Technical Notes

This website presents a conceptual model. The documents below are independent mathematical explorations inspired by the ideas described here. They are not part of the main theory and do not represent a validated physical model. Their purpose is to show how the conceptual framework could be formalised mathematically.

1. Membrane Curvature Model — First Mathematical Formulation v1.1

A concise 5‑page technical note that translates the gravity-first DMET concept into a testable weak-field model. It develops:

• a nonlinear curvature equation sourced by observed baryonic matter
• flat galaxy rotation curves and the baryonic Tully–Fisher relation
• a provisional link between the galactic acceleration scale and the larger geometric/tensional sector
• the distinction between established AQUAL mathematics and the specifically DMET interpretation
• a separate boundary-optics section explaining why lensing and cross-region redshift are distinct effects
• the relativistic frequency relation required for any proposed boundary-origin JWST source
• clear empirical tests and limits of the short formulation

This document is the simplest mathematical entry point to the theory. It does not claim that the displayed equation has yet been derived from a complete membrane action.

📄 Download: Membrane Curvature Model v1.1 (5 pages)

Permanent Zenodo record: DOI 10.5281/zenodo.22177538

2. Membrane Curvature Theory — Candidate Mathematical Framework v0.3

A revised 11‑page framework that carries the same gravity-first logic into relativistic and cosmological tests. It includes:

• the weak-field galaxy model and its relativistic requirements
• five-dimensional / brane-inspired geometric equations as a candidate framework
• gravitational lensing from the same geometry used for galaxy dynamics
• tidal curvature, geodesic deviation, and the distinction between uniform pull and expansion
• the Raychaudhuri equation and the need for an effective stress/curvature contribution capable of acceleration
• directional expansion and observational constraints
• boundary optics and an explicit cross-region redshift calculation based on the photon path, emitter, boundary and observer
• spectral, time-dilation, flux and photon-transfer requirements for the neighbouring-region/JWST extension
• explicit failure criteria separating the core model from the speculative boundary hypothesis

This document is not a completed theory of gravity. It is a candidate mathematical research programme designed to expose the assumptions DMET must eventually derive, calculate, and test.

📄 Download: Membrane Curvature Theory v0.3 (11 pages)

Permanent Zenodo record: DOI 10.5281/zenodo.22177645

Status

These documents are exploratory mathematical realisations of the conceptual idea. They should not be interpreted as established physics. The present development goal is narrower: derive a curvature law that predicts galaxy dynamics and lensing from baryonic matter, then test whether a consistent relativistic extension can also describe structure growth and cosmic expansion.

Website Version 1.4 — August 2026