{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CFFQ7NB5YDFVNZJK6GFSTATIL6","short_pith_number":"pith:CFFQ7NB5","schema_version":"1.0","canonical_sha256":"114b0fb43dc0cb56e52af18b2982685fafbdde453c8f5d23768fe8d981266380","source":{"kind":"arxiv","id":"1408.3858","version":3},"attestation_state":"computed","paper":{"title":"The approximate Loebl-Koml\\'os-S\\'os Conjecture I: The sparse decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Diana Piguet, Endre Szemer\\'edi, Jan Hladk\\'y, J\\'anos Koml\\'os, Maya J. Stein, Mikl\\'os Simonovits","submitted_at":"2014-08-17T21:02:52Z","abstract_excerpt":"In a series of four papers we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every $\\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$ every $n$-vertex graph $G$ with at least $(\\frac12+\\alpha)n$ vertices of degree at least $(1+\\alpha)k$ contains each tree $T$ of order $k$ as a subgraph.\n  The method to prove our result follows a strategy similar to approaches that employ the Szemer\\'edi regularity lemma: we decompose the graph $G$, find a suitable combinatorial structure inside the decomposition, and then embed the tree $T$ into $G$ using this structure."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.3858","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T21:02:52Z","cross_cats_sorted":[],"title_canon_sha256":"f74d2c2e57c69f6a34b4fc1752c8f60e8777139dac0910042fd825d9da400871","abstract_canon_sha256":"a92d91f82b6d38aa80c88b19ddcca0a6cf54d5b6f1885a17eb5912a21889772f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:18.647035Z","signature_b64":"iizHPVkPScKZlW/qkZX/F+LPWGPg8xVlntyfc2z2StTtSRlUZ+oIfmWlPDkIbt9K/XD5AJD7UwFSgXFDdnstDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"114b0fb43dc0cb56e52af18b2982685fafbdde453c8f5d23768fe8d981266380","last_reissued_at":"2026-05-18T00:39:18.646412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:18.646412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The approximate Loebl-Koml\\'os-S\\'os Conjecture I: The sparse decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Diana Piguet, Endre Szemer\\'edi, Jan Hladk\\'y, J\\'anos Koml\\'os, Maya J. Stein, Mikl\\'os Simonovits","submitted_at":"2014-08-17T21:02:52Z","abstract_excerpt":"In a series of four papers we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every $\\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$ every $n$-vertex graph $G$ with at least $(\\frac12+\\alpha)n$ vertices of degree at least $(1+\\alpha)k$ contains each tree $T$ of order $k$ as a subgraph.\n  The method to prove our result follows a strategy similar to approaches that employ the Szemer\\'edi regularity lemma: we decompose the graph $G$, find a suitable combinatorial structure inside the decomposition, and then embed the tree $T$ into $G$ using this structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3858","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.3858","created_at":"2026-05-18T00:39:18.646509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3858v3","created_at":"2026-05-18T00:39:18.646509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3858","created_at":"2026-05-18T00:39:18.646509+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFFQ7NB5YDFV","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFFQ7NB5YDFVNZJK","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFFQ7NB5","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6","json":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6.json","graph_json":"https://pith.science/api/pith-number/CFFQ7NB5YDFVNZJK6GFSTATIL6/graph.json","events_json":"https://pith.science/api/pith-number/CFFQ7NB5YDFVNZJK6GFSTATIL6/events.json","paper":"https://pith.science/paper/CFFQ7NB5"},"agent_actions":{"view_html":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6","download_json":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6.json","view_paper":"https://pith.science/paper/CFFQ7NB5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3858&json=true","fetch_graph":"https://pith.science/api/pith-number/CFFQ7NB5YDFVNZJK6GFSTATIL6/graph.json","fetch_events":"https://pith.science/api/pith-number/CFFQ7NB5YDFVNZJK6GFSTATIL6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6/action/storage_attestation","attest_author":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6/action/author_attestation","sign_citation":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6/action/citation_signature","submit_replication":"https://pith.science/pith/CFFQ7NB5YDFVNZJK6GFSTATIL6/action/replication_record"}},"created_at":"2026-05-18T00:39:18.646509+00:00","updated_at":"2026-05-18T00:39:18.646509+00:00"}