A Frozen Defect Network in the Dark Sector: A Consolidated, Self-Contained Account of K04 Crystallisation Debris in the Finite-QEC Substrate

Abstract

A consolidated, self-contained account of what dark matter could be in the finite-QEC substrate: not a new particle but crystallisation debris — defects left behind when the lattice ordered too quickly to heal. The June 2026 canon narrows the interpretation: this K04 fossil is a pinned, distinctive dark component and a falsification target, not the dominant mobile dark matter and not the carrier that completes the CMB third peak — that pressureless budget belongs to a separate R4 zero-mode / sterile-neutrino branch. It answers four questions a graduate scientist can follow without prior exposure to the programme. Taxonomy: using a standard topological argument, a defect is permanently locked only if it winds the system, so the smallest indestructible object is a one-dimensional string, not a point particle — every finite (local) defect can in principle heal, and explicit enumeration confirms it does. Mobility: the locked objects are extended and frozen, consistent with the separate result that such debris cannot be pushed by gravity — ruling it out as a free, collisionless particle gas but exactly what a frozen large-scale structure should do. Energy scale: the two defect tensions are computed exactly — a string costs w₄+4w₆ per lattice step, a frustrated domain wall 2w₄+12w₆ per cut cell — and, as a by-product, the cell crystal is hugely degenerate, so most domain walls cost nothing. Abundance: combining a Kibble–Zurek picture of defect formation with the above, the relic density takes the clean, falsifiable form ρ_dark ∼ (4/7) σ_wall/ξ(R), where ξ(R) is the correlation length set by the cooling rate; the fraction 4/7 — the share of domain walls that actually cost energy — is exact. The remaining unknowns reduce to two pre-existing open problems: the cooling law that fixes ξ(R), and the conversion of lattice energy units to physical units. Every numerical claim is reproduced by a short self-checking program.

Keywords

How to cite

Elliman, D. (2026). A Frozen Defect Network in the Dark Sector: A Consolidated, Self-Contained Account of K04 Crystallisation Debris in the Finite-QEC Substrate. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.20876178

@techreport{elliman2026defectnetwork,
  author      = {Elliman, David},
  title       = {A Frozen Defect Network in the Dark Sector: A Consolidated, Self-Contained Account of K04 Crystallisation Debris in the Finite-QEC Substrate},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.20876178},
  url         = {https://neusym.ai/papers/defect_network}
}