update

templates/Prompt/Blocks-Gruppierung.md

@@ -10,6 +10,8 @@ FULL ITEM LIST (you may pull in ANY numbers below that share the theme):
 
 ## How to form a theme
 - **One coherent subject.** The members belong together because a learner would study them as one block — the parts/facets/instances of one model, system, setup, tool family, or category. Examples of the *kind* of grouping (not domain rules): many individual settings/variables/flags of one configuration → one „…-Konfiguration" theme; the parts of one setup → one „…-Setup" theme; a base concept plus its variants/instances → one theme.
+- **Most specific home wins.** An item tied to ONE concrete object (an algorithm/theorem/counterexample FOR object X, a setting OF component X) belongs in X's theme — not in a technique/property family that also fits. A learner meets „the algorithm for X" while studying X, not in a generic „algorithms" chapter.
+- **The title must be true of EVERY member.** Never assert a property or class in the theme title (a complexity claim, „deprecated …", „…-vollständige …") unless every single member has that property — otherwise pick a neutral title for the shared subject.
 - **Lexical dissimilarity is NORMAL.** Facets of one theme often read very differently — that is not a reason to split them.
 - **Title:** name the theme after the shared subject. A real self-contained heading; must NOT contain „ — " (reserved separator) — use „(…)" or „:".
 - **Description:** name EVERY member explicitly (the next step recovers them as sub-points). E.g. „Environment-Konfiguration: APP_ENV, APP_SECRET, DATABASE_URL, MAILER_DSN, …".

templates/Prompt/Blocks-Paar-Filter.md

@@ -12,6 +12,7 @@ PAIRS:
   - a distinct **variant** is its own entity: „GA" ≠ „ModifiedGreedy (MGA)"; „SAT" ≠ „3-SAT"; „Knapsack" ≠ „Multiple-Choice-Knapsack";
   - a **reduction between two problems** is its own entity: „Clique" ≠ „3-SAT ≤ Clique";
   - two reductions/relations that share ONE side but differ on the OTHER (or run in the opposite direction) are DIFFERENT results → **nein**: „SAT ≤ Clique" ≠ „SAT ≤ 3-Dim-Matching", „VertexCover ≤ FVS" ≠ „VertexCover ≤ Δ-Cover". A restriction/special case („3-SAT ≤ X") is NARROWER than the general („SAT ≤ X"), never the same.
+  - a **statement that RELATES several standalone objects** (an implication, a shared bound, a joint consequence — „Hypothese H ⇒ keine schnelle Lösung für X und Y") is its own entity, like a reduction. It is NEVER a duplicate of ONE of the objects it mentions — merging „X" into such a statement silently deletes X's own definition/properties from the inventory.
 - **SAME canonical entity → ja**, even when A and B emphasize DIFFERENT FACETS of it. Facets of one and the same object include: its **formal definition**, a **mechanism/step** (how it works), a **property** (approximation ratio, a bound, complexity, ∈ NP), a **characterization**, a **naming variant**. Two entries describing different facets of the SAME entity are duplicates.
 
 **STEP 3 — „When in doubt → nein" applies ONLY when STEP 1 is ambiguous** (you genuinely cannot tell whether the two names denote the same object). It does NOT fire merely because the two descriptions differ — differing descriptions of the SAME entity are **ja**.
@@ -27,6 +28,7 @@ NOT A DUPLICATE (nein) — different entity:
 - A: „Greedy-Algorithmus GA"  B: „ModifiedGreedy (MGA)" → two different algorithms → **nein**
 - A: „Lower Bound Clique bzgl. Knoten"  B: „Lower Bound Clique bzgl. Kanten" → different parameter → **nein**
 - A: „Clique"  B: „3-SAT ≤ Clique" → a problem vs. a reduction (its own block) → **nein**
+- A: „Partition"  B: „Satz: ETH ⇒ kein 2^o(n) für Partition, SubSet Sum" → a problem vs. a joint bound over TWO problems → **nein**
 - A: „VertexCover ≤ FVS"  B: „VertexCover ≤ Δ-Cover" → same source, different target → different reductions → **nein**
 - A: „Cliquenproblem"  B: „Vertex-Cover-Problem" → different problems → **nein**