45 Neutrino Arrival-Time Structure and a Cross-Baseline Non-Dispersive Common Term

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and preserves the fixed structure. With unified timescales and near–far calibration, we compare arrival-time structures across beam, atmospheric, and astrophysical neutrino sources and multiple experiments/baselines. After subtracting Standard Model energy dependences (mass–spectrum–geometry), we test for a flavor- and energy-insensitive non-dispersive common term—a constant time shift or slow platform that aligns across baselines and replicates at zero lag across experiments and pipelines. If residuals scale or flip with energy/flavor, or fail under held-out/blinded tests, the claim is disfavored.

I. One-Sentence Goal

Determine whether a baseline-alignable, non-dispersive timing term exists in neutrino data across sources and detectors, independent of energy and flavor, and reproducible at zero lag across analyses.

II. What to Measure

• Common-term strength and robustness (text grades):
  After common bandpass/timestamp/selection, extract constant and slow-slope components from arrival-time residuals. On a grid of baseline (length × azimuth) × source type (beam/atmospheric/astrophysical) × detector × pipeline, grade strong / medium / weak; positive / negative; stable / unstable, and record cross-baseline alignability.
• Non-dispersion test (energy and flavor):
  Regress Standard-Model group-velocity and reconstruction biases via templates/inject–recover. In energy-quantile and flavor tomographies (ν_e/ν_μ/ν_τ or proxies), test that the common term does not vary systematically with energy or flavor.
• Near–far cancellation and source jitter removal (beam):
  Build an empirical emission profile from near detectors and transfer it event-by-event to the far site; test whether near–far differences retain a same-sign, same-width constant platform.
• Zero-lag co-occurrence (cross-experiment/pipeline):
  On a single external timescale, align residual sequences from independent experiments and pipelines and test for zero-lag synchronous steps/platforms/phase locks within the same geometry/environment window.
• Geometry–environment correlations:
  Versus mantle path angle, Earth-tide strain, geomagnetic indices (Kp/Dst), solar high-energy background, station temperature/pressure/humidity, tag monotonic/plateau/threshold profiles and assess forward-predictive regularities.
• Ratio invariance and rigid shift:
  Check that energy-bin fractions and phase relations stay stable across baselines/experiments, while absolute timing shows rigid shifts/slow platforms that can be aligned.
• Astrophysical triggers (optional):
  For supernovae/GRBs/blazars, compare neutrino–electromagnetic/gravitational-wave arrival differences for narrow constant offsets that do not broaden in energy-resolved slices.

III. How to Do It

1. Observation families and data planes:
   • Beams: at least two long-baseline beams with different lengths/azimuths and near–far detectors.
   • Atmospheric: deep detectors in northern/southern/equatorial hemispheres, covering up-going/down-going paths.
   • Astrophysical: time-tagged with multi-messenger networks, with independent trigger seasons held out.
2. Unified calibration and timing:
   Use a single external timescale (common-view/GNSS two-way/White Rabbit). Publish delay ledgers for sensors-to-disk chains with temperature→delay regression and inject–recover (LED/laser/pulse plates) to lock absolute offsets. Release reconstruction templates for energy/zenith/multipath and hold them out during fits.
3. Windows and event tomography:
   For beams, define short (ms) and long (s) windows around spill gates. For atmospheric/astrophysical, window by local time/tide phase/geomagnetic level and set control windows for bursts.
4. Processing and stacking:
   Run ≥ 2 independent pipelines (time-domain alignment / frequency-domain coherence / wavelet–empirical mode). Combine bandpass/high-pass filters and conditionally stack in baseline × source × energy × flavor × zenith to produce constant/slow-slope/synchrony text tables.
5. Forward prediction, blinding, arbitration:
   The forward team issues prediction cards using only geometry/environment variables. The measurement team independently reports non-dispersion/zero-lag/shape summaries. The arbitration team scores hit / wrong / null across baseline/experiment/source/pipeline/window and publishes decisions.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (support a non-dispersive common term):
   • Same-sign, similar-amplitude constant/slow platforms appear across multiple baselines/experiments/pipelines and are insensitive to energy/flavor slicing.
   • Near–far differencing preserves the platform, excluding source jitter.
   • The term tracks geometry/environment as monotonic/plateau/threshold, and prediction cards beat chance significantly.
   • Replication in held-out seasons/experiments/energy windows with high zero-lag synchrony.
2. Negative controls (argue against the term):
   • Residuals scale/flip with energy or correlate with flavor layers.
   • Signals exist only in one experiment/pipeline/window, or are highly sensitive to bandpass/window/alignment/reconstruction templates.
   • Label swaps/time reversals/parameter shuffles still “detect” signals—method bias.
   • With tighter delay budgets/temperature regressions/energy-reconstruction corrections, signals vanish or can be reproduced by timestamp bias/trigger thresholds/buffer latency.

V. Systematics and Safeguards (Three Items)

• Timescale unification/delay budgeting gaps: incomplete closures of GNSS/White Rabbit and trigger–buffer delays. Safeguard: two-way comparisons + inject–recover + redundant timing, plus published delay ledgers.
• Energy reconstruction and selection coupling: energy–time selection effects mimic non-dispersion. Safeguard: equal-statistics energy bins, template hold-outs, and inject–recover tests.
• Environmental confounders: temperature/geomagnetic/tidal co-drivers induce common drifts. Safeguard: co-monitoring, scenario-aware regression, and temporal permutation controls.

VI. Execution and Transparency

Pre-register baselines/azimuths/source types/detectors, timing scheme, criteria for non-dispersion/zero-lag/shapes, variable lists, positive/negative controls, exclusions, and scoring. Define held-out units by experiment/season/energy/flavor/zenith. Enable cross-team replication by sharing raw timestamps/trigger logs/delay ledgers/reconstruction weights/scripts and by running down-sampling/noise/kernel-variant/template-swap robustness tests. Release prediction cards, common-term strength tables, zero-lag indices, bandpass/alignment kernels, delay ledgers, and environment logs (text summaries), plus key intermediates.

VII. Pass/Fail Criteria

1. Support (passes):
   • In ≥ 2 experiments, ≥ 2 baselines, ≥ 2 pipelines and multiple source types, recover a non-dispersive, zero-lag common term.
   • The term follows predictable monotonic/plateau/threshold geometry–environment profiles and is robust to bandpass/alignment/templates/energy–flavor slicing.
   • Arbitration significantly exceeds chance and held-out units replicate.
2. Refutation (fails):
   • Results are dominated by energy/flavor dependence or timing/reconstruction systematics, or do not replicate across baselines/experiments/seasons.
   • Parameter fragility or disappearance/reversal in held-out sets.
   • Arbitration near chance—indistinguishable from system/method artifacts.