Square’ = 4 × Sun diameter).

These are the mile-diameters of the three classical luminaries. Moon = 2,160 mi diameter (near-correct: actual ~2,159 mi). Earth = 7,920 (rounded). Sun = 864,000 (close to ~865k).

4. The Protium / Great-Year coupling

The poster’s central axiom (paragraph 2 of the body):

• Protium [¹H] melting point = −259.2 °C
• This number, multiplied by 100, gives 25,920 → “Great Year” (Earth precession period).
• Specifically: 1,620 × 16 = 25,920 (“light frequency of −259.2 °C”, legend 8).
• Also: 259.2 × 1,000 / 10 = 25,920 ; or 259.2 × 100 = 25,920.
• And: 144,000 / 259.2 = 555.5̄ (5D anchor, NW panel line 5).

So the entire model treats the numerical coincidence between |melting-point of Protium| × 100 and the precessional Great Year (≈ 25,772 actual) as a design signature rather than coincidence.

5. The 25,920 → second / minute / hour / day cascade (TIME panel)

Each conversion exploits the fact that 25,920 = 2⁶ × 3⁴ × 5 × … etc. has a very rich divisor structure, so it tiles cleanly across the sexagesimal time/angle base.

6. The “9 ×” multiplication-table identity (MATTER panel)

So the “9-times-table” is treated as the matter-generating multiplier; every key diameter/radius is 9 × (an integer in the digital-root-9 family).

Note: 7920 (Earth diameter from legend) ÷ 9 = 880, but the panel uses 88 / 792 / 3,168 (i.e. it scales the Earth values × 0.1 vs the legend). The 88/792/3,168 row implies a secondary Earth-scale used elsewhere in the model.

7. The “1.666 / 6.666” rational identities (SUN panel)

POS = 1.6̄ is presented as a foundational ratio — it equals 5/3, the inverse of 3/5. This slot likely encodes “Position” / phase angle in the cycle.

8. The 24 / 16 / 32 / 64 grid (legend items 11–13, 23)

• Clock: 24 / 0 hour
• Compass: 360° / 0°
• Matter: 64 points = 32 resonant planes / 0
• Light: 144 / 0 (i.e. 144,000 / 1,000)
• RFEU: 1,296 (or 129,600)
• All Time: 5,184 (or 518,400 secs)
• Plasmoids: 7,200° / 0 ; 32 planes ; 64 radial points ; 1 zero point

So the geometric primitive is a toroidal lattice with 64 radial points × 32 planes = 2,048 elementary cells, plus a “zero point” at the centre. The “16-sector” mention in the body text refers to halving 32 planes (top / bottom).

7,200° / 0 is interesting: 7,200 = 20 × 360. The plasmoid traces 20 full revolutions. That equals 7,200 / 25,920 = 5/18 of one Great-Year sweep, or in seconds 7,200” of arc = 2°. Ambiguous from poster alone — patents may resolve.

9. The “Music” anchor (legend item 2)

Music (Do = C) = 24 × 11.111 = 266.6̄ Hz

So Bendall is asserting a tuning of C = 266.6̄ Hz. (Compare: standard C4 ≈ 261.63 Hz in 12-TET A=440; “scientific pitch” C = 256 Hz; Verdi C = 258.65 Hz; Bendall’s PUM C = 266.6̄ Hz is its own thing.)

Note 266.6̄ = 2,400 / 9 = 800/3. And 144,000 / 266.6̄ = 540, the “POS” line in the NW panel.

10. Candidate “generator” formula for the entire poster

Hypothesis: every PUM cardinal number is of the form

N = AETHER × 2^a × 3^b × 5^c × (10/3)^d × (40/9)^e × (50/9)^f × (20/3)^g

where a..g are small integers (often 0 or 1) and AETHER = 144,000.

Quick check (all match exactly): - 144,000 × 1 = 144,000 (AETHER) - 144,000 × (3/20) = 21,600 - 144,000 × (9/50) = 25,920 - 144,000 × (9/40) = 32,400 - 144,000 × (3/10) = 43,200 - 144,000 × 6 = 864,000 (SUN) - 144,000 × 24 = 3,456,000 (MATTER) - 144,000 × 3.6 = 518,400 (TIME) - 144,000 × (9/200) = 6,480 - 144,000 × (9/100) = 12,960

All Bendall’s “fundamental” numbers live in the multiplicative group generated by {144,000} × {2,3,5} and the four dimension fractions. This is computable — see the build-from-this section below.

11. What’s generative vs what’s just labelled

Generative (a small finite seed): - Seed scalar AETHER = 144,000. - Dimension fractions 10/3, 40/9, 50/9, 20/3. - Body-diameter set {2,160 ; 7,920 ; 864,000}. - Geometric primitive torus with 32 planes × 64 radial points + 1 centre. - Tuning anchor C = 800/3 Hz. - Element axis Protium melting point = −259.2 °C as the bridge between matter and the Great Year.

Everything else on the poster is a deterministic projection of those seeds onto a compass / clock / zodiac / periodic-table substrate.

12. Build candidates this enables

(For when we discuss what to construct.)

a) PUM calculator library — given any “PUM symbol” (TIME, RFEU, GREAT YEAR, SUN R, …) compute it from the seeds and verify the divisor identities. Pure data + tiny TS/Python module. Lets us audit the whole poster mechanically and flag any non-derivable numbers.

b) PUM ratio explorer / interactive wheel — re-render the four-quadrant rose as an interactive SVG (zoomable, hoverable) where each cell shows the algebra that produced it. Replaces the 60×80″ poster with something readable.

c) PUM tuning system — a microtonal scale built off C = 800/3 Hz with the four dimension fractions as interval ratios (3.3̄, 4.4̄, 5.5̄, 6.6̄ ≈ ~1.33, ~1.67, ~2.0 in octave-reduced form). Could be exported as a Scala (.scl) file for any synth.

d) PUM × periodic table mapping — map the standard periodic table onto the radial 16-spoke layout the poster uses, then plot any element property (m.p., b.p., abundance, Z, A) as a function of (group, period, valency, crystal-form) on the PUM wheel. Useful as an art object whether or not you accept the physics.

e) Plasmoid geometry generator — generative SVG / 3D mesh of the 32-plane × 64-point toroidal lattice with the “7,200° / one-zero-point” winding. Parametric in major/minor radius, twist, point density.

f) Numerical-claims audit ledger — the inverse of (a): scrape every numerical claim out of the poster + patents + decks, and tag each as {derivable from seeds | empirical measurement claim | interpretive label}. Foundation for any honest engagement.

g) MSAART engine / Vajra turbine geometry — once the patent series is read, extract the physical dimensions and tolerances Bendall specifies and render them as buildable CAD (parametric OpenSCAD or CadQuery). Separate from cosmology.