Book 4 · GTCT Vol IV

Dimensional Theory

The ascent from the one-dimensional fermion seed (ψ² = 0) through the contact 3-manifold and into the 5D+t arena where GTCT acts — then back down to a single, fully-proven dm³ ODE and a machine that can be poured in concrete.

20 numbered chapters · Vol IV formal core · supplements & the HVEH / G6 dossier

Ch 0How to Read This Book

0Student Edition — How to Read This Book

Part IThe Ascentseed → manifold → jet space

1The Fermion Seed 2Extended Phase Space 3The Contact 3-Manifold 4The Hypercube 5OPERA SATOR — Jet Space 6666 · The 111 Square 6½El Ojo — The Mystery That Rotates · interlude

Part IIThe HVEH Arc — Newarkfield · law · verification

7Map Newark — The Field and the Need 8Harrison — The Ordering Law Under Pressure 9Belleville — Verification and the Ladder's End

Part IIIThe Proof

10Helical Attractors on Contact 3-Manifolds

Part IVThe Arithmetic Turntoward the Riemann Hypothesis

11The Arithmetic Seed 12The Critical Contact 13The Adelic Tesseract 14The Positivity Rung 14AThe GTCT–Adelic Embedding Conjecture · companion to Ch 14 · roadmap, not a proof 15The Complex Turn 15A Virada Complexa · pt-BR

Part VThe Latticesthe operator chain across substrates

16The Crystalline Lattice 17The Magnetic Lattice 18The Seismic Lattice 19The Acoustic Lattice 20The Defect Lattice 21The Closing Field

Part VIThe Algebraic Turnwhere the ladder becomes algebraic geometry

22The Gauss Map, or What Survives the Lift 23Duality and the Discriminant 24The Bifurcation Set Is a Discriminant

Part VIIThe Selection Turnfrom what is available to what gets built

25The Selection Principle 26The Kaleidoscope Test 27The Measure That Binds 28What the Flow Pays

Vol IVFormal Core — The Orthogonality TheoremBrazil edition · pt-BR / en

0 · Prefácio (Lemniscata & Analema) 2 · O Campo Dimensional 3 · Operadores Dimensionais 4 · Teorema de Correspondência 5 · Orthogonality Theorem 6 · Teorema de Recursão 7 · Emergência como Ponto Fixo 8 · A Natureza do Tempo The Seven Axioms Appendices A–F

ExtraSupplements & Guest Lenses

Ch E · The Generative Time Circuit Ch τ · The Cosmic Tortoise Faraday · Geometry of EM Forces Hawking pela Lente GTCT Vol VI · Explicit Operator Realizations Note · The Lace Bootstrap in Intermediate Dimensions CatGT · Catalytic Generative Theory, Part I Ch E · GTCT for Everyone (alternate telling) The Ladder Polynomials · Working Note Preface · IMPA Edition — the Cajueiro and the helix The Euclidean Algorithm · the oldest algorithm, and what it measures Galperin’s Billiard · π from elastic collisions Logs Segment · log p as Root Length GOMC Opus · CatGT + Plasma

G6 LLCHVEH — Concept Portfolioapplied concepts · not planned for build

HVEH · Project Landing The Belleville / Second River Case · 365-day site HVEH + Compute · Riverside Edge Node (concept) Second River Pilot · Build Spec HALO · Investment Thesis & FEMA BCA Tri-county Site Map

Proved · kernel-checked

discriminant book21/Spiral.lean:75 Each name above is declared in this repository at the line shown and appears in an axiom report with no sorryAx. A clean axiom report is not a reading of the statement: per R20, a theorem can assume its conclusion and still report clean. Follow the link before citing one as evidence.