Glossary

Glossary

Physical objects

• BCC condensate — body-centred-cubic crystalline ground state of a Brazovskii-type order parameter $\phi(x)$. The topological background on which all TECT fields propagate.
• Brazovskii fluctuations — quasi-Goldstone modes of the BCC condensate; finite spectral gap $m^{*2}$ from broken translational symmetry to a discrete subgroup.
• Topological charge — winding number of $\phi$ around BCC defects; quantised by Pillar 5.
• $\hbar_{\rm TECT}$ — frozen-in adiabatic invariant of the BCC freeze-out, candidate origin of the Planck constant (Pillar 10 T2).

Status nomenclature (CLAUDE.md §7)

• T7 PROVED — unconditional mathematical theorem.
• T6 PROVED CONDITIONAL — theorem under named hypothesis set ${H_i}$.
• T5 CLOSED@N-LOOP — established at perturbative order $N$.
• T4 STRONG EVIDENCE — multi-line evidence, no rigorous theorem yet.
• T3 PROOF SKETCH — main logic written, technical gaps marked.
• T2 CONJECTURE — explicit hypothesis with falsification gate.
• T1 OPEN — unaddressed or in active research.
• T0 REFUTED — counter-example or audit-rollback.

Repository conventions

• Math note — atomic theory unit at note/TECT-MathNN-<descriptor>.tex.txt. Sequential numbering. Addenda: MathNN-AddA, MathNN-AddB, ….
• Theory tag — git tag annotating a Math-note acceptance milestone.
• Pillar status — canonical T-tier in status/TOE-FACT-SHEET.md, mirrored to website and to this Wiki.

Numerical objects

• *$m^{2} = 0.3138$ — Brazovskii spectral gap, Newton-Krylov solution.
• $h = 0.003$ — BCC lattice spacing in continuum-limit normalised units.
• Spectral Laplacian — $O(N \log N)$ FFT-based discretisation preserving BCC isotropy; canonical operator for all PDE solvers.