What I learned today

  Distinguishability Transport and Reconstruction Theory — DTRT TOC Core spine: PAIR → CARRIER → TRANSFORMATION → DISTINCTION PROFILE → SURVIVAL LAW → LOSS PROFILE → RECOVERABILITY → ADEQUATE CARRIER . PART I — FOUNDATIONAL OBJECTS 1. Probability States 1.1 Probability measures as states 1.2 Sample spaces and measurable structure 1.3 Probability law versus density representation 1.4 Support and effective support 1.5 Joint and marginal states 1.6 Conditional states 1.7 Process-valued states 1.8 Model families as sets of probability states 1.9 State equivalence 1.10 State comparison 2. Ordered Probability Pairs 2.1 (P,Q) as the primitive comparison object 2.2 Directionality of comparison 2.3 Symmetric versus asymmetric comparison 2.4 Pair equivalence 2.5 Pair orbits under transformations 2.6 Pair invariants 2.7 Pairwise distinguishability 2.8 Family-relative distinguishability 2.9 Pairwise versus multi-state comparison 2.10 Comparison without scalarization 3. Carriers 3.1 Definition...

  Kullback–Leibler Divergence: Basic Geometry and Dynamics of Probability Distributions Under Inference, Transport, Coarse-Graining, and Model Change Prologue — From Relative Entropy to a Theory of Distinguishability 0.1 Probability distributions as states of uncertainty 0.2 Comparison before distance 0.3 Why KL divergence is directional 0.4 D(P‖Q) as expected log-likelihood ratio 0.5 Distinguishability rather than geometric distance 0.6 Probability law ≠ density ≠ parameterization ≠ statistical model 0.7 Transformation of distributions as the central dynamical operation 0.8 Four basic transformation regimes: inference, transport, coarse-graining, model change 0.9 Preservation, contraction, amplification, and destruction of distinguishability 0.10 Local geometry versus global divergence 0.11 Empirical fluctuations versus dynamical trajectories 0.12 Relative entropy as the canonical empirical-measure large-deviation cost 0.13 Beyond large deviations: path ensembles, thermodynamic s...

  Kullback–Leibler Divergence: Geometry and Dynamics of Probability Distributions Under Inference, Transport, Coarse-Graining, and Model Change Prologue — KL Divergence as a Structural Object 0.1 Why KL divergence is more than a dissimilarity measure 0.2 Probability distributions as states rather than formulas 0.3 Distinguishability as the central organizing principle 0.4 Density representation ≠ probability law ≠ statistical model 0.5 Directionality: why D(P‖Q) ≠ D(Q‖P) 0.6 Local geometry versus global divergence 0.7 Inference, transport, coarse-graining, and model change as four transformation classes 0.8 KL as logarithmic discrimination cost 0.9 KL as excess coding cost 0.10 KL as large-deviation rate 0.11 KL as free-energy excess 0.12 KL as convex projection cost 0.13 KL as a bridge between probability, geometry, dynamics, and thermodynamics 0.14 When KL becomes symmetric 0.15 When KL becomes infinite 0.16 What KL forgets 0.17 What KL preserves 0.18 The central architecture: pr...

  Triadic Semantic Cloud Theory Federated Discovery Engines, Structural Descent, Carrier Invariance, and Demonstrated Discovery Table of Contents PART I — FOUNDATIONS OF TRIADIC SEMANTIC CLOUD THEORY 1. What Counts as Discovery Defines the difference between search, inference, recovery, prediction, proof, representation change, and genuine semantic discovery. 1.1 Representation versus consequential structure 1.2 Search versus discovery 1.3 Prediction versus discovery 1.4 Recovery versus discovery 1.5 Novelty versus discovery 1.6 Semantic mutation as the defining event 1.7 Discovery as a source-grounded, replay-stable change in semantic structure 2. The Sovereignty Stack Separates the layers that must not be collapsed into one another. 2.1 Source 2.2 Representation 2.3 Semantic cloud 2.4 Access 2.5 Readout 2.6 Discovery 2.7 Certification 2.8 Activation 2.9 Why authority cannot flow backward between layers 3. The Discovery Primitive Defines the operation that TSCT claims as its disti...