Phase 0.7 — True Status
🧭 Phase 0.7 — True Status (No Narrative, Just Ground Truth)
✅ What Is Solidly Established
1. The solver is now numerically trustworthy
You have eliminated the classic failure modes:
- Grid convergence: N = 2000 → 4000 gives <0.1% variation
✔ Not a resolution artifact - Observer invariance: ρobs = 10 ≈ 20
✔ Not path‑length accumulation - Peak integrity: Two distinct peaks, strong second echo (~85%)
✔ Not noise or boundary ringing - Return logic fixed:
✔ No silent corruption in peak detection
Translation: The solver is no longer lying to you numerically.
2. The velocity‑floor artifact is ruled out
You explicitly checked:
- min(veff) ≈ 0.6c (mass‑on)
- min(veff) ≈ 0.4c (clean‑flow)
Nowhere near the 10⁻⁶ clamp.
Translation: No “infinite delay” wall. No fake congestion.
3. You are measuring a real, stable delay signal
- Stable Δt extraction
- Stable dimensionless quantity Ξ = Δt / (Rc/c)
- Reproducible differences between runs
Translation: The signal exists as a computational object.
⚠️ What Is NOT Yet Proven
❗ 1. The signal is still model‑induced
Your propagation law explicitly contains mass:
v_eff(ρ, M) = c (1 − α S(ρ)) (1 − β (M/M₀) / ρ)
This guarantees:
- Larger M → slower propagation
- Slower propagation → larger Δt
- Larger Δt → larger Ξ
This alone can produce smooth, converged, observer‑invariant splits without any new physics.
❗ 2. Convergence ≠ Physicality
Your system can converge perfectly and still be solving the consequences of the equation you chose.
You have proven: consistency of the model
You have NOT proven: independence from the model
❗ 3. The “Split” is expected under your current law
A localized slowdown near ρ ≈ 1, combined with mass‑dependent propagation, naturally produces nonlinear delay amplification.
This alone can explain your ~20–40% effects.
🔥 What the Recent Audits Actually Proved
What survived:
- Clean‑flow (no stalling)
- Grid doubling
- Observer shift
- Strong peak structure
What that means: The effect is robust inside the model.
What it does NOT mean: The effect is a new physical invariant.
🎯 The Final Gate (Correctly Identified)
Everything now collapses to one question:
Does the effect survive changing the functional form of the mass coupling?
| Test Type | Status |
|---|---|
| Numerical stability | ✅ PASSED |
| Boundary artifacts | ✅ PASSED |
| Velocity floor | ✅ PASSED |
| Observer invariance | ✅ PASSED |
| Peak integrity | ✅ PASSED |
| Functional independence | ❌ NOT CLEARED |
🧠 Interpreting the Multi‑Model Results
Linear / inverse‑square forms: Large, unstable divergence → artifact‑prone.
Saturating / tanh / capped forms: Small, stable residual (~3%) → the only interesting regime.
Why? No singular behavior, no runaway slowdown, yet still a measurable difference.
🧭 Your Real Current Status
You are not at “gate cleared.” You are not at “gate closed.”
You are here:
A high‑confidence numerical system testing a still‑unverified physical hypothesis.
🚫 What Not to Do Yet
- No spectral analysis
- No Phase 0.8
- No observational claims
Until functional independence is proven, all downstream analysis is meaningless.
✅ What to Do Next (Precise)
Run the decisive test:
- Fix δ = 0.05, grid = 2000 or 4000, ρobs = 10
- Compare M = 10 and 60
- Use 3–4 coupling forms:
- (1 − β M / ρ)
- (1 − β M / ρ²)
- 1 / (1 + β M / ρ)
- (1 − β tanh(M/ρ))
Compute the split ratio:
Split Ratio = Ξ₆₀ / Ξ₁₀
Decision rule:
- If all forms give similar ratios → Gate CLEARED
- If ratios vary wildly or collapse → Gate NOT CLEARED
🔚 Bottom Line
You are one test away — not from validation, but from falsification resistance.
Run the coupling‑variant comparison cleanly. Bring back Ξ₁₀ and Ξ₆₀ for each form. No interpretation.
That’s the moment where this becomes either:
- a real signal, or
- a beautifully constructed illusion.
