30 Full-Parameter Phase Diagram for Vacuum “Tensor Wall” Analog Platforms

Home ／ Appendix-Prediction and Falsification

I. One-Sentence Goal

Under a unified external time–frequency and energy scale, construct a full-parameter phase diagram across multi-physics analog platforms—superconducting–microwave networks, cavity quantum electrodynamics (QED), photonic/phononic metamaterials, cold-atom Bose–Einstein condensates (BEC), plasma/dielectric waveguides, and nonlinear optical lattices. After removing geometric/relativistic, medium, and readout-chain effects, test for a cross-platform “tensor wall” phase characterized by the co-occurrence of steady high reflection, local density of states (LDOS) suppression, and group-delay steps; non-dispersion across carriers and state types; and a post-threshold neighborhood featuring breathing and channelization with zero-lag co-occurrence. If conventional nonlinear saturation, thermally driven phase changes, or dispersive scattering explain the observations—or if results lack cross-platform/team robustness—the claim is disfavored.

II. What to Measure

• Phase-region fingerprints (text grades):
  At co-located, co-window settings, grade reflection/transmission steps, group-delay steps, ringdown prolongation, and LDOS suppression as strong / medium / weak; uplift / depression. Tag each operating point with a phase label: no-wall → precursor → steady-wall → breathing → channelized → collapse.
• Non-dispersion consistency:
  With carrier and state switches—direct current (DC), radio frequency (RF), terahertz (THz), and optical; polarization, time window, and mode—require stable phase boundaries and fingerprint ordering. Any flip/scale that follows λ² or 1/ν laws indicates medium/link dispersion, not a common tensor-wall term.
• Zero-lag co-occurrence:
  Require zero-lag peaks (with strong/medium/weak side-lobe contrast) among reflection steps, group-delay steps, LDOS suppression, and nonequilibrium emission, indicating a single common driver rather than stacked causes.
• Thresholds and neighboring phases:
  Record thresholds and post-threshold trajectories versus drive amplitude, static bias, nonlinear coupling, and dissipation. Note hysteresis, multistability, and critical slowing down around phase boundaries.
• Cross-material/geometry robustness:
  Under changes of material (superconductor/dielectric/metal/atomic gas), geometry (plane/ring/honeycomb/superlattice), disorder level, and temperature band, phase boundaries may shift slightly but not flip direction.
• Environment and external-field dependence:
  Grade monotonic/plateau/uncorrelated trends versus temperature, pressure, magnetic field, mechanical vibration, and ionization fraction. Purely linear drifts with a single environment variable suggest exogenous artifacts.

III. How to Do It

1. Platforms and drive families:
   • Superconducting–microwave / Josephson networks: tune coupling/dissipation/disorder; measure scattering parameters (S‑parameters), group delay, and ringdown.
   • Cavity quantum electrodynamics / integrated photonics: combine high‑quality‑factor cavities, waveguides, and metamaterials; track reflection/transmission steps and spontaneous‑emission suppression.
   • Photonic/phononic metamaterials and mechanical lattices: engineer anisotropic tensors/effective permittivity/elastic moduli; scan frequency–mode–incidence angle.
   • Cold atoms / Bose–Einstein condensate analog horizons: tune interactions/potentials/flows; read out density fluctuations and correlation functions.
   • Plasma/dielectric waveguides and nonlinear optical lattices: at high fields and long‑range coupling, monitor mode blocking and channelization.
2. Unified calibration and de‑systematics:
   • Time–frequency/energy scale: lock all platforms to a single external reference, with published stability logs.
   • Geometry/medium/readout chain: unify beams/spot sizes/point spread function (PSF); correct bandpass, sidelobes, dispersion, and readout nonlinearity/dynamic range.
   • Source and thermal control: operate in a closed temperature–load loop; hold out anomalous epochs.
3. Full-parameter phase-map scanning:
   • Primary axes: drive amplitude – static bias – nonlinear coupling – dissipation – disorder – geometric scale.
   • Secondary axes: temperature – magnetic field – pressure – incidence angle – polarization – time window.
   • Co-located, co-window sampling: fix spatial sector, detection aperture, and time granularity; produce a text-labeled phase grid.
4. Dynamics and cross-validation:
   • Post-threshold dynamics: sweep frequency and duty cycle through steady-wall → breathing → channelized, recording period, duty, and phase ordering.
   • Multi-proxy concordance: co-measure transmission/reflection, group delay, ringdown, LDOS, and correlated emission to test zero-lag co-occurrence.
   • Cross-platform alignment: align boundaries at matched dimensionless parameters—normalized by noise floors, window functions, and stability metrics—to obtain an overlaid cross-platform phase map.
5. Forward prediction, blinding, arbitration:
   • Model-forward team: using coupling–dissipation–disorder–geometry and environments only, issue prediction cards (thresholds, neighboring phases, breathing expected or not).
   • Blinded measurement: run two independent cleaning paths and two distinct readout schemes in parallel.
   • Arbitration: compute hit / wrong / null rates under pre-registered rules; publish by platform/institution/method strata.

IV. Positive/Negative Controls and Artifact Removal

1. Positive controls (supporting a tensor-wall phase):
   • Zero-lag co-occurrence among high reflection, LDOS suppression, and group‑delay steps, with non-dispersion across carriers/state types.
   • Neighboring phases (breathing/channelized) follow repeatable trajectories with drive–dissipation–disorder and agree on boundary locations across platforms.
   • Switching materials/geometry yields only threshold micro‑shifts without direction flips; forward‑prediction hits exceed chance.
2. Negative controls (against a tensor-wall phase):
   • Fingerprints flip/scale with λ² or 1/ν or co-vary with bandpass/dispersion/sidelobes.
   • Significance appears only in one platform/path/readout, or is hyper‑sensitive to initialization/regularization choices.
   • Thermal phase changes, conventional nonlinear saturation, or scattering blockage reproduce all fingerprints; label swaps/time misalignment/open bypass still “detect” signals.

V. Systematics and Safeguards (Three Items)

• Readout dynamic range and nonlinear saturation: can fake reflection and group‑delay steps. Safeguard: power/gain dual scans against linearity standards with saturation hold‑outs.
• Bandpass/dispersion and sidelobe coupling: may misread frequency dependence as a non‑dispersive common term. Safeguard: inject–recover tests and band‑edge hold‑outs; unify to a common bandpass kernel and point spread function, and publish kernel uncertainty.
• Thermal/structural transitions and mechanical drift: can confuse post‑threshold neighborhoods. Safeguard: closed‑loop temperature control and structural sensing; re‑measure under cold/warm/perturbed conditions; down‑weight epochs that exceed drift thresholds.

VI. Execution and Transparency

Pre-register platform and axis lists, unified calibration/de‑systematics steps, text labels for phases, and criteria for non‑dispersion / co‑occurrence / neighboring‑phase identification, plus all positive/negative controls, exclusions, and arbitration scoring. Define held‑out parameter blocks and readouts near key boundaries for final confirmation. Enable cross‑team/platform replication by exchanging raw scattering parameters/time‑domain waveforms/emission spectra and scripts; run down‑sampling/noise/kernel‑variant/initialization‑perturbation robustness tests. Publicly release phase‑map prediction cards, phase‑grid tables, non‑dispersion and co‑occurrence summaries, and calibration/bandpass/thermal/mechanical logs, with key intermediates. This chapter cross‑checks Chapters 19 (Josephson “tensor‑wall breathing”), 25 (steady‑state Schwinger crossing and “mediator‑free” behavior), 11 (dynamic Casimir nonlinearity above threshold), and 12 (engineered vacuum in cavity quantum electrodynamics) to close a vacuum–analog–strong‑field loop.

VII. Pass/Fail Criteria

1. Support (passes):
   • Across two or more platform classes, two or more institutions, and two or more independent pipelines, recover the steady‑wall → breathing → channelized sequence with zero‑lag co‑occurring fingerprints and carrier/state non‑dispersion.
   • Phase boundaries shift mildly (materials/geometry/disorder/environment) but do not flip; forward‑prediction hits exceed chance.
   • Conclusions remain stable under bandpass/point‑spread/readout settings and across temperature bands/perturbations.
2. Refutation (fails):
   • Fingerprints follow dispersion laws or are dominated by thermal/structural transitions, and do not replicate across platforms/teams.
   • Neighboring‑phase trajectories are extremely sensitive to initialization/regularization/geometry minutiae, preventing boundary alignment.
   • Arbitration hit rates are near chance, and signals vanish in held‑out parameter blocks.