1 Path “Frequency-Independent Common Term” Cross-Probe Corroboration

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This chapter follows the standardized four-block structure specified for the falsification program and is written for publication. It uses plain language and avoids equations or symbols. Terms that may be unfamiliar to general readers are defined at first mention.

I. One-Sentence Goal

Detect and compare, along the same sky path or a nearby corridor, a residual shift that is independent of observing frequency and shares the same direction across independent instruments. If this frequency-independent common term appears consistently across multiple classes of probes and varies with large-scale environment, it supports the path term claimed by Energy Filament Theory (EFT). If it does not appear, or if it shows no environmental dependence, it counts against the claim.

Definitions for general readers:

• A frequency-independent common term is a leftover timing or phase shift that does not flip sign or scale with observing frequency and shows up in the same direction on different instruments.
• Environment refers to large-scale structure along the line of sight—voids, filaments, and nodes—rather than conditions at the source or inside the instrument.

II. What to Measure

• Common timing residual on the same path after standard de-dispersion: After each team finishes its usual frequency-dependent corrections, check whether different bands and stations still show a same-direction residual shift along the same path or a tightly adjacent corridor.
• Same-shape residuals across independent probes: On the same path, compare whether residual curves line up in time across different probes such as Fast Radio Burst (FRB) / pulsar timing, deep-space spacecraft dual-frequency coherent carrier links, Very Long Baseline Interferometry (VLBI) multi-band phase delay, and strong-lensing multi-image light curves. After this first mention, use the full names—Fast Radio Burst, Very Long Baseline Interferometry, and so on.
• Environmental dependence: Test whether the strength of the common term changes monotonically with environment class—stronger along filament-dominated corridors and weaker through void-dominated corridors.

Reader note: In Energy Filament Theory, path redshift is the intuitive idea of a slowly accumulated offset along the observing path, unrelated to the source engine or the instrument chain.

III. How to Do It

1. Sample and path selection:
   Choose several “sky corridors” that deliberately span different environments (filament-dominated versus void-dominated). Each corridor must have at least two independent probe classes with usable data. Pair every target corridor with a nearby control corridor that differs in environment but sits close in sky position to reduce unrelated differences. Candidate probes include repeated or lensed Fast Radio Burst sources, stable pulsar timing targets, standard radio calibrators for Very Long Baseline Interferometry with multi-band observations, dual-frequency coherent carrier links from planetary or deep-space spacecraft, and strong-lensing systems with well-sampled multi-image variability. Use public catalogs or predetermined surveys to avoid cherry-picking.
2. Processing and contrast design:
   Each probe team first applies its routine pipeline (ionospheric and interstellar plasma corrections, geometry, instrumental paths, clock chains, solar-wind windows). Teams do not share parameters or code to prevent artificial alignment. Then run a blinded comparison: share only timestamps and path labels, not residual amplitudes. An independent arbitration group aligns timelines and evaluates three plain-language criteria:
   • Same direction: Do final residuals across bands and stations move the same way?
   • Same timing: Do key turns occur in the same time window?
   • Environmental contrast: Is the effect stronger in filament corridors than in their nearby void controls?

Treat as positive controls any case where at least two probe classes on the same path show a shared step, plateau, or slow drift, more pronounced in filament corridors. Treat as negative controls any case where the alignment fades when moving to a nearby corridor with a different environment, or where a single probe shows the effect everywhere, which would suggest a spurious background.

1. Systematics and safeguards (three items):
   • Timebase common-mode: Use two-way time transfer and multi-system common-view checks; cross-validate independent time standards and explicitly remove any network-wide common-mode in the analysis.
   • Near-Earth and solar-side plasma: Prefer quiet space-weather windows; isolate near-Sun link segments as a labeled subset with reduced weight; use an independent near-Sun link as a reference track.
   • Pipeline coupling: Reprocess the same raw data with at least two independent pipelines. Any common term that appears in only one pipeline is flagged as spurious and excluded from positives.
2. Execution and transparency:
   Pre-register the corridor list, probe combinations, plain-language criteria, and the exclusion list before joint analysis. Keep a hold-out set in each corridor for final confirmation. Repeat across seasons or years to check stability and seasonality. Publicly release key intermediate products—timestamp indexes, path labels, environment class, and plain-language summaries of final residuals—to enable outside replication. This chapter forms a closed loop with the chapters on lensed Fast Radio Burst timing, planetary radar near-Sun links, and time-delay cosmology; cross-reference results across those chapters.

IV. Pass/Fail Criteria

1. Support (passes):
   • Along the same path, at least two independent probe classes show same-direction, time-aligned residual features.
   • The effect is significantly stronger in filament corridors than in void corridors and weakens in nearby control corridors.
   • The alignment survives changes of station, clock standard, and processing pipeline, and does not flip sign or re-scale with observing frequency.
2. Refutation (fails):
   • Cross-probe alignment is consistently absent, or it appears only within a single institution or a single pipeline.
   • Any apparent alignment reverses with frequency or changes amplitude in a way that signals a frequency-dependent (dispersive) origin.
   • Differences between target and control corridors are insignificant, showing no link to environment class.