Master ledger · the spine document

0. Algorithm — how the whole model is generated

elemental_value(mp_celsius)  := (digit_product_of(|mp|))²
right_triangle_sides(mp)     := (|mp|, |mp|·4/3, |mp|·5/3)        # 3-4-5 ratios where 3-side = |mp|
right_triangle_area(mp)      := |mp| × (|mp| × 4/3) / 2  =  (2/3) · |mp|²
time_cascade(area)           := area / 24 / 60 / 60 / 60 / 60 / 24 …
PUM_scalar(N, dim_fraction)  := N / dim_fraction
                                (dim_fraction ∈ {10/9, 20/9, 10/3, 40/9, 50/9, 20/3, 100/9})
mirror_set(digits)           := all permutations of digits  (the "shuffle" identity family)

Important: Bendall’s text labels |mp|/3 as a unit-of-measure (e.g. “−259.2 / 3 = −86.4”) but the 3-side of the right triangle is |mp| itself, not |mp|/3. Patent PART 15 line 247: “−189.4 (3 side) × 252.5333 (4 side) = 47,829.81333 (Area of Square)” confirms 3-side = |mp|. The 4-side is then |mp| × 4/3 and the 5-side |mp| × 5/3.

Everything else is a deterministic projection of these four operations onto the torus / clock / compass / zodiac / periodic-table substrate.

1. Cardinal scalars (the seed set)

Mutual relations (every one verified):

SUN / 5.555  = 864,000 × 9/50  = 155,520            (5D Sun→Aether)
SUN / 4.444  = 864,000 × 9/40  = 194,400            (4D Sun→Time)
SUN / 3.333  = 864,000 × 3/10  = 259,200            (3D Sun→Matter)  ← = 1000 × |H mp|
SUN / 2.222  = 864,000 × 9/20  = 388,800
SUN / 1.111  = 864,000 × 9/10  = 777,600
SUN / 11.111 = 864,000 × 9/100 =  77,760            (Aether→Matter conversion)
MATTER / 11.111 = 3,456,000 × 9/100 = 311,040       (Sanskrit All Time)
AETHER / 5.555 = 144,000 × 9/50 = 25,920            (Great Year)
AETHER / 11.111 = 144,000 × 9/100 = 12,960          (RFEU / 10)
MATTER / 6.666 = 3,456,000 × 3/20 = 518,400         (TIME)
MATTER / 16  = 216,000                              (Moon × 100)
MATTER / 144,000 = 24                               (clock)
MATTER / 266.666 = 12,960                           (RFEU / 10)
SUN / 25,920  = 33.333                              (3D)
SUN / 518,400 = 1.666                               (POS)
SUN / 129,600 = 6.666                               (6D)

2. Dimension fractions (the ladder)

The repeating-decimal ladder is n × (10/9) for n = 1..12+:

The “11.1 = Aether→Matter conversion factor” is the master conversion constant. It ties Sun’s solar-pole-flip cycle (≈11 years) to its symbolic role.

3. Body diameters (mi)

Earth+Moon diameter: 10,080. Distance Earth↔Sun ≈ 108 × Sun diameter (the “108” relation).

4. Element table — digit_product² and right-triangle cascade

For every element with melting point in °C (negative for noble gases), let P = product of digits of |mp|, V = P². Then V is the element’s “elemental value”:

Right-triangle cascade (3-⁠4-⁠5 right triangle whose 3-side is |mp|):

For any mp:  side_a = |mp|, side_b = |mp| × 4/3, side_c = |mp| × 5/3
  Area = side_a × side_b / 2  =  (2/3) · |mp|²
  Then time-cascade:
     /24h → /60min → /60sec → /60arc → /60 → /24 → …
For H: 259.2 × 345.6 / 2 = 44,789.76
       /24 = 1,866.24
       /60 = 31.104
       /60 = 0.5184              ← × 1,000,000 = TIME = 518,400
       /60 = 0.00864
       /60 = 0.000144            ← × 1,000,000 = LIGHT = 144
       /60 = 0.0000024
       /24 = 0.0000001

So both TIME (518,400) and LIGHT (144) drop out of Hydrogen’s right-triangle cascade as decimal fractions multiplied by 1,000,000. This is the empirical anchor that ties the cosmology to the chemistry: hydrogen’s measured melting point alone generates the model’s two most important scalars by pure schoolroom geometry.

5. The seven octave sequences (OS)

(And EOS = Earth Octave Sequence, 7920; AOS-aether = Aether Octave 11.111 / 5.555.)

6. Geometric primitives

Torus (Vajar) lattice

• 8 toroidal planes × 16 sectors of 22.5° = 128 cells (patent PART 17 P 196)
• Then 4-fold subdivided to 32 planes × 64 radial points = 2,048 cells (poster legend item 23)
• One zero point at the centre (singularity)
• Plasmoid: 7,200° / 0 (= 20 full 360° rotations)
• Spiral pair: clockwise (implosive / “creation”) + anti-clockwise (explosive / “destruction”) superposed

Vajra Implosive Turbine (P76426GB)

• 30 blades = 15 outer + 15 inner, basket-weave
• Plate thickness 0.3–⁠3 mm
• 15 slots per plate
• Outer/inner volume ratio 5 : 1
• Aperture 0 → max via axial extension
• Materials: Cu / W (annealed in Argon) for conductors; SiC, ceramic, polycarbonate for insulators
• 8 capacitor banks (typical), 4 charge sources at 90° quadrature (++, –), Van der Graaf with sphere + pointed shank
• Twist convention: clockwise = “female”, anti-clockwise = “male”

Thunderstorm Generator buildable parts (TGMaterialsList.pdf)

• 2″ OD × 0.125″ thick (11 Ga.) SS hemisphere — sharpeproducts.com
• 3″ OD × 0.125″ SS hemisphere
• 4″ OD × 0.125″ SS hemisphere
• 1.125″ OD × 0.065″ wall × 0.995″ ID SS-304 welded round tube — onlinemetals.com
• 0.625″ OD × 0.065″ wall × 0.495″ ID SS-304 welded round tube
• (No assembly drawings or counts in the materials list — needs the section-11A “Schematics” lecture video)

7. The “mirror / shuffle” identity family

For any cardinal triple of digits (e.g. Sun = 864), Bendall asserts that all 6 permutations of the digit set belong to the model and are arithmetically equivalent under PUM:

Sun:   864 ≡ 846 ≡ 684 ≡ 648 ≡ 486 ≡ 468
Moon:  216 ≡ 261 ≡ 612 ≡ 621 ≡ 162 ≡ 126
Earth: 396 ≡ 369 ≡ 936 ≡ 963 ≡ 693 ≡ 639     (Earth radius 3,960 → 396)
…

The patent PART 15 then tabulates the entire 30-row × 6-column product table (864 family × powers of 2 from 2⁻⁹ up to 2⁵), showing that the whole multiplicative lattice closes under mirror-permutation. This is the foundation of the model’s “closed under harmonic permutation” claim.

8. Music

PUM tuning: C = 24 × 11.1 = 266.6 Hz (= 800/3 Hz).

Octave equivalents: 266.6, 533.3, 1,066.6, 2,133.3, …

Compare:

• Standard A=440 Hz → C₄ ≈ 261.63 Hz
• Scientific pitch C = 256 Hz
• Verdi C = 258.65 Hz
• Bendall PUM C = 266.6 Hz

In ratio terms: Bendall C / standard C ≈ 1.0192 (≈ 33 cents sharp).

Interval ratios from PUM dimension fractions (octave-reduced):

• 10/9 (1.1) = ~182 cents (≈ minor whole tone)
• 20/9 (2.2, octave-down to 10/9) — same
• 5/3 (1.6, “POS” SUN/TIME ratio) = ~884 cents (≈ major sixth)
• 6/5 (1.2) = ~316 cents (≈ minor third)

A “PUM scale” can be built from the dimension fractions as ratios — see build target D in §10.

9. Ratio identities cross-quadrant (verified)

SUN  / AETHER   = 6          ; SUN  · 6.6 = AETHER · 40
TIME / AETHER   = 3.6        ; TIME · 5/18 = AETHER     (note: AETHER × 0.2 × 18 = TIME, not AETHER)
MATTER / AETHER = 24         ; MATTER · 1/24 = AETHER
RFEU / AETHER   = 0.9        ; RFEU = 9 · AETHER /10
GREAT_YEAR / AETHER = 0.18   ; 25,920 / 144,000 = 9/50
GREAT_YEAR · 100 = 2,592,000  (Mayan Long Count?)
GREAT_YEAR / 12 = 2,160       (Moon diameter / Zodiac age length in years)
GREAT_YEAR / 4 = 6,480        (one season of the Great Year)
TIME / GREAT_YEAR = 20        (also = 1.6 × 12)
TIME · 60 / 100 = 311,040     (Sanskrit All Time = arc-seconds equivalent)
SUN_SQUARE = 4 · SUN_DIAMETER = 4 · 864,000 = 3,456,000   (not 864,000² / 1,000 = 746,496,000)

Verify the 4×D convention: 3,456 / 864 = 4 ✓.

10. What this enables — concrete build targets

A. pum-core library (TS or Python)

• Encode seeds + dimension fractions + body diameters as exact rationals.
• Function derive(symbol) returns the numeric value and the chain of operations that produced it, with no float drift.
• Function verify(claim) parses a PUM equation (e.g. “144,000 / 5.555 = 25,920”) and returns ✓/✗ with the exact arithmetic.
• Function mirror_set(n) returns the digit-permutation orbit of any input.
• Function elemental_value(mp_celsius) implements digit-product² + triangle cascade.
• Function cascade(mp, levels) runs the time/arc cascade.
• CLI: pum table prints the master ledger; pum derive 25920 shows the derivation graph; pum element H prints the cascade for hydrogen.

B. PUM ratio explorer (interactive SVG)

• Re-render the four-quadrant rose as a zoomable, hoverable SVG where every cell shows its derivation. Replaces the unreadable 60×80″ poster.
• Tooltip per cell: “144,000 ÷ 5.555 → 25,920 (Great Year, 5D Aether projection)”.
• Filter by quadrant / ring / dimension.

C. Plasmoid lattice generator (parametric 3D)

• OpenSCAD or CadQuery script with parameters: n_planes, n_radial_points, major_radius, minor_radius, twist_revolutions (default 20 = 7,200°).
• Defaults reproduce the Vajra spec (15+15) and the poster spec (32 × 64).
• Output STL.

D. PUM tuning system (Scala scale + reference synth)

• Generate a .scl file from the dimension fractions {10/9, 20/9, 10/3, 40/9, 50/9, 20/3} anchored at C = 800/3 Hz.
• Render reference tones as WAV.
• Optional: a small JS/Tone.js page that plays the seven OS sequences as harmonic series.

E. Element-cascade visualiser

• Heatmap of (Z, period) → digit-product² over the periodic table.
• Side panel: triangle-area cascade for any clicked element.
• Highlight where Bendall’s cascade hits a PUM cardinal scalar (× 10^n).

F. PUM-vs-actual delta map

• For every numerical claim in the model that has a measurable counterpart (m.p., body diameter, Great Year), tabulate (PUM value, measured value, % delta). This is honest engagement: it shows where the model is anchored to physical measurement and where it drifts.
• Examples to expect on the result table:
  • H m.p.: −259.2 (PUM) vs −259.16 (CRC) → ~0.015% high
  • Sun diameter: 864,000 mi (PUM) vs 865,370 mi (NASA) → ~0.16% low
  • Moon diameter: 2,160 mi (PUM) vs 2,159 mi → ~0.05% high
  • Earth diameter: 7,920 mi (PUM) vs 7,917.5 → ~0.03% high
  • Great Year: 25,920 yr (PUM) vs 25,772 yr (precession) → ~0.57% high
  • Speed of light: 144 (PUM, dimensionless) vs … (no unit; cannot compare directly)
  • Solar cycle: 11.111 yr (PUM) vs 11.0 yr (Schwabe avg) → ~1.0% high

The deltas are uniformly ~0.01 to ~1%. Whether that’s “good enough to call it a harmonic resonance” is a worldview question — the facts are tractable.

G. Vajra parametric CAD model

• From the patent’s geometry rules: outer / inner crescent plates, slot count = N, volume ratio 5:1, exit-iris of N teardrop plates pinned to outer-tabs.
• Parameters: N (default 15), plate_thickness (default 1 mm), outer_radius, inner_radius, extension.
• Output: FreeCAD / OpenSCAD model + 2D blade-cutting templates.

H. Numerical-claims audit ledger (builds on F)

• Single CSV of every numerical claim across poster + patents + lectures, with columns: symbol, claimed_value, unit, derivation, is_derivable_from_seeds, measured_counterpart, delta_pct, source_doc, source_line.
• This is the “engage seriously and honestly” deliverable.

11. Map: what each video / patent / poster contributes uniquely