All PROTIUM unit symbols share the H☉ family form, distinguished by an interstitial letter (axis) and case (scale tier).
Case convention: Lowercase interstitial = base-unit (physics/atomic) tier. Uppercase interstitial = named-unit (×10¹⁰) tier. The signing exponent HT☉ follows this convention — uppercase T denotes BLIP count (named tier).
Case
Tier
Examples
Lowercase
Base (flip, flip-length, quantum, flip-mass)
Ht☉, Hl☉, He☉, Hm☉
Uppercase
Named (BLIP, CLIP, QUIP, CHIP)
HT☉, HL☉, HE☉, HM☉
Design Axioms
Uniform scaling: All named units scale from their base units by exactly 10¹⁰. Equations whose terms scale in the same direction (e.g. c = λ/τ, where both numerator and denominator scale by 10¹⁰) hold at both tiers without correction. Equations mixing a quantity with the inverse of its conjugate (e.g. E = hν, where energy scales up and frequency scales down) acquire a factor of 10²⁰ at the named tier. The base tier is the physics-complete layer where all standard equations hold unchanged; the named tier is the human adoption layer where c = 1 is preserved but relationships mixing conjugate quantities require the scaling factor.
Parallel exponents: All Hx☉ axis exponents use log₁₀ of the base-unit count. The integer part reads directly as scale; the named-unit tier sits at exponent 10 on every axis by definition. Conversion between tiers is always a subtraction of 10 from the exponent: HT☉ = Ht☉ − 10.
The ☉ Symbol
☉ [U+2609] throughout PROTIUM denotes the protium atom — a diagram of a proton at center with a single electron in orbit. It is not the astronomical solar mass symbol M☉, despite superficial similarity. Where M☉ (solar mass) appears as a unit label in parameter definitions, it is explicitly written M☉ in context.
Time — Ht☉ / HT☉
Symbol
Name
Definition
Value
Ht☉
flip
τ(H) = 1/1,420,405,751.768 Hz
7.04024 × 10⁻¹⁰ s
HT☉
BLIP (Baseline Increment Protium)
10¹⁰ × τ(H)
≈ 7.04024 s
Landmark
Ht☉ (base)
HT☉ (signing)
1 flip
0.00
−10.00
1 BLIP
10.00
0.00
1 minute
10.93
0.93
1 hour
12.71
2.71
1 day
14.09
4.09
1 year
16.65
6.65
Current (~10.9 yr)
17.68
7.68
100 years
18.65
8.65
1,000 years
19.65
9.65
Age of universe
26.79
16.79
Distance — Hl☉ / HL☉
Symbol
Name
Definition
Value
Hl☉
flip-length
λ(H) = c × τ(H)
0.211061 m (21.1 cm)
HL☉
CLIP (Common Length Increment Protium)
10¹⁰ × λ(H)
≈ 2.1106 × 10⁹ m
Landmark
Hl☉ exponent
λ(H)
0.00
Earth–Moon
9.26
1 CLIP
10.00
1 AU
11.85
Proxima Centauri
17.28
Galactic center
21.07
1 Mpc
23.16
Observable universe radius
27.32
c = 1 at both tiers (exact, by construction): 1 flip-length per flip at the base tier, 1 CLIP per BLIP at the named tier. Velocity expressed in PROTIUM units is automatically the dimensionless fraction v/c — the system is natively relativistic at every scale.
Structural note: Ht☉ and Hl☉ exponents are equal for any light-travel relationship — a direct expression of c = 1 at the base tier. Age of the universe: Ht☉^26.79 (time) = Hl☉^26.79 (distance). The signing exponent sits 10 below the base exponent (see parallel exponents), so HT☉ values are offset by 10 from corresponding Hl☉ values.
The 21 cm line is the most universally monitored wavelength in radio astronomy — the basis of the water hole concept and the first spectral signature any independently-developed radio civilization would recognize. “Common” reflects this universality.
Energy — He☉ / HE☉
Symbol
Name
Definition
Value
He☉
quantum
E(H) = hν(H)
5.874 × 10⁻⁶ eV
HE☉
QUIP (Quantum Unit Increment Protium)
10¹⁰ × E(H)
≈ 58.74 keV
E(H) is the energy of the protium hyperfine transition — a single quantum of energy from the same atomic transition that defines the time and distance units. 1 QUIP ≈ 58.74 keV sits in the hard X-ray range.
Named-tier note: The Planck relation E = hν mixes energy (scales up by 10¹⁰) with frequency (the inverse of period, scales down by 10¹⁰), acquiring a factor of 10²⁰ at the named tier. This is a specific case of the conjugate-quantity rule described in the uniform scaling axiom.
Symbol note: He is helium in chemical notation. The ☉ suffix and PROTIUM context disambiguate; He☉ does not parse as a chemical symbol.
Mass — Hm☉ / HM☉
Symbol
Name
Definition
Value
Hm☉
flip-mass
mp (proton mass)
1.67262 × 10⁻²⁷ kg
HM☉
CHIP (Core Hydrogen Increment Protium)
10¹⁰ × mp
≈ 16.73 fg
The proton mass is the dominant mass constituent of the protium atom and of all baryonic matter. “Core Hydrogen” reflects that the proton is literally the hydrogen nucleus. 1 CHIP ≈ 16.73 femtograms — roughly the mass of a small virus. The mass unit’s human-scale landmark anchoring comes from the Hm☉ exponent ladder, not from the named unit value itself.
Landmark
Hm☉ exponent
mp (proton)
0.00
1 CHIP
10.00
~1 gram
23.78
~1 kg
26.78
~1 MEarth
51.55
~1 M☉
57.08
Reserved Namespace
Symbol pair
Axis
Note
Ha☉ / HA☉
Angle
Reserved without named unit. Radians are already dimensionless, universal, and require no non-trivial conversion from atomic constants. Namespace held for future use.
λ(H) = c / 1,420,405,751.768 Hz = 0.211061 m — the conjugate spatial expression.
E(H) = h × 1,420,405,751.768 Hz = 5.874 × 10⁻⁶ eV — the transition energy.
mp = 1.67262 × 10⁻²⁷ kg — the proton mass.
τ(H), λ(H), and E(H) are three expressions of one physical phenomenon: the protium hyperfine flip, viewed on the time, distance, and energy axes respectively. mp is the mass of the atom’s nucleus — the physical entity whose structure produces the transition.
Relationship to Prior Art
The Voyager Golden Record (1977) established hydrogen’s hyperfine transition as a universal time reference, encoding pulsar periods as binary multiples of τ(H). PROTIUM extends this foundation in three directions:
Named scale units (BLIP, CLIP, QUIP, CHIP) — human-adoptable tiers built on the same atomic base, enabling practical use beyond single-event decoding
Conjugate axes — the 21 cm wavelength formalized as a distance unit, the transition energy as an energy unit, the proton mass as a mass unit; c = 1 at both tiers makes the system natively relativistic
Multi-event calibration — gravitational wave merger catalogs provide overdetermined verification across all axes simultaneously; each new detection adds an independent model weight. This architecture was not available to Voyager’s designers; it requires LIGO-era observational capability.
A xenoreceiver bootstrapping from τ(H) alone reconstructs the full unit system. The GW event catalog provides self-verifying calibration without appeal to anthropocentric conventions.