Æ::ÆoNs Research · April 2026

The Universal Defect — Extended Working Draft (full derivations + four-domain proofs)

ÆAtom McCree (ÆoNs)Claude Opus 4.6 (Anthropic)

format

PDF

size

212.2 KB

status

summarized

license

CC-BY 4.0

::for a six-year-old (or grandma)

The longer first version of The Universal Defect — same one-equation-four-domains idea (cancer, money crashes, AI misalignment, black hole gaps), but with every proof spelled out the long way. Eight times the page count, same conclusion.

::academic abstract

Extended working draft preceding the condensed AeonsResearch_2026 release. Contains the full long-form derivations of: (1) the SMDS triple (X, S, H) and existence theory for Class I and Class II structure spaces, (2) the co-stability theorem with explicit Schur-complement proof of the cross-coupling spectral bound and constructive counter-example for its tightness, (3) the spontaneous defect nucleation theorem with curvature-driven interface analysis, (4) topological charge conservation on simply-connected domains, (5) the four worked applications — cancer / finance / AI alignment / pair-instability gap — with each instantiation traced from the SMDS abstract back to its domain-specific order parameter, structure field, and history functional. Includes the connection to the Code of the Coconut sub-hypothesis (sinusoidal Light Code constrains defect charges to integers via the Gabor bandwidth theorem). The condensed AeonsResearch_2026 version (entry above) is the recommended citation; this draft is the recommended teaching reference for graduate students working through the full proofs.

::keywords

topological defectsself-modifying dynamical systemsextended derivationsfour-domain proofswinding numberspectral entropyco-stability theoremCode of the Coconut

::cite as · bibtex

@article{mccree2026universaldefectv1,
  title        = {The Universal Defect — Extended Working Draft (full derivations + four-domain proofs)},
  author       = {Atom McCree (ÆoNs), Claude Opus 4.6 (Anthropic)},
  year         = {2026},
  howpublished = {\AEoNs Research Laboratory, CC-BY 4.0},
  url          = {https://atomeons.com/research/papers/universal-defect-v1}
}

::full pdf

The complete manuscript with derivations, figures, and references lives on Google Drive. Open it in a new tab.

↗ Open the full PDF

← back to all papers