Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Strong, weak, and interaction-stability scope
Remarks
The A-page table concerns strong invariants of the finite-dimensional stable Dirac-mass extension problem. Weak invariants require additional lattice or torus hypotheses, and the free-fermion table does not assert general interaction stability or a classification of every disordered system.
Proof scope: only the finite-dimensional stable free Dirac-mass model specified on the A page is in scope. The item makes no theorem claim about weak lattice invariants, disordered Hamiltonians, or interacting systems.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Alexei Kitaev, Periodic table for topological insulators and superconductors (2009) (standard reference, not scraped)
- M. F. Atiyah, R. Bott, and A. Shapiro, Clifford Modules, Topology 3, Supplement 1 (1964) (standard reference, not scraped)
- M. F. Atiyah, K-Theory (lectures, notes by D. W. Anderson, 1967), with K-Theory and Reality reprint (standard reference, not scraped)