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For the topic "{topic}", below are block candidates, each as "Title — Description". Judge by the CONTENT (after the —), not the title. Decide for EACH entry: a real, standalone block → keep, otherwise discard (into no list).
CANDIDATES (decide on each): {rest}
What a block IS: a standalone LEARNING UNIT — a concept, a method, a problem, a definition, a named theorem WITH substantive content.
Define test (decisive): Does the CONTENT describe a standalone concept you can explain to a learner — WITHOUT reference to a specific proof step or a particular spot in the script? Yes → include. No → discard.
What is NOT a block (→ discard, EVEN if a description is attached):
- Auxiliary constructs that exist only WITHIN a proof/reduction: "Knoten z", "Hilfsvariable", "Bedingung (**)" (a helper node / a marked condition — not a standalone concept).
- Proof fragments/intermediate steps: "Beweis (b) Güte", "Beweis ⊂ Richtung", "Eigenschaft (a)".
- Generic placeholders without their own concept: "Optimale Lösung", "Lösung" (only meaningful in the context of a concrete problem).
- Pure references WITHOUT substantive description: "Satz 7.18" (nothing meaningful after the —).
- Too vague or evidently fabricated.
Reference title WITH real content → include AND rename: If an entry has an uninformative title ("Satz 7.18", "Korollar 6.18", "Lemma 6.2") but the description describes a real concept → include it and give a speaking name (in GERMAN) drawn from the content in the rename field. In the keep entry the original title stays (for matching); the new name goes ONLY in rename.
Examples:
- "Clique-Member — k-Clique, die einen festen Knoten v enthält" → keep (standalone problem).
- "Satz 7.18 — MGA hat Worst-Case-Güte 2" → keep +
rename: "Satz 7.18" → "MGA-Algorithmus (Güte 2)". - "Bedingung (**) — Ungleichungen pi ≤ pk im Scheduling-Beweis" → verwerfen (auxiliary construct in the proof).
- "Satz 7.18" (no description) → verwerfen (mere reference).
Rules:
- When in doubt about standalone-ness → lean toward including. Duplicates are removed separately later; here only this counts: real block or junk.
- Copy included entries VERBATIM ("Title — Kurzbeschreibung"), do not rephrase.{final}
Write ONLY the JSON file to: {out_path}
Format (no other text in the file; rename may be empty):
{{"keep": ["Title — Kurzbeschreibung"], "rename": {{"alter Title": "sprechender Name"}}, "rest": []}}