READABLE PAPER MAP · EXPERIMENTAL The Factor-Two Hardness Threshold for Vertex Cover Follow the argument. Find the definition. Check the source.
Map JSONReading aid, not a proof certificate. Solid connections record explicit references; dashed connections are inferred. A reference may provide context rather than a necessary proof step. External sources have not been retrieved.
Argument map 94 Notation 33 Checks 26
Explore a node Select a result (39 matches) Theorem 1.1 · p. 1 Corollary 1.2 · p. 1 Theorem 2.1 · p. 4 Lemma 3.1 · p. 6 Lemma 3.2 · p. 7 Proposition 3.3 · p. 7 Lemma 3.4 · p. 8 Proposition 3.5 · p. 9 Lemma 4.1 · p. 10 Lemma 5.1 · p. 12 Lemma 6.1 · p. 17 Lemma 6.2 · p. 18 Proposition 6.3 · p. 20 Lemma 7.1 · p. 21 Corollary 7.2 · p. 22 Reference [1] · p. 24 Reference [2] · p. 24 Reference [3] · p. 24 Reference [4] · p. 24 Reference [5] · p. 24 Reference [6] · p. 24 Reference [7] · p. 24 Reference [8] · p. 24 Reference [9] · p. 24 Reference [10] · p. 24 Reference [11] · p. 25 Reference [12] · p. 25 Reference [13] · p. 25 Reference [14] · p. 25 Reference [15] · p. 25 Reference [16] · p. 25 Reference [17] · p. 25 [10] Theorem 8.1 · p. 2 [5] Theorem 1.1 · p. 2 [6] Theorem 6.2 · p. 4 [4] Definition 1.1 · p. 4 [4] Theorem 1.3 · p. 4 Vertex cover and τ(G) · p. 1 Source value val(Φ) · p. 4 Theorem 2.1 → Theorem 1.1: cited-in-proof Proposition 3.3 → Theorem 1.1: cited-in-proof Proposition 3.5 → Theorem 1.1: cited-in-proof Corollary 7.2 → Theorem 1.1: cited-in-proof Vertex cover and τ(G) → Theorem 1.1: defines theorem Theorem 2.1 p. 4 proposition Proposition 3.3 p. 7 proposition Proposition 3.5 p. 9 corollary Corollary 7.2 p. 22 definition Vertex cover and τ(G) p. 1 theorem Theorem 1.1 p. 1 6 / 94 nodes · 8 connections Connections around the selected result. Drag the background to pan; zoom in for labels. Click a node to read its statement; click a connection to read the supporting passage. Solid lines: explicit references. Dashed: inferred.
All matching nodes (39) Theorem 1.1theorem · p. 1 Corollary 1.2corollary · p. 1 Theorem 2.1theorem · p. 4 Lemma 3.1lemma · p. 6 Lemma 3.2lemma · p. 7 Proposition 3.3proposition · p. 7 Lemma 3.4lemma · p. 8 Proposition 3.5proposition · p. 9 Lemma 4.1lemma · p. 10 Lemma 5.1lemma · p. 12 Lemma 6.1lemma · p. 17 Lemma 6.2lemma · p. 18 Proposition 6.3proposition · p. 20 Lemma 7.1lemma · p. 21 Corollary 7.2corollary · p. 22 Reference [1]external · p. 24 Reference [2]external · p. 24 Reference [3]external · p. 24 Reference [4]external · p. 24 Reference [5]external · p. 24 Reference [6]external · p. 24 Reference [7]external · p. 24 Reference [8]external · p. 24 Reference [9]external · p. 24 Reference [10]external · p. 24 Reference [11]external · p. 25 Reference [12]external · p. 25 Reference [13]external · p. 25 Reference [14]external · p. 25 Reference [15]external · p. 25 Reference [16]external · p. 25 Reference [17]external · p. 25 [10] Theorem 8.1external · p. 2 [5] Theorem 1.1external · p. 2 [6] Theorem 6.2external · p. 4 [4] Definition 1.1external · p. 4 [4] Theorem 1.3external · p. 4 Vertex cover and τ(G)definition · p. 1 Source value val(Φ)definition · p. 4
Browse connections around this result (8) Theorem 2.1 → Theorem 1.1cited in proof · explicit reference Proposition 3.3 → Theorem 1.1cited in proof · inferred Proposition 3.5 → Theorem 1.1cited in proof · inferred Corollary 7.2 → Theorem 1.1cited in proof · inferred Vertex cover and τ(G) → Theorem 1.1defines · agent inferred Proposition 3.3 → Theorem 1.1supports · agent inferred Proposition 3.5 → Theorem 1.1supports · agent inferred Corollary 7.2 → Theorem 1.1supports · agent inferred
AI assistantThink through the argument. Keep what helps.
READING WITH YOU Theorem 1.1 Selected statement · 25 source passages
Keep an insight Your own note Save note to this paperSave this result’s reading guide Open my paper insights → Guest insights stay in this browser, separate from signed-in accounts. Export them from My library. Chats are temporary until you save an answer.
Extraction and provenance Numbered headings, explicit cross-references, nearby proof boundaries, and candidate notation contexts. PDF text can be incomplete.
Agent-authored source-linked notes on selected results. Remaining extraction is automatic.
PDF SHA-256: 4c8faec31a1af3d0c640485e464ecedd99fb984f4a2c3b457f032685013804abreadable-paper 0.1.4 · 25 pages · 529 text blocks
Get the open-source skill