13 Neighboring-Object Redshift Mismatch: Environmental Sequence of Source-Side Tensor Differentials

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and keeps the structure fixed. For general readers: a source-side tensor differential means a small, stable intrinsic frequency shift between distinct emitting or absorbing regions within the source because they reside in slightly different local tensor/gravitational conditions—not because of bulk motion or dispersive media.

I. One-Sentence Goal

Within close-separation or same-host pairs, compare redshifts (or systemic velocities) from multiple line families and probes to test for a repeatable neighboring-object redshift mismatch. Interpret any stable, non-kinematic offset as a source-side tensor differential. Support for the claim requires that the mismatch grows systematically in filament/node corridors, weakens in void corridors, is insensitive to observing band, and remains robust to pipelines and instruments. If kinematic layering, radiative-transfer effects, or frequency-reference issues explain the offsets—or if no environmental link appears—the claim is disfavored.

II. What to Measure

• Existence and sign of a near-neighbor mismatch: After standard de-motion and frequency-reference calibration, grade the residual redshift difference across representative line families for close pairs (same host or small-angle neighbors). Use text intervals and strong/medium/weak tiers; test whether the offset’s sign and rank order are repeatable.
• Line–probe consistency: Check whether mismatch directions agree across molecular / atomic / ionized-gas lines; emission vs absorption; narrow lines vs maser/fine/hyperfine features. Verify that conclusions match across radio, millimeter, and optical/near-infrared bands for the same object.
• Epoch and neighborhood robustness: In multi-epoch repeats, ask whether sign and ordering stay stable while amplitudes drift slowly. Within the same environment grade, assess whether different objects show a reproducible narrow distribution.
• Environmental monotonicity: Across the void → filament → node sequence, test for a monotonic relation between mismatch amplitude and environment proxies (void fraction, filament strength, distance to nodes, external convergence). Compare target vs control corridors for significant differences.
• Band independence (separating path terms): Confirm that mismatch does not flip with band and does not rescale with wavelength in a dispersive way. If a dispersive pattern appears, classify it as medium/chain and exclude it from source-side conclusions.

III. How to Do It

1. Samples and “neighbor” definitions:
   • Same-host neighbors: distinct emission zones within one galaxy/nucleus (for example, narrow-line region vs molecular disk; starburst ring vs absorbing cloud; maser clumps vs narrow-line gas).
   • Small-angle neighbors: close pairs (quasar pairs, galaxy pairs, multiple clumps within an arc) that traverse similar lines of sight but terminate at different sources.
   • Mirror-image neighbors (caution): use strong-lens multiple images only for within-source, cross-line checks; image–image path differences are out of scope for positive calls here.
     Each target receives an environment-matched control (similar sky position/redshift/brightness but a different environment grade) and a pseudo-neighbor (sky-near but physically unrelated) to probe blind-judgment bias.
2. Observing and processing (blinded and independently reproduced):
   • Line lists and bands: adopt a unified line catalog per class (molecular rotational ladders; atomic fine/hyperfine; narrow vs maser pairs) spanning radio–millimeter–optical/near-infrared.
   • Absolute referencing and de-motion: use absolute frequency/time references and apply consistent corrections for observer/antenna motion, known medium dispersion, and instrumental chains. Independent teams reprocess without sharing parameters or code.
   • Blinded comparison: the environment team issues prediction cards (expected direction and strength of mismatch) using only environment templates. The measurement team shares line names and epoch labels but not redshift numbers. An arbiter aligns and scores outcomes by pre-registered rules.

IV. Positive/Negative Controls and Removal of False Positives

1. Positive controls:
   • In filament/node corridors, same-host and small-angle neighbors show same-sign multi-line mismatches whose amplitude tracks environment strength.
   • Across epochs and bands, direction and rank order remain stable without band flips.
   • In void corridors, mismatches shrink and their distribution narrows.
2. Negative controls:
   • Shuffle environment labels or swap prediction cards: hit rates drop toward chance.
   • Injected rotation/outflow models may reproduce line-family differences but should fail to match environment monotonicity and band independence.
   • Intra-band sub-channels that shift with a wavelength-squared law indicate Faraday/dispersion and are excluded from source-side claims.

V. Systematics and Safeguards (Three Items)

• Kinematic layering and line-of-sight blending: rotation/outflow/turbulence can mimic inter-line shifts. Safeguard: favor narrow, co-spatial line groups; use integral-field spectra or symmetric-quadrant extractions to suppress rotational projection.
• Radiative-transfer and optical-depth effects: self-absorption or shielding can bias line centers. Safeguard: pair emission vs absorption and combine multi-depth lines; down-weight or hold out high-optical-depth lines.
• Frequency-reference and chain common-mode drift: absolute-reference drift can forge mismatches. Safeguard: deploy dual references/dual chains for cross-checks, swap local oscillators and playback order in repeats, and use nearby standard sources as same-night zero baselines.

VI. Execution and Transparency

Pre-register neighbor definitions, environment grading, line lists and conventions, prediction cards, decision rules, and exclusions. Keep hold-out objects/lines within each environment grade for final confirmation. Exchange raw spectra and processing scripts across institutions for independent reprocessing, including subset/down-sampling robustness tests. Publicly release environment summaries, prediction cards, text intervals for mismatches, band-consistency summaries, and key intermediate artifacts. This chapter forms a closed loop with the chapters on same-source multi-line “rigid shift, ratio-invariant” calibration, environment-forward potential terms in time delays, and path-redshift tomography; cross-references are required.

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more neighbor types and two or more environment grades, environment-forward predictions of mismatch direction and strength achieve significantly above-chance hit rates, with a void → filament/node monotonic increase.
   • Mismatch is band-insensitive and stable in sign/order across epochs/institutions/pipelines.
   • Conclusions hold after excluding dispersion/Faraday/rotation–outflow effects.
2. Refutation (fails):
   • Hit rates hover near chance or are driven by one pipeline/institution.
   • Mismatch flips or rescales with band, or is fully explained by kinematic layering/radiative transfer/frequency-reference drift.
   • Target–control and environment-gradient differences are insignificant, undermining the source-side tensor-differential sequence.