Research

47 published works · 4 software packages · 37 Zenodo DOIs. All open access.

Every paper below is available as a free PDF download. The formal papers are registered with Zenodo DOIs. The biological research corpus is published as a structured body of work within the GitHub repository. Categories flow from foundational algebra through physics, topology, biology, and validation.

Equation (C) — α⁻¹ + Sα = 4π³ + π² + π · low-energy α · standing note on this site · separate from the corpus below

Collapse Algebra — Foundations

A Formal Algebra of Collapse-Based Computation Death as the Exhaustive Veto Partition Generative Fixed Points and the Open Problems of Grothendieck Existence as Fixed Point: A Meta-Theory of Deterministic Collapse

Fine Structure Constant — From Identity to Measurement

The Fine Structure Constant as Self-Consistency Condition The Constitutional Constant: c, E=mc², and Physical Law Solving for π: Recovering Geometry from Physics Algebraic α⁻¹ Indistinguishable from Most Precise Measurement Alpha Precision: Derivation to Validation From Identity to Instrument: Algebraic α as Metrological Reference Metrological Dominoes: Algebraic α Restructures Time Precision Dominoes: From Algebraic α to G The 4.4σ Systematic: Cs Outlier Pulls Every CODATA Constant One Measurement Derives Them All: Algebraic Dimensional Structure from the Eigenvalue Tower The Fifth Link: Deriving G from the Tower Equation

Constraint Surface — Topology & Fixed Points

Oxygen as Fixed Point: Wind, Blood, and the Constraint Surface The Möbius Strip as Fixed Point of Existence Osmotic Selectivity: α to σ Klein Bottle Eigenvalue: Technetium, Parity Violation, and the Tower The Edgeless Spreadsheet: Toroidal Self-Reference Tetrahedral Zinc: The Shape of Existence The Repair Station: Weak-Force Transmutation The Samarium Shield: Promethium's Daughter and Nuclear Remediation Polynomial Descent: Elemental Coupling of the Eigenvalue Tower The Periodic Table Inside α The Observation Deck: The Zero-Loss Fixed Point of Existence Where You Exist, Inside Yourself: The Obex as Fixed Point

Gestational Biology — Mathematical Formalisations

Formal layer of the Gestational Timing Framework — week-by-week vulnerability, HIF pathway, and OPC maturation arrest mapped to mathematics. See also JJ’s Fingerprint for the personal thread on the same axis.

Pseudohypoxic Transfer: Asymmetric Boundary Passage Le Chatelier, Banach, and the Oxygen Fixed Point Lyapunov Stability Windows in Gestational Development Umbilical Channel: Information-Theoretic Constraints

Synthesis, Narrative & AI Reports

Existence as Fixed Point: A Synthesis (v2) The Story: How a Substrate Became a Theory of Everything The Null Result at Scale — 9,925 Repositories Tested R-001: Convergence Under Stochastic Load R-002: Neurotrophic Capability Baseline R-003: Extended Convergence Mapping R-004: Biological Fidelity Assessment R-005: E/I Balance Sweep Exploration R-006: Structural Forensics Sweep R-006b: Maturity-Controlled Structural Forensics R-007: Structural Age Regression (9,925 repos) Documentation Era Shift Analysis Token Economics: Three Modes of Intelligence Spend Turing Inverted: What Survives When You Remove the Human Computational Redundancy: What a Strand-Native Constant Eliminates

Software Packages

mobius-constant — PyPI mobius-number — PyPI mobius-integer — PyPI mobius-units — crates.io

Biological Research Corpus

A 46-document research corpus exploring gestational oxygen timing, OPC maturation arrest, developmental injury pathways, and clinical validation. Organised into seven streams. The integrated narrative lives on the Gestational Timing Framework page — organ windows, demand spikes, treatment convergence, and testable predictions in one view.

Synthesis Papers

Master Gestational Timing Extraction Index Gestational Impact Zones — Oxygen Demand Alignment Paper 1 — OPC Maturation Arrest and ASD Paper 2 — Multi-Organ Gestational Oxygen-Timing Paper 3 — Treatment Convergence on Oxygen-OPC Axis Paper 4 — Gestational Hypoxia and Cancer Predisposition Paper 5 — LMIC Neonatal Oxygen Natural Experiment Paper 6 — Epigenetic Biomarkers of Gestational Hypoxia Paper 7 — Maternal Triggers of Placental Anti-Angiogenic Cascade Paper 8 — SIDS as HIF-1α Autonomic Programming Failure Paper 9 — The Insular Timing Hypothesis Paper 10 — Developmental Trauma & Oxygen-Timing Convergence Paper 11 — Gestational Oxygen as Personality Variation Axis

Extension Tracks

Track 1 — Paternal Epigenetic Germline Transmission Track 2 — Colostrum as Personalised Neonatal Repair Biomarker Track 3 — Environmental Exposures & Placental Hypoxia Track 4 — Maternal Immune Activation & OPC Window Track 5 — Cord Clamping, DCC, FiO₂ & NICU Targeting Track 6 — Spiral Artery Remodelling & Trigger Taxonomy Track 7 — Preeclampsia as Mate-Pair Compatibility Phenotype

Foundational Reference

Week-by-Week HIF/Vulnerability Timeline Gestational Injury Across 10 Organ Systems PHD-VHL-FIH Counter-Regulation Machinery Core Neonatal Physiology Reference 10 Organ Systems: Peak Vulnerability Windows Unified OPC Maturation Arrest Theory

Neurodevelopmental

Resource Redistribution Hypothesis in ASD Brain Deep Dive: 5 Brain Regions & White Matter Desaturation Structured Evidence Tables: 5 Brain Areas Hippocampal White Matter and ASD Myelination Latent WMI → Language Delay Pathway Neonatal Brain Development Across 5 Areas White Matter and Social Cognition in ASD

Clinical Evidence

Regression Timing Aligned to Myelination Schedule PRISM Study Designs & Monitoring Technology Epigenetic Markers of Gestational Hypoxia in "Idiopathic" Conditions LMIC Oxygen Technology as Natural Experiment Preeclampsia → Hypoxia → ASD Pathway PE Onset Timing → Organ-Specific Outcome Mapping 11 Therapies Converging on O₂ + OPC Maturation

Validation

Adversarial Stress Test of the Unified Model Dataset Audit: Intermittent Hypoxia, DTI, Language Angelman Syndrome — HIF-1α/UBE3A Ubiquitin Severity Axis

Narrative Bridges

From Beehives to Governed Systems From Frogs to Human Biology