The base units
The physics-complete layer.
The ground truth
One measured constant anchors three of the four axes: the hydrogen-1
hyperfine transition frequency,
ν(H) = 1,420,405,751.768 Hz.
Combined with two exact SI definitions — the speed of light
c and Planck’s constant h
— it yields time, distance, and energy. The fourth axis,
mass, is the independently measured proton mass.
Four definitions
Ht☉ Time — the flip
τ(H) = 1 / ν(H) = 7.04024 × 10⁻¹⁰ s
The period of one hyperfine transition — how long the spin flip takes.
Hl☉ Distance — the flip-length
λ(H) = c · τ(H) = 0.211061 m (21.1 cm)
How far light travels during one flip. This is the 21 cm line familiar from radio astronomy.
He☉ Energy — the quantum
E(H) = h · ν(H) = 5.874 × 10⁻⁶ eV
The energy of the photon the hyperfine transition emits.
Hm☉ Mass — the flip-mass
mₚ = 1.67262 × 10⁻²⁷ kg
The proton mass — the particle whose spin produces the transition.
A complete, structural system
Because distance is defined as light-travel during one flip,
the speed of light is structurally unity:
c = λ/τ = 1 Hl☉/Ht☉.
Because energy is the photon of that same flip, Planck’s
constant is also unity:
h = E·τ = 1 He☉·Ht☉.
Neither is an approximation or a convention — both fall
out of the anchoring.
That is what makes these four axes a system rather than
four isolated constants. Every other quantity is a combination of
them — velocity is
Hl☉/Ht☉, momentum is
Hm☉·Hl☉/Ht☉, power is
He☉/Ht☉ — with no fifth base
unit ever required. The four span the whole of mechanics, and
because c and h are unit-free
structural properties, the standard equations hold at the base
tier exactly as written. Many combinations simplify as a result:
velocity comes out as a fraction of c, with no
conversion. This is what physics-complete means.
The independent fourth
Mass stands apart. Time, distance, and energy are three views of the same photon event — one anchor, the transition frequency, yields all three. Mass needs a second: the proton, anchored by dynamics rather than photon counting. A receiver reconstructing PROTIUM therefore makes two independent measurements, not one.
This is by design, not a shortfall. The second anchor is what
lets the mass axis be verified separately from the others
— and it is why mass and energy stay distinct quantities
rather than collapsing into one. The unity of c
and h ties distance, time, and energy together;
mass sits outside that knot, joined to it only by a measured
bridge. That separation is the source of the framework’s
redundancy: a receiver can check the mass axis against the
energy axis and confirm both are right.