BLIP Fingerprint Notation

BLIP Fingerprint Notation — Legend

Universal Compact Binary Merger Fingerprint · v0.4.1 · redacted.space

HBES (Hydrogen Blip Exponential Scale) is the framework. BLIP is the named time unit and the public-facing name. CLIP is the named distance unit.

H☉^9.064181778 [28.3 | 0.82 | −0.04 | 0.67 | ∅ ‖ 0.09 | 410]

Notation

H☉^N [ℳ_det | q | χ_eff | a_f | Λ̃ ‖ z | D_L]

A signed timestamp notation. The H☉ power is derived at the moment of signing — it encodes the elapsed blip count from the referenced GW event to the instant the signature is created. The bracketed parameters identify which event serves as the time anchor.

The same event referenced in two signatures made at different moments will carry different H☉ powers. The difference between them is the blip interval between signing moments, independently verifiable by any party who knows the event’s absolute timestamp. The notation is not a static record. It is a derived value, valid at the moment of creation.

Signing Convention — redacted.space

Base event: GW150914 · 2015-09-14T09:50:45Z

All signatures on redacted.space use GW150914 as the signing base. This is a site convention, not a property of the notation. The notation is agnostic about which event serves as anchor — any catalogued GW event with a known absolute timestamp is a valid signing base. The bracketed fingerprint always identifies which event is referenced, so signatures from different sources using different base events remain unambiguous.

Bare signature shorthand: once GW150914 is established as the signing base in a given context, subsequent signatures may use a shortened fingerprint:

H☉^9.064181778[GW150914]

The full bracketed form is used in version headers and any context where the base event is not already established.

Signing Procedure

Obtain the base event’s absolute timestamp
Compute elapsed seconds to now
Divide by 7.04024 to get blip count
Compute N = log(blips) / log(7.04024)
Record N at 9 decimal places

const H_BLIP = 7.04024;
const GW150914_UNIX = 1442224245; // 2015-09-14T09:50:45Z
const elapsed = (Date.now() / 1000) - GW150914_UNIX;
const blips = elapsed / H_BLIP;
const N = Math.log(blips) / Math.log(H_BLIP);
// → 9 decimal places for single-blip precision

Convention note (flagged for v0.5 examination): the exponent base 7.04024 is the blip duration expressed in seconds. As a declared convention it is exact and verifiable; however, the numeric value of the base depends on the SI second and is not independently derivable from physical constants alone. A fully xenographic time exponent would use log₁₀ of the blip count (parallel to the Hl☉ distance convention below). Changing the time exponent is a breaking change to signed history and is deferred to a deliberate v0.5 decision.

Precision Tiers

Anchored at H☉^9.064087065[GW150914] — 2026-06-11T23:17:05Z. 9 decimal places always resolves to single-blip precision regardless of elapsed time.

Decimal places	Resolves to	Resolution	Use case
2	H☉^9	~1.35 years	Scale notation, cosmological reference
5	H☉^6	~1.4 days	Document timestamping
7	H☉^4	~41 minutes	Event or meeting precision
9	H☉^1	~7 seconds	Cryptographic signing, maximum resolution

Versioning Principle

Time-dependent values are anchored to a signing epoch rather than marked as approximate or subject to drift. A value does not expire — it was precisely correct at its reference epoch and remains a precise historical record of that moment. Recomputation from any later epoch is always possible given the signing base event timestamp and the hydrogen flip period.

HBES Unit System

H☉ is the framework identifier. All unit symbols are members of the H☉ family, distinguished by an interstitial letter indicating axis and case indicating scale tier.

Design axiom: 1 named unit = 1 base unit × 10¹⁰. All mathematics is valid at either layer. Conversion is always a power of 10 applied to the same physical constant. Base units are the universal (xenographic) layer; named units are the human adoption layer.

The ☉ symbol [U+2609] throughout HBES 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

Symbol	Name	Definition	Value
Ht☉	flip	τ(H) = 1/1,420,405,751.768 Hz	7.040242 × 10⁻¹⁰ s
HT☉	BLIP (Baseline Interval Protium)	10¹⁰ × τ(H)	≈ 7.04024 s

Distance

Symbol	Name	Definition	Value
Hl☉	flip-length	λ(H) = c × τ(H)	0.211061 m (21.1 cm)
HL☉	CLIP (Common Length Interval Protium)	10¹⁰ × λ(H)	≈ 2.1106 × 10⁹ m

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 HBES units is automatically the dimensionless fraction v/c — the system is natively relativistic at every scale.

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.

Hl☉ exponent convention: Hl☉^N denotes 10^N flip-lengths. The base is 10; the unit is λ(H). The integer part reads directly as scale: Hl☉⁰ is the wavelength itself, Hl☉¹⁰ is one CLIP, Hl☉¹⁷ is nearest-star territory, Hl☉²⁷ approaches the cosmic horizon. Named-tier conversion: CLIPs = 10^(N−10).

Landmark	Hl☉ exponent
λ(H)	0
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	~27.3

Mass

Symbol	Name	Definition	Value
Hm☉	flip-mass	m_p (proton mass)	1.67262 × 10⁻²⁷ kg
HM☉	[name TBD]	specification pending	see Mass Verification Protocol

Flagged: the 10¹⁰ scaling convention applied to mass yields ≈16.7 femtograms — roughly the mass of a small virus, with no natural physical landmark. The 10¹⁰ convention may not serve the mass axis as it serves time and distance; an independently motivated exponent is under consideration. The geometric flip expression of chirp mass is already defined and verifiable regardless.

Reserved Namespace

Symbol pair	Axis	Physical anchor	Note
Ha☉ / HA☉	Angle	2π (full rotation)	Dimensionless; scaled unit utility TBD
He☉ / HE☉	Energy	hν(H) hyperfine transition energy	He = helium in chemical notation; the ☉ suffix disambiguates in context. Hε☉ noted as fallback.

Base Unit Reference

τ(H) = 1 / 1,420,405,751.768 Hz — the hydrogen hyperfine transition period.

λ(H) = c / 1,420,405,751.768 Hz = 0.211061 m — the conjugate spatial expression of the same transition.

τ(H) and λ(H) are two expressions of one physical phenomenon: the protium hyperfine flip, viewed on the time axis and the distance axis respectively.

Verification

Timestamp Verification

A decoder who receives two or more signed lines:

Converts each H☉ power to a blip count
Subtracts from each event’s known absolute timestamp
Obtains an independent estimate of the signing moment from each line
Confirms all lines agree — agreement verifies the unit system, GR framework, and signing integrity simultaneously

Mass Verification Protocol

Each GW event in the catalog carries an independently observable chirp mass. Expressing that mass in geometric flip units produces a conversion ratio verifiable without anthropocentric unit conventions. Consistency across multiple events confirms the HBES mass convention.

Conversion chain (human entry point → universal):

ℳ (M☉)
  × GM☉/c³ = 4.92549 × 10⁻⁶ s per M☉   → ℳ in geometric seconds
  ÷ τ(H) = 7.04024 × 10⁻¹⁰ s            → ℳ in geometric flips

GM☉ = 1.3271244 × 10²⁰ m³/s² (IAU 2015 nominal solar mass parameter). The nominal GM☉ is measured directly from planetary dynamics to far higher precision than G or M☉ separately — using it removes the gravitational constant’s measurement uncertainty from the verification chain entirely.

Event	ℳ_det (M☉)	ℳ_det (geometric flips)
GW150914	28.3	~197,992
GW170817	1.186	~8,297

Consistency of the flip-count ratio across catalog events confirms the convention. M☉ is recovered as a byproduct of the verification — it is not assumed.

1 M☉ = 6,996.2 geometric flips. This relationship between solar mass and the hydrogen flip period is a consequence of the physical constants governing stellar mass scales — not a definition. A decoder who independently derives ~6,996 flips per solar mass has confirmed both the HBES time unit and the geometric mass conversion simultaneously.

Delimiters

Symbol	Role
\|	Parameter separator within group
‖ (U+2016)	Group separator — intrinsic / extrinsic boundary
[ ]	Fingerprint boundary

Null State Symbols

Symbol	Meaning	Physical basis
∅	Physically absent	Parameter does not exist for this system by physical law — e.g. Λ̃ for black holes by the no-hair theorem.
⧖	Physically present, not yet measured	Exists in nature but beyond current detector capability — marks the sender’s instrumental frontier.

Parameters

Intrinsic — directly measured at detector · ℳ is detector-frame · independent of cosmological model

ℳ_det Detector-frame chirp mass M☉ · one decimal place

The dominant mass parameter governing inspiral frequency evolution, as directly measured by the detector. Equal to (1+z)ℳ_source — cosmological redshift stretches the observed waveform, making the source appear more massive than it is.

ℳ_det = (1+z) × (m₁m₂)^(3/5) / (m₁+m₂)^(1/5)

Source-frame ℳ is a derived quantity: ℳ_source = ℳ_det / (1+z). Recovering it requires importing z from the extrinsic column — the two columns are not fully independent. The fingerprint encodes what an interferometer directly measures, without assuming a cosmological model.

In geometric units (G=c=1): 1 M☉ = GM☉/c³ ≈ 4.9255 μs ≈ 6,996 τ(H). Chirp mass is directly expressible as a geometric flip count — see Mass Verification Protocol.

q Mass ratio dimensionless · range 0–1 · two decimal places

m₂/m₁ where m₂ ≤ m₁. Always ≤ 1 by convention.

χ_eff Effective inspiral spin dimensionless · range −1 to +1 · two decimal places

Mass-weighted aligned spin component. Governs inspiral phase evolution. Distinct from final remnant spin.

Near-zero values are common — do not confuse with a_f, which can be large even when χ_eff ≈ 0.

a_f Final remnant spin dimensionless · range 0–1 · two decimal places

Kerr spin parameter of the merged object. Derived from the post-merger ringdown waveform.

⧖ for BNS — post-merger ringdown above current detector frequency ceiling.

Λ̃ Effective tidal deformability dimensionless · integer

Mass-weighted tidal deformability. Encodes the neutron star equation of state — the physics of matter at nuclear density. Imprinted on the late-inspiral waveform phase.

∅ for BBH — black holes have no tidal deformability by the no-hair theorem.

Extrinsic — positional properties · observer-dependent · encodes sender location

z Cosmological redshift dimensionless · three decimal places

Fractional wavelength increase due to cosmological expansion along the signal path. For multi-messenger events, measurable spectroscopically from the host galaxy. Observer-dependent — two senders at different locations measure different z for the same event. This is the parameter that enables positional reconstruction. z is model-free and universally derivable from spectroscopic observation.

D_L Luminosity distance Mpc · integer

Distance derived from GW waveform amplitude. With z, gives an independent H₀ measurement for multi-messenger events. Retained in Mpc for human adoption.

Universal expression (Hl☉ convention, log₁₀ of flip-length count): 1 Mpc = 1.462 × 10²³ flip-lengths = Hl☉^23.165.

D_L (Mpc)	Hl☉ exponent
1 Mpc	Hl☉^23.165
40 Mpc (GW170817)	Hl☉^24.767
410 Mpc (GW150914)	Hl☉^25.778

The Hl☉ exponent is provided for universal verification. Mpc remains the primary fingerprint value.

Schema Selection

In-band duration functions as an event type discriminator before parameter estimation. The duration gap between stellar-mass BBH and BNS events spans nearly three orders of magnitude with no overlap — making duration an unambiguous classifier even at blip resolution.

Duration	Schema	Notes
> ~10 seconds	BNS	Λ̃ measured, a_f = ⧖
< ~1 second	BBH	a_f measured, Λ̃ = ∅

Reference Events

H☉ GW events are explicit zero points. H☉ powers shown are reference values, not current — recalculate from the signing procedure for a live timestamp. ℳ values are detector-frame — divide by (1+z) to recover source-frame.

GW150914 BBH 2015-09-14T09:50:45Z

H☉GW150914 [28.3 | 0.82 | −0.04 | 0.67 | ∅ ‖ 0.09 | 410]

First gravitational wave detection. Signing base for redacted.space.

ℳ_det = 28.3 M☉ = ~197,992 geometric flips.

ℳ_det	q	χ_eff	a_f	Λ̃	z	D_L
28.3 M☉ ±2	0.82 ±0.05	−0.04 +0.12/−0.14	0.67 +0.05/−0.07	∅	0.09 +0.03/−0.04	410 Mpc · Hl☉^25.778

GW170817 BNS 2017-08-17T12:41:04Z

H☉GW170817 [1.19 | 0.90 | 0.00 | ⧖ | 800 ‖ 0.008 | 40]

First multi-messenger GW event. z directly measured spectroscopically from host galaxy NGC 4993. GRB 170817A delay of 1.7s constrains GW/photon speed difference to < 10⁻¹⁵.

ℳ_det = 1.186 M☉ = ~8,297 geometric flips.

ℳ_det	q	χ_eff	a_f	Λ̃	z	D_L
1.186 M☉ ±0.001	~0.90 (0.73–1.0)	0.00	⧖	≤800	0.008 +0.002/−0.003	40 Mpc · Hl☉^24.767

Position Reconstruction

Four or more signed lines with measured z and D_L place the sender on intersecting spherical shells. Four well-separated events uniquely determine position in the observable universe. Precision scales with event count and angular separation; systematic floor ~tens of Mpc from cosmological model uncertainty and weak lensing.

Inverse Strain Metric (ISM): The pattern of strain amplitude residuals across many events encodes a local gravitational environment fingerprint, raising positional fidelity beyond the systematic floor.

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). HBES extends this foundation in three directions:

Named scale units (BLIP, CLIP) — human-adoptable tiers built on the same atomic base, enabling practical use beyond single-event decoding
Conjugate spatial axis — the 21 cm wavelength formalized as a distance 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.