🌐 Geodetic Codex V9.5

🔍 Objectives

• Resolve trough ↔ counterweight pairings at corridor, basin, and global scales.
• Estimate symmetry (S), time lag (τ), and coupling strength (κ) for each pair.
• Produce a Balance Score used to modulate forecast intensity in V9.7.

🧠 Key Concepts

• Mass/torque complementarity: lithospheric deficits balanced by distant surpluses.
• Hemispheric seesaws: N↔S handoffs tracked by cap dominance (from dataset).
• Memory repair: symmetry recovers following cryosphere pulses & rebound.

📦 Data Inputs

• Geoid/gravity anomalies (Bouguer, satellite), heat-flow, topography/bathymetry, crustal thickness.
• Seismicity & focal mechanisms, GNSS strain, GIA fields, uplift/subsidence time series.
• V9 dataset fields: epoch/cycle, cap dominance, rift (−), counterweight (+), meltwater vectors, VGP ties.
• V3 geodesic mesh & corridors; V9.4 ranked node set.

🧪 Methods

1. Pairing: for each trough center, search great-circle corridors for candidate uplifts (within angular windows); minimize cost by distance, corridor alignment, and anomaly sign.
2. Signal normalization: z-score geoid/heat-flow/topo and construct composite A− / A+ indices.
3. Symmetry index (S): S = 1 − |A− − A+| / (|A−| + |A+| + ε) (0=asymmetric, 1=balanced)
4. Lag (τ): time of peak cross-correlation between paired anomaly time series (positive = counterweight follows).
5. Coupling (κ): coherence of derivatives (dA/dt) with sign-corrected phase agreement (0–1).
6. Balance score: B = wS·S + wK·κ − wT·|τ|/τref (clipped to 0–1).
7. Bootstrap & CV: resample epochs and corridors to estimate uncertainty σ_B.

🧮 Practical Defaults

• Angular search window: 40° along-corrridor / 25° cross-corridor; great-circle sampling Δ=0.25°.
• τ window: ±200 kyr (late Cenozoic); ±5–10 Myr for Mesozoic deep-time panels.
• Weights: wS=0.5, wK=0.35, wT=0.15, τref set by epoch bin.

🗺️ Figures

• Chord map: troughs (−) ↔ counterweights (+) with link opacity ∝ B.
• Lag histograms per epoch; hemisphere seesaw timelines with cap dominance overlay.
• Corridor panels showing paired anomaly time series and cross-correlograms.

✅ Outputs

• pairs.csv — id_minus,id_plus,epoch,S,kappa,lag_kyr,B,sigma_B,corridor,hemisphere
• pairs.geojson — FeatureCollection with great-circle links and node properties.
• balance_summary.json — per-corridor & global stats for V9.7 throttling.

🧰 Minimal Schema (pairs.csv)

id_minus,id_plus,epoch_kya,S,kappa,lag_kyr,B,sigma_B,corridor,notes
AMZ_TRGH_01,AND_UPLF_02,120,0.76,0.62,18,0.69,0.08,72.66W,"seesaw N→S; strong meltwater vector"

🔧 QA & Sensitivity

• Shuffle controls: randomize pairings within corridors → expect S, κ to collapse toward 0.
• Leave-one-sensor-out (geoid/heat-flow/topo) to test metric robustness.
• Weight sweep (wS,wK,wT) to bracket B; report σ_B and stable ranges.

🔗 Integration

• V9.4: multiply each node’s Multiplier by the local B (or corridor mean B).
• V9.7: catastrophe windows prioritize nodes in low-B regions (unstable symmetry) during aligned forcing.
• V9.8: export pair classes (e.g., rift–orogen, back-arc–superswell) for analogue-planet testing.

📚 References (to stage)

• Global gravity/geoid & heat-flow datasets; GIA/uplift models; plate boundary & crustal thickness grids.