Intrinsic Compression--Information Duality and Phase Transitions in Scientific Observability (ICS)

This work introduces a structural framework connecting information-theoretic distinguishability, thermodynamic measurement cost, and intrinsic observational compression. An intrinsic compression measure (ICS) is defined to quantify the largest latent-state separation that remains observationally indistinguishable under finite measurement resources. Dual bounds are derived linking intrinsic compression and information supply, establishing a tradeoff between hidden structural variability and physically realizable distinguishability. A thermodynamic embedding is developed relating information supply to entropy production and measurement energy dissipation. The framework predicts phase-transition-like regimes in observability and proposes candidate scaling laws relating compression behavior to effective information dimension. Toy model analyses and cross-domain predictions are presented for diffusion sensing and photon-limited imaging systems. Practical estimation methods and simulation validation protocols are provided. The work is positioned as a candidate theoretical framework and research program for studying fundamental limits of scientific observability under physical resource constraints. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/