The Logic Field Information System: A Unified Coordinate Framework for Climate Stability, Memory-Kernel Dynamics, and Phase-Coupled Tipping

The Logic Field Information System is a unified coordinate framework for climate stability, built around the recognition that the climate system is a stack of nested memory reservoirs — atmosphere, ocean, soil, vegetation, cryosphere — each integrating forcing over its own characteristic time-scale and storing the low-frequency content as bound water, bound carbon, bound heat. The framework parameterises this stack through eight coordinates: a coupling strength Q, a memory time τ, a forcing gradient ∇Φ, a stochastic noise σ, a survivability functional S, a thermal anomaly δT, a Boltzmann coupling κ_B, and a kernel-deformation coordinate χ. The central object is the layer-specific memory kernel and its evolution in time; the framework's claim is that climate stability is the survivability of these kernels and that the recent surge of critical-slowing-down signatures observed across disparate Earth-system components — Amazon resilience loss, ocean heat content acceleration, AMOC trajectory, Greenland threshold approach — are co-symptoms of one underlying cause, the kernel coordinate χ rising across multiple layers in a coordinated way. Three theorems anchor the framework: a kernel-collapse bifurcation theorem establishing a critical deformation threshold χ_c for canonical memory-kernel families; a cascade theorem showing that memory loss at one reservoir layer necessarily propagates increased variability upstream; and a phase-decoupling theorem showing that ecosystems can fail through trophic timing collapse even when no individual subsystem breaches a conventional threshold. Six predictions are pre-registered for falsification testing against existing observational data products: that χ_soil should rise faster than a red-noise null in degrading regions (testable against SMAP and ESA-CCI soil-moisture records), that χ_vegetation should co-vary with χ_soil at the same spatial scale (testable against MODIS and VOD records), that trophic decoherence should appear in temperature-cued/photoperiod-cued links (testable against USA-NPN and PEP725 phenology databases), that ocean heat content variance should cascade to atmospheric variance (testable against Argo and reanalysis records), that χ-rises across multiple layers should be coordinated rather than independent, and that cueing-asymmetry magnitude should predict mismatch magnitude. The paper commits in advance to a canonical χ-estimator of the form χ_ℓ(t) = a · |∂_t log τ_ℓ| + b · |∂_t H_ℓ|, with weights chosen to give equal contribution over a ten-year reference window, so the statistic against which the predictions will be tested is fixed before any data work. The paper introduces the framework and its predictions only and does not claim empirical confirmation; the empirical operationalisation is in preparation as LFIS-2. A plain-language companion note (DOI 10.5281/zenodo.20045659) is deposited alongside this preprint.