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arxiv: 2604.25116 · v1 · submitted 2026-04-28 · 🌀 gr-qc · astro-ph.HE· astro-ph.IM

Recognition: unknown

Gauge Theoretic Signal Processing II: Zero-Latency Whitening for Early Warning Pipelines

James Kennington , Joshua Black , Zach Yarbrough , Yun-Jing Huang , Chad Hanna , Leo Tsukada , Amanda Baylor , Olivia Godwin
show 4 more authors
Prathamesh Joshi Cody Messick Surabhi Sachdev Ron Tapia
Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:37 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEastro-ph.IM
keywords gravitational-wave detectioncausal filteringminimum-phase filterswhiteningnon-stationary noiseearly-warning alertssignal processinggauge theory
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The pith

Parallel transport along a minimum-phase connection on power spectra enables causal whitening filters that reduce latency by one second in gravitational-wave early-warning pipelines without losing matched-filter performance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that parallel transport along the minimum-phase connection on the manifold of power spectra provides an exact update rule for causal whitening filters under drifting noise. This rule preserves the minimum-phase property exactly and conserves matched-filter SNR, allowing pipelines to use only past data instead of look-ahead buffers. If the claim holds, early-warning searches for multimessenger transients can issue alerts faster while retaining the same detection sensitivity and sky-localization accuracy as current acausal methods. Numerical certification shows the connection is flat, making the optimal filter a path-independent state function of the instantaneous noise. Implementation in the production sgnl pipeline on O3 data confirms a 33 percent latency cut at a four-second noise cadence.

Core claim

The central claim is that parallel transport along this connection strictly preserves the minimum-phase property while exactly conserving the matched-filter SNR, and that the connection is flat so the optimal causal filter is a path-independent function of the current noise power spectrum. An injection campaign with 15,347 binary black hole signals on LIGO-Virgo O3 data verifies that detection sensitivity, inter-detector timing, and phase accuracy remain unchanged relative to the linear-phase baseline.

What carries the argument

The minimum-phase connection on the manifold of power spectra, which supplies the geometrically exact parallel-transport rule for updating causal filters.

If this is right

  • Parallel transport strictly preserves minimum phase while exactly conserving matched-filter SNR.
  • The optimal filter becomes a path-independent state function of the instantaneous noise.
  • Whitening latency drops by 1.0 s (33 percent) at a 4-second noise estimation cadence.
  • Detection sensitivity and inter-detector timing accuracy stay identical to the acausal baseline.
  • Up to 91 percent of baseline trigger latency can be removed with sub-second pipeline cadence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same geometric transport rule could be tested in other real-time domains that track non-stationary noise spectra, such as radio transient searches.
  • Lower whitening latency directly shortens the interval from gravitational-wave arrival to multimessenger follow-up observations.
  • Varying the noise-estimation cadence in controlled replays would map the precise latency-sensitivity frontier achievable with this architecture.

Load-bearing premise

The minimum-phase connection supplies a geometrically exact update rule for causal filters that preserves the minimum-phase condition and matched-filter SNR under non-stationary noise.

What would settle it

A controlled test in which a filter updated by parallel transport under realistic non-stationary noise either loses minimum-phase character or yields lower matched-filter SNR than the acausal linear-phase filter on identical data.

Figures

Figures reproduced from arXiv: 2604.25116 by Amanda Baylor, Chad Hanna, Cody Messick, James Kennington, Joshua Black, Leo Tsukada, Olivia Godwin, Prathamesh Joshi, Ron Tapia, Surabhi Sachdev, Yun-Jing Huang, Zach Yarbrough.

Figure 1
Figure 1. Figure 1: FIG. 1. Z-plane root migration during a realistic LIGO PSD transition. (Left) Standard linear cross-fade: roots are pushed view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical holonomy comparison across five connection types. (a) Mean holonomy on a log-scale: the MP connection view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Covariant SNR conservation ( view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Detection sensitivity on O3 data with 15,347 BBH view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Inter-detector timing accuracy on O3 data. (a) Scatter of the per-event timing residual (GTSP view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Inter-detector phase accuracy on O3 data. (a) Scatter of the per-event phase residual (GTSP view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Inter-detector phase recovery vs. injected truth on O3 data for LP (left) and drift-corrected GTSP view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Real-time pipeline latency measured from the production view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Online validation of the whitening latency gain on view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Per-stage cumulative latency vs. pipeline stride, measured from the production view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Signal-flow graph of the LP pipeline (top) and GTSP pipeline (bottom). Shared upstream (data source) and view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Unit-level demonstration of the holonomic correction kernel at three PSD perturbation levels (15%, 30%, 50% RMS). view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Residual distributions of inter-detector timing (top) and phase (bottom) relative to injected truth values on O3 data, view at source ↗
read the original abstract

Low-latency gravitational-wave search pipelines provide early-warning alerts for multimessenger astrophysical transients. Current pipelines whiten the data stream using acausal, linear-phase filters, which require a look-ahead buffer that introduces several seconds of algorithmic latency. Eliminating this latency requires causal, minimum-phase whitening filters using only past data. However, operating causal filters under non-stationary noise is non-trivial: the drifting power spectral density must be tracked without degrading the matched-filter signal-to-noise ratio (SNR), filter updates must preserve the minimum-phase condition, and the altered phase response must be compensated to maintain sky-localization accuracy. In Paper I we introduced a gauge theoretic signal processing framework and showed that the minimum-phase connection on the manifold of power spectra provides a geometrically exact update rule for causal filters. Here we validate that framework numerically and operationally, demonstrating that parallel transport along this connection strictly preserves the minimum-phase property while exactly conserving the matched-filter SNR. We numerically certify the flatness of this connection, showing that the optimal filter is a path-independent state function of the instantaneous noise. Through an injection campaign on O3 data with 15,347 binary black hole signals across the LIGO-Virgo network, we confirm that this architecture preserves the detection sensitivity and inter-detector timing and phase accuracy of the linear-phase baseline. Implementing the framework in the production sgnl pipeline reduces whitening latency by 1.0 s (33%) at a 4-second noise estimation cadence, confirmed in controlled tests and on live O3 replay data at production scale. Stride reduction experiments show that up to 91% of baseline trigger latency can be eliminated with sub-second pipeline cadence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims to numerically and operationally validate a gauge-theoretic signal processing framework for zero-latency causal whitening in gravitational-wave early-warning pipelines. Building on the minimum-phase connection introduced in Paper I, it asserts that parallel transport along this connection on the manifold of power spectra strictly preserves the minimum-phase property, exactly conserves matched-filter SNR, and yields a path-independent optimal filter as a state function of instantaneous noise. This is supported by numerical certification of connection flatness, an injection campaign with 15,347 binary black hole signals from O3 data across the LIGO-Virgo network (showing preserved detection sensitivity, timing, and phase accuracy relative to linear-phase baselines), and production-scale implementation in the sgnl pipeline that reduces whitening latency by 1.0 s (33%) at a 4-second noise estimation cadence, with stride-reduction experiments indicating up to 91% baseline trigger latency elimination.

Significance. If the reported preservation of SNR and minimum-phase properties holds under general non-stationary noise, the work offers a principled geometric method to eliminate look-ahead buffers in GW search pipelines, directly benefiting multimessenger early-warning capabilities. The scale of the O3 injection campaign and live replay tests at production cadence constitute substantial empirical evidence for practical viability. The framework's ability to handle drifting PSDs without post-hoc tuning or SNR loss addresses a key operational bottleneck, though its significance is tempered by the numerical (rather than analytic) nature of the flatness certification and dependence on the prior paper.

major comments (1)
  1. [Numerical certification of flatness] The section reporting numerical certification of flatness (referenced in the abstract and results): the manuscript certifies flatness via selected paths and O3 replay data but provides no analytic computation of the curvature 2-form on the manifold of positive power spectra equipped with the Hilbert-transform minimum-phase relation. Since the central claim of path-independent SNR conservation and minimum-phase preservation for arbitrary noise trajectories rests on this flatness, finite sampling, the 4-second cadence, and floating-point precision leave open the possibility of non-vanishing curvature on unsampled trajectories, which could introduce undetected phase errors or SNR degradation not captured by the 15,347-signal injection campaign.
minor comments (1)
  1. [Abstract and Introduction] The abstract and introduction would benefit from a brief, self-contained recap of the minimum-phase connection and parallel-transport update rule from Paper I, including the key geometric axioms, to improve standalone readability without requiring readers to consult the prior work.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Numerical certification of flatness] The section reporting numerical certification of flatness (referenced in the abstract and results): the manuscript certifies flatness via selected paths and O3 replay data but provides no analytic computation of the curvature 2-form on the manifold of positive power spectra equipped with the Hilbert-transform minimum-phase relation. Since the central claim of path-independent SNR conservation and minimum-phase preservation for arbitrary noise trajectories rests on this flatness, finite sampling, the 4-second cadence, and floating-point precision leave open the possibility of non-vanishing curvature on unsampled trajectories, which could introduce undetected phase errors or SNR degradation not captured by the 15,347-signal injection campaign.

    Authors: We acknowledge that the manuscript provides numerical certification of the connection's flatness rather than an analytic computation of the curvature 2-form. The manifold of positive power spectra is infinite-dimensional, rendering a closed-form analytic treatment of the curvature difficult. Our certification proceeds by evaluating the holonomy of the connection along numerous closed loops constructed from O3 noise PSD trajectories at the operational 4 s cadence. These tests confirm path-independence to machine precision, with relative discrepancies in the transported filter coefficients below 10^{-12}. The large-scale injection study (15,347 signals) and production-scale replay in the sgnl pipeline further corroborate that no measurable SNR degradation or phase errors arise under realistic non-stationary conditions. While we agree that finite sampling cannot exhaustively rule out curvature on all possible trajectories, the empirical evidence across diverse noise realizations supports the practical validity of the zero-latency whitening approach. In the revised version we will add a dedicated paragraph in the numerical certification section explicitly discussing the scope and limitations of the numerical tests, including the path-sampling strategy and precision thresholds employed. revision: partial

standing simulated objections not resolved
  • Analytic derivation of the curvature 2-form for the minimum-phase connection on the infinite-dimensional PSD manifold

Circularity Check

1 steps flagged

Minor self-citation of geometric framework from Paper I with independent numerical validation on external O3 data

specific steps
  1. self citation load bearing [Abstract]
    "In Paper I we introduced a gauge theoretic signal processing framework and showed that the minimum-phase connection on the manifold of power spectra provides a geometrically exact update rule for causal filters. Here we validate that framework numerically and operationally, demonstrating that parallel transport along this connection strictly preserves the minimum-phase property while exactly conserving the matched-filter SNR. We numerically certify the flatness of this connection, showing that the optimal filter is a path-independent state function of the instantaneous noise."

    The strict preservation, exact SNR conservation, and path-independence are properties first asserted in Paper I; the present manuscript imports the connection without re-deriving its curvature or transport rules and then numerically checks those imported properties on selected paths and O3 replay data.

full rationale

The paper imports the minimum-phase connection and parallel transport properties from Paper I but does not treat them as unverified; instead it performs new numerical certification of flatness, an injection campaign with 15,347 signals on real O3 data, and production pipeline tests that measure latency reduction. These external benchmarks make the central claims (SNR preservation, minimum-phase retention, path-independence) falsifiable outside the imported construction. The self-citation is therefore not load-bearing for the reported results.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the framework rests on a geometric structure whose details are deferred to Paper I.

free parameters (1)
  • noise estimation cadence
    Set to 4 seconds in the production implementation that yields the reported 1 s latency reduction.
axioms (1)
  • domain assumption The minimum-phase connection on the manifold of power spectra provides a geometrically exact update rule for causal filters.
    Invoked as the foundation imported from Paper I; no independent derivation supplied here.
invented entities (1)
  • gauge theoretic signal processing framework no independent evidence
    purpose: Supplies the minimum-phase connection and parallel-transport update rule for causal whitening.
    Introduced in Paper I and treated as given; no independent falsifiable handle provided in this abstract.

pith-pipeline@v0.9.0 · 5652 in / 1456 out tokens · 38286 ms · 2026-05-07T15:37:10.508451+00:00 · methodology

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Reference graph

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