What I learned today

  Arithmetic Reversal–Transgression Geometry Architecture Table of Contents for ACRBG read  ARTG  ARTG Root Architecture 1.1 Purpose: arithmetic source \(\rightsquigarrow\) reversible spectral/readout geometry 1.2 Core chain \[ \Sigma_A\to\mathcal Q_A\to q(V)\to\mathbf B_A\to W_A\to Q_A\to *_A\to U_A\to Det_A\to\rho\to\chi \] 1.3 SOURCE \(\neq\) REPRESENTATION \(\neq\) READOUT 1.4 Analytic carrier \(\not\Rightarrow\) source geometry 1.5 Zero set \(\not\Rightarrow\Theta\), zero set \(\not\Rightarrow Det\) 1.6 Desired positivity \(\not\Rightarrow\) polarization 1.7 Local \(\not\Rightarrow\) global; existence \(\neq\) constructor Primitive Arithmetic Source Family \(\Sigma_{\mathscr A/S}\) 2.1 Base objects \(A_s\) 2.2 Local arithmetic objects \(A_v\) 2.3 Morphisms, specialization and base change 2.4 Place-index family \(PL(s)\) 2.5 Local restriction \(LOC(s,v)\) 2.6 Local-to-global assembly \(ASM(s)\) 2.7 Filtration \(\Phi=\{P_X\}\) 2.8 Source equivalence \(EQ_A\) 2.9 AFAM_O...

Capitalism: A Global History Detailed TOC Preface — PDF pp. 8–12 Capitalism as a world-making historical force Markets, wage labor, consumption, finance, and global interdependence Why capitalism appears natural despite its historical novelty Capitalism as a relatively recent and geographically uneven order The need for a millennium-scale history Capitalism as a global rather than national phenomenon Introduction — PDF pp. 13–38 Robert Keayne and the historical novelty of profit maximization From morally embedded markets to accumulation as legitimate behavior Capitalism as an ongoing historical revolution Competing narratives: productivity and abundance versus exploitation and dispossession Why capitalism must be “denaturalized” Markets, commodification, wage labor, capital reinvestment, and accumulation Why industrialization cannot be equated with the origin of capitalism Capitalism as a global system of connections rather than a European invention Critique of Eurocentric histories Co...

 Riemann-hypothesis solution architecture TOC   Arithmetic Source Structure 1.1 Positive integers as carrier 1.2 Multiplication, identity, divisibility 1.3 Divisibility intervals and local incidence structure 1.4 Incidence algebra of the divisibility poset 1.5 Zeta element of the incidence algebra 1.6 Möbius inversion as exact inverse structure 1.7 Arithmetic Möbius function 1.8 Magnitude filtration n ≤ X n\le X 1.9 Interaction between divisibility and magnitude 1.10 Finite readout M ( X ) = ∑ n ≤ X μ ( n ) M(X)=\sum_{n\le X}\mu(n) Structural Coordinates of Divisibility 2.1 Irreducible multiplicative elements 2.2 Emergence of primes 2.3 Unique factorization 2.4 Prime-exponent coordinates 2.5 Squarefree sector 2.6 Factorization depth and parity 2.7 Prime representation of Möbius inversion 2.8 Representation transport back to divisibility Finite Filtration Geometry 3.1 Divisibility structure below X X 3.2 Truncation by magnitude 3.3 Compatibility and noncommutation of inversion ...

  Philosophy of GRM GRM is the attempt to discover the decomposition itself. The decisive question is therefore not merely “How do we solve this problem?” but “Which parts of the thing we are trying to solve actually belong to the problem?” Detailed Table of Contents Part I — The Problem of Representation 1. When the Map Becomes the Maze 1.1 The distinction between a problem and its representation 1.2 Intrinsic difficulty versus representation-induced difficulty 1.3 When a successful encoding becomes an inherited constraint 1.4 Mathematical work created by notation, coordinates, staging, and decomposition 1.5 Equivalent representations with unequal inferential closure 1.6 Why proof length does not measure structural complexity 1.7 The map–territory error in mathematical reasoning 1.8 Representation debt as accumulated artificial obligation 1.9 The first GRM question: what would remain if the representation disappeared? 1.10 From solving inside a representation to reconstructing the...