Grouped research library

Orientation pages that explain the public site, current status, and canon boundary.

• Curated research library Note

  Organizes the currently selected packets from APO core, the Navier-Stokes undecidability track, the Riemann Hypothesis track, and proof-supporting code.

• Project Dashboard Status

  A compact status page for active tracks, proof packets, verification work, and next review targets.

• APO master index Canon link

  Links the canonical APO master index to the curated APO, NS, and RH site selections.

Core APO selections, canonical entry links, proof PDFs, and supporting derivation scripts.

• APO core selections Overview

  Links the canonical master index, selected PDFs, and proof-support scripts without duplicating the canon wholesale.

• APO Einstein-derivation scripts Code

  Surfaces relevant APO Python helpers as downloadable public artifacts rather than hiding them in the research repo.

• APO master paper Paper

  Wraps the primary APO master paper PDF in a note page with context and links into the rest of the site.

• APO spectral-collapse paper Paper

  Provides a site page for the spectral-collapse proof PDF and links it back into the APO core chain.

The public seven-paper Navier-Stokes sequence and its track overview.

• Navier-Stokes pedagogical overview Overview

  Explains how the ergodic and FTLE layer frames the Navier-Stokes undecidability stack.

• Navier-Stokes paper stack Paper

  Presents the entire NS selection as a coherent sequence while keeping the public page readable and navigable.

• NS paper 1 — independence Paper

  Opens the seven-paper sequence with the independence result.

• NS paper 2 — K-inside-B companion Paper

  Companion note for the K-inside-B step in the seven-paper NS sequence.

• NS paper 3 — forward profile universality Paper

  Presents the forward-profile universality paper from the NS sequence.

• NS paper 4 — ergodic connection Paper

  Frames the ergodic-theoretic connection to the wider NS undecidability program.

• NS paper 5 — ergodic FIM theory Paper

  Continues the NS line through the information-geometric ergodic layer.

• NS paper 6 — Tao cascade resolution Paper

  Carries the NS stack into the Tao-cascade resolution layer.

• NS paper 7 — I-prime exclusion Paper

  Final paper in the current seven-paper NS sequence.

RH proof papers, Lean verification notes, pedagogical summaries, and numerical scripts.

• RH proof structure Overview

  Organizes the RH-facing chain across arithmetic/Fisher foundations, spectral triples, numerical checks, and remaining gaps.

• Formal Verification Breakthrough: Riemann Zeta Schwarz Reflection Verification

  Successfully established the formal proof of Λ(s̄) = Λ̄(s) in Lean 4, resolving long-standing notation mismatches and establishing a pristine structural foundation for the APO RH proof chain.

• Pedagogical Breakdown: APO Theory & Lean Proofs Note

  Provides a verbose, pedagogical explanation of the APO theoretical framework (Paper I) and the five layers of the machine-checked proofs achieved in the April 2026 verification session.

• RH paper 1 — arithmetic APO route Paper

  Opens the public RH set with the arithmetic APO paper.

• RH paper 2 — arithmetic spectral triple Paper

  Highlights the spectral-triple framing of the RH program.

• RH paper 3 — parsimony Paper

  Exposes the parsimony paper as part of the RH publishing set.

• RH paper 4 — Solomonoff compactification Paper

  Pairs the Solomonoff-facing paper with the downloadable numerical verification scripts.

• RH verification scripts Code

  Surfaces concrete numerical and operator-comparison scripts alongside the RH papers.

• Riemann Hypothesis selections Overview

  Exposes the strongest current RH-facing public materials without turning the site into a full duplicate of the source track.

Reader-friendly bundles that collect related PDFs, code, and context into a single doorway.

• APO core packet Packet

  Collects the core canon entry point, the master paper PDF, the spectral proof PDF, and two APO gravity-derivation Python helpers.

• Navier-Stokes packet Packet

  Surfaces the seven-paper Navier-Stokes sequence as a coherent packet, with the first paper embedded and the rest linked as a set.

• Proof-supporting code Code

  Exposes a small number of Python helpers that clarify derivation steps and numerical checks in APO and RH.

• Riemann Hypothesis packet Packet

  Exposes the RH proof-structure markdown, the arithmetic/spectral papers, the Solomonoff paper, and the strongest supporting Python verification scripts.

Process notes and non-canonical demonstrations of the site mechanics.

• The Epistemic Machine: Reasoning as Cognitive Sovereignty Workflow

  How the Epistemic Machine treats reasoning as a repeatable truth-testing practice: coherence, evidence, anomaly pressure, and human ownership of conclusions.

• The Expert Interrogations: Stress-Testing APO Against Its Strongest Critics Workflow

  A dialogue-style stress test of the Axioms of Pattern Ontology: six expert personas press APO on syntax, continua, spin, gauge groups, Lorentzian geometry, Born probabilities, Landauer cost, Kolmogorov complexity, Bell nonlocality, and first cause.

• Agentic Workflow Workflow