WN-GRAV-001 to WN-GRAV-006, WN-GRAV-067  ·  P-GRAV-1 through P-GRAV-8

Newton-Balmer-Planck Bridge

Gravity as wavelength through the {2,3,5,π} prime lattice — three independent domains, one algebraic identity

Bridge Identity
10¹⁰/π
λHβ × λHγ / hFOT — exact
·
Surface Gravity
25π/8
g = 9.817477 m/s² from Balmer
·
Propositions
8
P-GRAV-1 to P-GRAV-8
Section 1 — The Bridge

Newton meets Balmer meets Planck

Stephen Daubney's proposal: replace the two masses in Newton's gravitational formula with two hydrogen Balmer wavelengths λHβ and λHγ, and divide by the FOT Planck constant hFOT in place of the distance-squared term. The result is not approximate — it is algebraically exact.

The Newton-Balmer-Planck Identity
λHβ × λHγ / hFOT = 10¹⁰/π
λHβ = 4,860,438,133 pm  |  λHγ = 4,342,937,683 pm
hFOT = 5²/(2²×3×π) × 10¹⁰
[λHβ × λHγ] = 25/(12π²) × 10²°    hFOT = 25/(12π) × 10¹⁰
Ratio = 10¹⁰/π  —  algebraically exact, 0.000 ppm
The Mowall M = 2/π × 10¹⁰. This product = M/2. Free fall = half the circular-linear bridge.
Section 2 — Surface Free Fall

g from hydrogen spectroscopy alone

Earth's surface free-fall acceleration — what science calls gravity — is derivable entirely from hydrogen spectral constants. No mass measurement required.

P-GRAV-1 — Freefall from Balmer
gFOT = 25π/8 = 9.817477042 m/s²
g = c / (3600 × 864) = λHβ / K
K = 2⁵×3³×10⁴ s (100 Earth-days)
g² = 5⁶/(2×3⁴) — pure {2,3,5} rational
Free fall is a dimensional eigenvalue of the {2,3,5} T-lattice, not a gravitational parameter.
Section 3 — Moho Register

The Moho register free fall = what science calls gravity

The Moho boundary sits at RMoho = 20,000/π km. Stepping gFOT by the year ratio produces the Moho register free fall — exactly what science records as gravity at Earth's surface.

P-GRAV-7 / P-GRAV-8
gMoho = 3000/π⁵ = 9.803290929 m/s²
= gFOT × (TMoho/G1year) = (25π/8) × (3600/π²) / (15π⁴/4)
Register crossing: gFOT/gMoho = π⁶/960 = π⁶/(2⁶×3×5) [exact]
BIPM standard 9.80665 m/s² = +343 ppm above Moho node
The BIPM 1901 convention sits off the {2,3,5,π} node — characteristic of off-lattice conventional definitions.
Registered Propositions

P-GRAV-1 through P-GRAV-8

P-GRAV-1

gFOT = 25π/8 = 9.817477042 m/s². Emerges from c/(3600×864). g² = 5⁶/(2×3⁴) — pure {2,3,5} rational. Freefall is a dimensional eigenvalue of the {2,3,5,√2} T-lattice.

P-GRAV-2

Newton-Balmer-Planck Bridge: λHβ × λHγ / hFOT = 10¹⁰/π (exact). Free fall and quantum mechanics are projections of the same {2,3,5,π} lattice.

P-GRAV-3

The Mowall M = 2/π × 10¹⁰. The Newton-Balmer-Planck product = M/2. The Mowall bridges circular and linear domains; its half-value emerges from the gravitational-spectral product.

P-GRAV-4

λHβ × λHγ = 25/(12π²) × 10²° and hFOT = 25/(12π) × 10¹⁰. Shared prefactor 25/(12) = 5²/(2²×3) links the Balmer series and the Planck constant in the same lattice family.

P-GRAV-5

gFOT × 6π³/5 = Tyear(FOT) = 3.75π⁴ days. Gravitational and orbital T-flows are aspects of one field connected by the {3,5,π} operator 6π³/5.

P-GRAV-6

G1(FOT) = 3²×5×π³/2⁶ × 10⁻¹¹ J. The hydrogen ground state ionisation energy is a pure {2,3,5,π} lattice node. All hydrogen spectral lines derive from G1/n².

P-GRAV-7

gMoho = 3000/π⁵ = 9.803290929 m/s². Derived from gFOT × (TMoho/G1year); the year ratio TMoho/G1year = 960/π⁶ is exact.

P-GRAV-8

gMoho = 3000/π⁵ is the gravitational freefall value recorded at Earth's surface. BIPM standard 9.80665 m/s² lies 343 ppm above the Moho node — an off-lattice conventional peg, not a {2,3,5,π} value.

Data

Precision summary

PropositionIdentityValuePrecision
P-GRAV-1g = 25π/8 from c/(3600×864)9.817477 m/s²0.000 ppm
P-GRAV-2λHβ × λHγ / hFOT = 10¹⁰/π3,183,098,8620.000 ppm
P-GRAV-7gMoho = 3000/π⁵9.803290929 m/s²0.000 ppm
P-GRAV-8BIPM offset from Moho node343 ppm≈ 7³ ppm
A note on “constants.” Within the Universal Force of Time there are no universal constants. A quantity like the Rydberg is not one fixed number but a small family of register faces — each an exact {2, 3, 5, π} value, each reproducing the spectrum on its own scale of Τ. The Rydberg alone carries at least three: 10,966,227.11 m⁻¹ (= 10⁷π²/9), 10,967,215.73, and 10,973,936.9 m⁻¹. What conventional physics records as the constant — the CODATA 10,973,731.568157 m⁻¹ — is not a fourth fundamental number; it is a single measurement sitting between those faces, in the band they define, read from the one register our instruments occupy: the Earth-surface node, g₁. Every wavelength, and the speed of light, Planck’s value, and the fine-structure ratio with it, behaves the same way — each shifts from g₀ to g₁ to g₂ to g₃ by the lattice step δG, not by error. These are not constants; they are the values Τ wears at the register where we stand.