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.
Hadamard three-lines and complex interpolation
The normalization in Hadamard three-lines theorem is the scalar mechanism behind complex interpolation arguments. One builds a bounded holomorphic scalar function on a strip, estimates its two boundary lines, and lets the three-lines inequality interpolate the interior exponent. Turning that mechanism into an operator interpolation theorem requires additional normed-space and duality hypotheses; no such operator theorem is asserted here.
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Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
11 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
- J. A. Tropp, Matrix Analysis, Lecture 7, §7.3 (standard reference, not scraped)