Illumina — Carrier Pigeon · Jupiter

Abstract

We map the phrase Carrier Pigeon · Jupiter · Lighthouse to operational roles inside the Illumina rendezvous framework: courier (store–and–forward artifact), address & clock (Jupiter/Io as universal reference), and beacon (wide–area minimal header). All modes use the same “Illumina-1” packet: prime-length header, compact ECC, and dimensionless anchors. We give cadences, DIY tests, and safety notes. All math uses HTML entities (no external libraries).

1. Concepts & Roles

Carrier Pigeon → Courier

Store–and–forward via artifacts, probes, or ultra–narrowband links.
High sender τ/bit, very low recipient τ/bit.
Ideal for long–life archives; embed Illumina-1 verbatim.

Jupiter → Address & Clock

Use Jupiter rotation / Io phase as a shared timebase.
Encode a compact ephemeris key; no units required.
Acts as a rendezvous address, not a physical lensing scheme.

Lighthouse → Beacon

Repeat a minimal header + parity at a fixed cadence.
Minimizes acquisition τ for unknown receivers.
Payload optional; header alone is recognizable.

2. Illumina-1 Packet

2.1 Handshake header

M = { prime length p, Barker–like autocorrelation, checksum } .

Recommended p: 31 or 47.
Checksum: 16–bit parity or extended Golay(24,12,8) syndrome.

2.2 ECC layer

Reed–Solomon RS(31,19) over GF(32) — compact, widely tooled.
Extended Golay (24,12,8) — ultra–compact, robust.

2.3 Dimensionless anchor tuple

a = ( α, m_e/m_p, Q, Gℏ/c³ ) .

Prefer symbolic reference or sub–noise perturbations; keep well below cosmology/spectroscopy bounds.

3. Jupiter: Address & Clock

Embed a compact, unit–free ephemeris key that any observer can invert with public ephemerides:

K = { \mathrm{YYYY\!-\!DOY\ bucket},\ \mathrm{Jup\ rotation\ bucket},\ \mathrm{Io\ phase\ bucket} \rbrace; \quad \mathrm{bits}\ \mathrm{per}\ \mathrm{field}\ \mathrm{pre\!-\!registered}.

Clocking: align beacons to a rational function of Jupiter rotation or Io phase.
Why: universal sky reference; no cultural units needed.

4. Lighthouse: Beacon

Repeat just the header + parity on a fixed cadence; receivers use a fixed statistic to lock:

\mathrm{Beacon}(t) = M \ \|\ \mathrm{parity} \quad \mathrm{every}\ \Delta t .

Cadence example: Δt = k × (Jupiter rotation) / 47, with small co–prime k.
Alternate: prime–spaced gaps between repeats.

5. Carrier Pigeon: Courier

For artifacts or slow links, embed Illumina-1 plus metadata:

\mathrm{Courier} = \langle M,\ \mathrm{ECC}(payload),\ K,\ \mathrm{provenance},\ \mathrm{checksums} \rangle .

Two independent physical carriers (e.g., etched plate + ceramic code) recommended.
Include human–readable redundancy and a machine–readable block.

6. Schedules & Cadences

Mode	When	Why
Lighthouse	Fixed Δt (Jupiter–locked or prime–spaced)	Predictable discovery; minimal acquisition τ
Courier	One–off; include epoch via key K	Long–life archive; near–zero recipient τ

7. Tests & Validation

7.1 Header detectability

Inject a 31/47–bit header at < 5σ into noisy data.
Use a fixed normalized autocorrelation statistic for lock.
Measure false positive/negative under a pre–registered threshold.

7.2 Ephemeris key round–trip

Encode a timestamp as K; share only K.
Can peers reconstruct the intended epoch within tolerance?

7.3 ECC sanity

Flip random bits in the payload; confirm RS/Golay correction within design bounds.
Publish syndrome/decoder used for replication.

8. Safety & Governance

Prefer diagnostic encodings that do not perturb structure formation or violate spectrum allocations. Pre–register code families, statistics, and thresholds; use multi–party review; publish null ensembles; encode pro–social norms alongside the handshake.

Appendix A — Header Examples

Any short prime–length, low–sidelobe header is acceptable. Example (illustrative only):

p = 31; \quad M_{31} \in \lbrace 0,1 \rbrace^{31} :\ 1011101001101010010110010010111

For production, select from a pre–registered set with measured sidelobe profiles.

Appendix B — Ephemeris Key K

Compact, unit–free fields (bit widths are examples):

Field	Meaning	Bits
Y	Year mod 64	6
D	Day–of–year bucket (0–91)	7
J	Jupiter rotation bucket	6
Io	Io orbital phase bucket	6

Publish the exact bucketization and reconstruction tolerance with the deployment.

Appendix C — Detection Statistic (Sketch)

Use a fixed normalized autocorrelation deviation against a prime–length reference:

S = \max_{\text{shifts}} \frac{\sum_{i} (x_{i} - \bar{x})(m_{i} - \bar{m})}{\sqrt{\sum_{i}(x_{i}-\bar{x})^{2} \sum_{i}(m_{i}-\bar{m})^{2}}}

Set a pre–registered threshold for S and correct for multiple testing if scanning several headers.