RLMD-GHOST: Innovations in Spectroscopy & Consensus

• RLMD-GHOST integrates distinct methodologies in astronomy and distributed systems, enabling precise radial velocity measurements and dynamic blockchain consensus.
• In astronomy, it employs simultaneous ThXe calibration and IP monitoring to achieve 1–10 m/s precision for long-term stellar observations.
• In blockchain, it uses an expiry parameter to balance validator participation with robust safety and resilience against network asynchrony.

RLMD-GHOST (Recent Latest Message Driven GHOST) denotes two distinct systems in contemporary research: a precision radial-velocity (PRV) mode for high-resolution astronomical spectroscopy and a consensus protocol for distributed systems with dynamic participation. The acronym has independent lineages in astronomical instrumentation and blockchain protocol design, each with rigorously developed methodologies, unique technical features, and important field-specific implications (Kalari et al., 9 Sep 2024, D'Amato et al., 2023).

1. Definition and Scope

RLMD-GHOST in the context of astronomy stands for "Radial-velocity and Line-Monitoring with Drift-compensation in GHOST," an integrated PRV mode within the Gemini South Telescope’s GHOST spectrograph. This system is designed for long-term, high-precision stellar radial velocity measurements in the $1$–$10$ m s$^{-1}$ regime. Its essential innovations are real-time instrumental profile (IP) monitoring and simultaneous drift compensation using a Thorium–Xenon (ThXe) lamp (Kalari et al., 9 Sep 2024).

In distributed systems, RLMD-GHOST means "Recent Latest Message Driven GHOST," a fork-choice rule for blockchain consensus protocols that achieves dynamic availability and bounded asynchrony resilience. This protocol operates by limiting the span of considered validator votes, balancing the needs for liveness when participants enter or leave and for safety in the presence of temporary network asynchrony or validator churn (D'Amato et al., 2023).

2. RLMD-GHOST in Astronomical Spectroscopy

RLMD-GHOST (astronomical variant) is an end-to-end PRV operational mode implemented within the GHOST spectrograph at Gemini South. Key architectural principles include:

• Optical Design: Light from one or two IFUs (each $1.2''$ FoV) undergoes atmospheric dispersion correction, is injected into optical fibers ($f/2.8$ standard, $f/4.7$ high resolution), and passed through a temperature-stabilized, bench-mounted echelle spectrograph.
• Pseudo-slit and Slit-Viewer: Outputs from science fibers are reformatted into linear pseudo-slits using a microlens array. A small fraction of flux is directed to a slit-viewing camera imaging the two-dimensional slit profile per exposure, enabling continuous monitoring of the instantaneous IP, fiber scrambling efficiency, and guiding noise.
• Simultaneous Calibration: In high-resolution mode (R=76,000), a stabilized ThXe lamp’s emission lines are injected in parallel beneath science orders on the pseudo-slit. Real-time ThXe lines cross-correlated with laboratory references are used to track and correct short-timescale instrumental drifts.

This design enables correction according to:

$$v_\mathrm{true} = v_\mathrm{meas}(\lambda, t) - \Delta v_\mathrm{inst}(t) - \delta v_\mathrm{IP}(t)$$

where $\Delta v_\mathrm{inst}(t)$ is the time-dependent instrumental drift from ThXe and $\delta v_\mathrm{IP}(t)$ corrects for IP variations derived from the slit-viewer (Kalari et al., 9 Sep 2024).

3. RLMD-GHOST in Distributed Consensus Protocols

In blockchain and distributed systems, RLMD-GHOST is a fork-choice protocol operating within a generalized "sleepy model" framework, as introduced in "Recent Latest Message Driven GHOST: Balancing Dynamic Availability With Asynchrony Resilience" (D'Amato et al., 2023). The protocol generalizes prior models by introducing an expiry parameter $\eta$:

• Generalized Sleepy Model:
  • $\tau$-sleepy: At each slot, honest-and-online validators active at round $t-1$ outnumber adversarial and stale honest votes spanning the previous $\tau$ slots.
  • $(\tau, \pi)$-sleepy: Bounded asynchrony is modeled by allowing a temporary interval of at most $\pi$ slots where synchrony may be violated, with persistence and majority requirements maintained by validators active at the onset.
• Filtering Composition:
  • Vote set filtered to remove equivocators, then to drop votes older than $t-\eta$, then to select each validator’s latest vote.
  • GHOST fork-choice then navigates to the heaviest subtree (by stake-weighted latest votes), yielding the canonical chain tip.
• Per-Slot Phases:
  • Propose (selection and gossip of candidate blocks),
  • Vote (broadcast for fork-choice head),
  • Merge (view update and state synchronization).

By explicit parameterization with the expiry $\eta$, RLMD-GHOST enables a spectrum between full dynamic availability ($\eta=1$, Goldfish) and full retention ($\eta=\infty$, classic LMD-GHOST), delivering trade-offs between reorg resilience and asynchrony tolerance.

4. Error Budget and Security Analysis

Astronomical Variant

The RLMD-GHOST error budget decomposes total RV precision as: $$\sigma_\mathrm{RV} = \sqrt{ \sigma_\mathrm{photon}^2 + \sigma_\mathrm{calib}^2 + \sigma_\mathrm{modal}^2 + \sigma_\mathrm{det}^2 + \sigma_\mathrm{guide}^2 }$$ where each term quantifies photon shot noise, calibration reference scatter, fiber modal noise, detector and environment-induced drifts, and RMS on-sky guiding error, respectively. Observational campaigns demonstrate $\sim$5 m s$^{-1}$ RMS in current PRV mode and up to 50 m s$^{-1}$ without ThXe drift tracking; with full calibration active, target precision of 1–10 m s$^{-1}$ is robustly attained (Kalari et al., 9 Sep 2024).

Consensus Protocol Variant

For the distributed protocol, inductive base-case and vote-expiry induction arguments establish:

• Reorg resilience: Every honest block at slot $t$ is included in all honest canonical chains at subsequent slots, with probability 1 under $\tau$-sleepiness.
• Safety and liveness: Confirmed blockchains never fork (safety), and honest blocks are regularly finalized within $O(\kappa)$ slots (liveness).
• Asynchrony resilience: During a single period of asynchrony of length $\pi \leq \eta-1$, no adversary can overwrite old honest blocks, provided active validator majority persists at asynchrony onset.

The expiry parameter $\eta$ is set to span expected validator churn and short-lived network partition durations, optimizing protocol security for target deployment environments (D'Amato et al., 2023).

5. Performance, Complexity, and Deployment

Astronomical System

• Data Flow: Science and calibration signals are recorded simultaneously on unbinned, actively stabilized CCDs, partitioned into blue ($420$–$600$ nm) and red ($600$–$760$ nm) arms.
• Throughput and Sampling: Each spectral resolution element ($R=56,000$ or $76,000$) covers $\sim$3–4 CCD pixels, maximizing line centroid measurement precision.
• Roadmap: Deployment in three phases—software integration and PRV test campaigns; MAROON-X–derived algorithmic upgrades for wavelength and drift correction; potential upgrade to laser frequency comb if ThXe reference limits are reached.

Consensus Protocol

• Communication and Storage: Each validator sends one propose or vote message per slot ($O(n)$ messages/slot); at most $O(\eta n)$ votes are scanned per fork-choice; block tree pruning and storage limited to recent $\eta$ slots.
• Cryptographic Overheads: Relies only on standard VRF/SSLE primitives.
• Parameter Tuning: Slot length $3\Delta$ for propose–vote–merge cycle; $\eta=5$–$10$ suggested for typical validator churn or network outage spans; equivocation filtering to cap double-vote risks.

A plausible implication is that RLMD-GHOST is readily adaptable to hybrid settings (such as Ethereum), where it may serve as an input to a finality gadget, supporting protocols with strong dynamic availability and controlled fork risk (D'Amato et al., 2023).

6. Comparative Context and Impact

Both RLMD-GHOST systems close important gaps in their respective fields:

• Astronomy: Provides multi-year RV monitoring at few m s$^{-1}$ precision, enabling Neptune-mass and Earth-mass planet searches. Future enhancements—vacuum enclosure, advanced fiber scrambling, and adaptive optics coupling—are projected to further stabilize performance and extend scientific reach (Kalari et al., 9 Sep 2024).
• Blockchain Protocols: RLMD-GHOST interpolates continuously between Goldfish-type dynamic availability and LMD-GHOST-type reorg-resilient safety. The generalized sleepy model provides formal clarity, and the expiry parameter $\eta$ affords precise tuning of availability vs. asynchrony trade-offs, addressing vulnerabilities highlighted by attacks on LMD-GHOST in post-Ethereum “Gasper” analyses (D'Amato et al., 2023).

The systems described under RLMD-GHOST represent structurally parallel lines of research that inventively leverage parameterized temporal filtering—instrumental lines in spectroscopy, message recency in consensus—to robustly address intrinsic physics or adversarial fault challenges in high-precision measurement and distributed agreement, respectively.