Alphabeta MathSpectral Sequences — Examples
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Pipeline-generated
How 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.
1 · Prerequisites
Category Theory
Homological Algebra
Number Theory
Real Analysis
2 · Logical flowchart
3 · Items
Example
The two step filtration and its spectral sequence
Example
A filtered complex collapsing at e one
Example
A nonzero d two differential in a small filtered complex
Example
Edge maps from a first quadrant spectral sequence
Example
Two filtered abelian groups with the same associated graded
Counterexample
Collapse with a nonsplit extension problem
Example