The Four Roots of Necessity: Why a Quantity Is “Fixed” — A Census of Distinct Roots across Topology, Symmetry, Algebra, and Dimension.

From Galois to Noether — Symmetry as the Arbiter of the Possible: The Lineage of Papers 79 and 80, yet Discrete and Continuous Are Distinct Roots.

The Principle of Least Action — The Foundation Beneath the Phase-Space Trilogy (Euler), yet Not Teleology.

Why Does a Maximum Speed Exist? — The Two Relativities (Galilean and Lorentzian) and the Theorem of Ignatowski.

Time as a Renko Chart: Time as the Accumulation of Events — An Open Framework across Proper Time, Coarse-Graining, and Relational Time.

The Poincaré Recurrence Theorem and the Arrow of Time: The Microscopic Always Returns, but the Universe Ends First — The Companion to Paper 77.

Conservation Laws Are the Shadow of Symmetry: Reading Noether’s Theorem on Phase Space T*M — Why Things Are “Conserved”.

The Hidden Symmetry Unique to n=2: Why Inverse-Square Orbits Close — The Laplace–Runge–Lenz Vector and the Dynamical Twin of Paper 01.

Friction and Dissipation as Coarse-Graining: Why Energy Conserved in the Fine-Grained Appears “Lost” — The Fluctuation–Dissipation Theorem as the Brid

Liouville’s Theorem and the Arrow of Time: Fine-Grained Conservation and Coarse-Grained Growth — Closing the Arc of Paper 75 on the Hamiltonian Hinge