16 Coexistence of “High Supply + Slow Leakage” in Massive Black Holes at High Redshift

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. For general readers: we look for two signals in the same object—evidence of high supply (sustained inflow of mass/energy) and of slow leakage (inefficient or delayed release of radiation, momentum, or angular momentum). We then test whether their coexistence strengthens with cosmic-web environment.

I. One-Sentence Goal

In massive black holes at high redshift (prioritize z ≥ 5–6), identify simultaneous signatures of high supply and slow leakage within the same source. The claim is supported if both signals coexist stably in an object, their joint strength increases monotonically from voids to filaments/nodes, and the conclusion replicates across bands and teams. If coexistence fails, or if lensing magnification, modeling degeneracies, pipeline bias, or environmental neutrality explain the data, the claim is disfavored.

II. What to Measure

1. High-supply indicators (choose any three; text grades):
   • Cold-gas reservoir: large molecular/neutral-gas masses inferred from CO/[C II]/dust continuum (strong/medium/weak).
   • Accretion sufficiency: Eddington-like or super-Eddington energy budgets from multi-band spectral energy distributions (described as text thresholds).
   • Inflow traces: stable evidence for inflowing material (for example, redshifted absorption, red-wing asymmetry, high-density narrow-line diagnostics).
   • Star-formation accompaniment: co-spatial, high star-formation rates that track gas replenishment, implying open large-scale supply channels.
2. Slow-leakage indicators (choose any three; text grades):
   • High covering obscuration: Compton-thick–leaning X-ray absorption and elevated dust–gas covering factors.
   • Delayed energy release: high infrared reprocessing fractions and long reverberation lags (infrared/millimeter versus UV/X), graded short/medium/long.
   • Inefficient outflows/jets: low momentum/energy flux per unit accretion, mild velocity fields, or jets “trapped” by free–free/self-absorption.
   • Slow angular-momentum shedding: molecular disks/dust rings with thickness/shear patterns indicating inner viscous pile-up.
3. Coexistence criterion: assign each object a High-Supply Index and a Slow-Leakage Index (strong/medium/weak). Record simultaneous medium–strong values that persist across epochs with consistent sign.
4. Environmental monotonicity: confirm that coexistence is significantly stronger in filament/node corridors than in voids, rising with void fraction ↓, filament strength ↑, distance to nodes ↓, external convergence ↑.
5. Cross-band and pipeline robustness: require consistent direction and ranking of the coexistence verdict across ALMA (mm/submm), JWST/ground-based NIR, deep X-ray, and radio.

III. How to Do It

1. Samples and environment templates:
   • Target pool: high-z, ultra-massive black hole quasars/bright nuclei with strong [C II]/CO and mid/far-infrared detections, plus usable X-ray and radio data.
   • Environment skeleton: from public surveys, build a filament–node–void skeleton with labels for principal axis, distance to nodes, local density, and external convergence.
   • Matched controls: for each target, select redshift/brightness/depth–matched controls at different environment grades; add lensing-suspect and void subsets as dedicated controls.
2. Acquisition and processing (blinded and independently reproduced):
   • Unified conventions: pre-register strong/medium/weak grading rules per indicator and text normalization across bands.
   • Forward prediction (environment team): using only environment templates, issue a prediction card per source with probabilities/tiers for high supply, slow leakage, and coexistence.
   • Measurement team (independent pipelines):
     1. Supply side: use ALMA CO/[C II]/dust continuum plus JWST/NIR line diagnostics to grade reservoir–accretion–inflow.
     2. Leakage side: use X-ray obscuration, IR/mm reverberation windows, outflow momentum rates/velocities, and radio compactness to grade obscuration–delay–leakage efficiency.
     3. Share only source IDs and epoch labels, not grades or prediction cards.
   • Arbitration: align prediction cards with grades by pre-registered rules; compute hit, wrong, and null rates, stratified by target vs control and environment grade.
3. Spatial and temporal axes:
   • Spatial: report qualitative enhance/plateau/decay trends for coexistence across nuclear, 100-pc, and kpc scale tiers.
   • Temporal: across multiple epochs, test whether high supply and slow leakage keep stable directions with slow amplitude drift, avoiding short-lived flares as false positives.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls:
   • In filament/node environments, the same source shows coexisting high supply + slow leakage, stable across epochs and bands.
   • Coexistence strengthens monotonically with external convergence/local density.
   • Restricting to non-lensed subsets leaves conclusions unchanged.
2. Negative controls:
   • In voids, coexistence fractions drop significantly.
   • Rotate environment labels or swap controls; hit rates should fall toward chance.
   • If “high supply” appears only with anomalous optical brightness and lensing cues, while mm/X-ray do not support it, treat as lensing/selection.
   • If “slow leakage” appears only in one band or pipeline, or jumps with instrument state, classify as pipeline/instrument.

V. Systematics and Safeguards (Three Items)

• Strong/ micro-lensing: can boost ordinary supply into apparent high supply. Safeguard: diagnose with image quality anomalies, differential absorption, and multi-image evidence; isolate or exclude suspect subsets.
• SED/line-diagnostic degeneracies: dust temperature, metallicity, and excitation can bias reservoir and obscuration inference. Safeguard: combine multiple independent indicators (CO ladder + [C II] + dust continuum + X-ray obscuration) and use model ensembles to report stable intervals not single numbers.
• Outflow detection thresholds and projection: low S/N or geometry can understate outflow efficiency. Safeguard: repeat with multi-tracer (ionized/molecular/dust) and multi-resolution data; report resolution dependence and viewing-angle sensitivity, and down-weight edge cases.

VI. Execution and Transparency

Pre-register indicator definitions and grading, environment proxies and strata, control/exclusion rules, and arbitration scores. Keep hold-out sources/epochs per environment grade for final confirmation. Conduct cross-facility replications across ALMA–JWST–X-ray (Chandra/XMM)–deep radio arrays, and exchange raw data for independent reprocessing. Publicly release the environment templates, prediction cards, text-grade tables for supply and leakage, and the coexistence verdict, plus key intermediate artifacts. This chapter forms a closed loop with Chapters 8 (axial perforation of AGN jets), 7 (co-located scaling near black-hole rings), 15 (polarization group alignment—filament synergy), and 27 (path-redshift tomography); cross-references are required.

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more environment grades and two or more independent teams/pipelines, high supply + slow leakage coexist in the same object with significantly above-chance hits.
   • Coexistence increases monotonically from void → filament/node, with consistent direction across mm–NIR–X-ray–radio.
   • Findings remain robust after excluding lensing suspects, using model ensembles, and multi-epoch tests.
2. Refutation (fails):
   • High supply and slow leakage rarely co-occur or appear only in one band/pipeline.
   • Coexistence shows no environmental monotonicity, or can be explained by lensing/degeneracies/projection.
   • Rotation/substitution controls drive hit rates to chance, and cross-team replication fails.