CHAMBER XXXVI — Ω-Gravity Diagnostics (UI Overhaul)

Joint Admissibility (Ajoint) · Ω-Drift · σ(Ω) · Mode A–D boundary tests · v1.3 engine behavior preserved
Mode A β 10 λ 0.10 Engine v1.3
The UI is designed to surface falsification *immediately* (A_joint + gates), not after inspection.
λ = 0.10
k = 1.0
β = 10
Ω–τ STRUCTURAL COUPLING MODES

Each mode specifies how source geometry (Σ), selection structure (Ω), and stabilizing dynamics (τ) are allowed to interact. No outcomes or expectations are implied.

Mode A — Fixed Ω Background
Σ → Ω → τ
τ evolves on a fixed Ω geometry. Ω does not respond to τ.
Demonstrates: Layer-respecting dynamics (τ admissible, Ω stationary, Joint: PASS)
Classical background
Mode B — Structurally Non-Stationary Ω
Σ → Ω ↔ τ
Ω and τ evolve simultaneously with mutual feedback. Tests whether τ can remain admissible when Ω becomes structurally unstable.
Demonstrates: τ survives but Ω coherence fails (τ admissible, Ω non-stationary, Joint: FAIL)
Non-stationary Ω / Recursive coupling
Mode C — Semiclassical Backreaction
Σ → Ω ⇢ τ
τ evolves within Ω. Ω responds slowly via accumulated τ stress.
Demonstrates: τ survives but Ω coherence fails via stress accumulation (Joint: FAIL)
Mediated coupling
Mode D — Direct Layer Violation
Σ → τ → Ω
τ rules are applied directly to Ω without mediation or selection hierarchy.
Demonstrates: True layer violation (everything collapses, Joint: FAIL)
Boundary stress test
LAYER VIEW
All
Σ Focus
Ω Focus
τ Focus
Σ Layer seed geometry
Ω Layer selector / geometry
τ Layer field dynamics
Note: β parameter controls Ω stability. In Mode B, higher β creates stronger gating of τ updates based on geometric stability.
JOINT ADMISSIBILITY VERDICT
Primary Verdict
τ-admissible
Ω-stationary
Joint: PASS/FAIL
Mode B/C: τ survives, Ω fails → Joint: FAIL. Mode A: both pass → Joint: PASS. Mode D: both fail → Joint: FAIL.
A(τ)
Ω-drift
σ(Ω)
Ω-coherence ⟨w⟩
A_joint
Step
0
Joint admissibility gates
A(τ) ≥ 0.70
Ω-drift ≤ 0.30
σ(Ω) ≤ 0.50
The three gates must all pass for joint admissibility. Mode B typically shows layer-independent τ coherence (τ-pass) with Ω non-stationarity (Ω-fail), resulting in pipeline rejection (joint-fail).
Mode B vs C Diagnostic
Ω-coherence ⟨w⟩ distinguishes coupling mechanisms:
• Mode B: Direct recursive coupling → ⟨w⟩ drops sharply as Ω destabilizes
• Mode C: Stress-mediated coupling → ⟨w⟩ decays gradually via accumulation
• Mode A/D: ⟨w⟩ stays high (A) or collapses completely (D)
Run status
Ready.
MULTI-SEED TABLE
Seed A(τ) Ω-drift σ(Ω) A_joint
Run “5 Seeds” to populate.
RUN LOG