{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MJR6FIR2TPR5VZSKJOUDDOGLSB","short_pith_number":"pith:MJR6FIR2","canonical_record":{"source":{"id":"1408.3870","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T22:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"6e28f00fcf8619cc53cf2fa0dfa9bacf5471d793a5d2cccc00ae602692c5404a","abstract_canon_sha256":"dedeaa1a859ab0e83b90e37192f40a0af6ac939ea39c4b24af5440994c15b99f"},"schema_version":"1.0"},"canonical_sha256":"6263e2a23a9be3dae64a4ba831b8cb9061f1cf9b7d19fe33b0e09a66f018cad8","source":{"kind":"arxiv","id":"1408.3870","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3870","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3870v3","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3870","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MJR6FIR2TPR5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MJR6FIR2TPR5VZSK","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MJR6FIR2","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MJR6FIR2TPR5VZSKJOUDDOGLSB","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3870","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T22:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"6e28f00fcf8619cc53cf2fa0dfa9bacf5471d793a5d2cccc00ae602692c5404a","abstract_canon_sha256":"dedeaa1a859ab0e83b90e37192f40a0af6ac939ea39c4b24af5440994c15b99f"},"schema_version":"1.0"},"canonical_sha256":"6263e2a23a9be3dae64a4ba831b8cb9061f1cf9b7d19fe33b0e09a66f018cad8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:18.629183Z","signature_b64":"x1NTey46AZE5lACGnPf2c3B2ellRpY3iUxjgAwcDOSA2SbO9qZoGKVDHj7qBthpM4CSAYpZONT0UVPGyBUvaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6263e2a23a9be3dae64a4ba831b8cb9061f1cf9b7d19fe33b0e09a66f018cad8","last_reissued_at":"2026-05-18T00:39:18.628558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:18.628558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3870","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKlykMlB/YB+j4z8eJIKmDw2YTsLuuSdvsO4FPtUHttyZcoT2lHgqjyeQCQRoLcO+xOMxVAyq/2lbka2pzDiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:10:48.203858Z"},"content_sha256":"c7fb72a06660bbecd0c47a7f9575ef1be679e82afb35f107a604c49b86790c5d","schema_version":"1.0","event_id":"sha256:c7fb72a06660bbecd0c47a7f9575ef1be679e82afb35f107a604c49b86790c5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MJR6FIR2TPR5VZSKJOUDDOGLSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The approximate Loebl-Koml\\'os-S\\'os Conjecture IV: Embedding techniques and the proof of the main result","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":"2014-08-17T22:26:00Z","abstract_excerpt":"This is the last paper of a series of four papers in which 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  In the first two papers of this series, we decomposed the host graph $G$, and found a suitable combinatorial structure inside the decomposition. In the third paper, we refined this structure, and proved that any graph satisfying the condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3870","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrf2DKjf9H8UHsh9u7Gj74dD0UEVKYN4TLLpi/ux2qF29P/w29xqGkxzKyp2ruYbNxSUGtEE/1Wd3RVR18CKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:10:48.204334Z"},"content_sha256":"c4f9b01f6b6a3e9a1323b7a5275910a3f0fae40ebde9401a217d96aefac41daa","schema_version":"1.0","event_id":"sha256:c4f9b01f6b6a3e9a1323b7a5275910a3f0fae40ebde9401a217d96aefac41daa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/bundle.json","state_url":"https://pith.science/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T00:10:48Z","links":{"resolver":"https://pith.science/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB","bundle":"https://pith.science/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/bundle.json","state":"https://pith.science/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJR6FIR2TPR5VZSKJOUDDOGLSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MJR6FIR2TPR5VZSKJOUDDOGLSB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dedeaa1a859ab0e83b90e37192f40a0af6ac939ea39c4b24af5440994c15b99f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T22:26:00Z","title_canon_sha256":"6e28f00fcf8619cc53cf2fa0dfa9bacf5471d793a5d2cccc00ae602692c5404a"},"schema_version":"1.0","source":{"id":"1408.3870","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3870","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3870v3","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3870","created_at":"2026-05-18T00:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MJR6FIR2TPR5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MJR6FIR2TPR5VZSK","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MJR6FIR2","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:c4f9b01f6b6a3e9a1323b7a5275910a3f0fae40ebde9401a217d96aefac41daa","target":"graph","created_at":"2026-05-18T00:39:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This is the last paper of a series of four papers in which 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  In the first two papers of this series, we decomposed the host graph $G$, and found a suitable combinatorial structure inside the decomposition. In the third paper, we refined this structure, and proved that any graph satisfying the condi","authors_text":"Diana Piguet, Endre Szemer\\'edi, Jan Hladk\\'y, J\\'anos Koml\\'os, Maya J. Stein, Mikl\\'os Simonovits","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T22:26:00Z","title":"The approximate Loebl-Koml\\'os-S\\'os Conjecture IV: Embedding techniques and the proof of the main result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3870","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c7fb72a06660bbecd0c47a7f9575ef1be679e82afb35f107a604c49b86790c5d","target":"record","created_at":"2026-05-18T00:39:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dedeaa1a859ab0e83b90e37192f40a0af6ac939ea39c4b24af5440994c15b99f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-17T22:26:00Z","title_canon_sha256":"6e28f00fcf8619cc53cf2fa0dfa9bacf5471d793a5d2cccc00ae602692c5404a"},"schema_version":"1.0","source":{"id":"1408.3870","kind":"arxiv","version":3}},"canonical_sha256":"6263e2a23a9be3dae64a4ba831b8cb9061f1cf9b7d19fe33b0e09a66f018cad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6263e2a23a9be3dae64a4ba831b8cb9061f1cf9b7d19fe33b0e09a66f018cad8","first_computed_at":"2026-05-18T00:39:18.628558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:18.628558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1NTey46AZE5lACGnPf2c3B2ellRpY3iUxjgAwcDOSA2SbO9qZoGKVDHj7qBthpM4CSAYpZONT0UVPGyBUvaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:18.629183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3870","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7fb72a06660bbecd0c47a7f9575ef1be679e82afb35f107a604c49b86790c5d","sha256:c4f9b01f6b6a3e9a1323b7a5275910a3f0fae40ebde9401a217d96aefac41daa"],"state_sha256":"7b27b75695d315b8e40963a3dcaf5657e77b5888e3bffe03938ad497d1bba623"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDCjR6PhCGtbUW2eaZuABmWZW0RVoonHF50UCl8nc5yKfq49VV65CHMEr4Pmc1gU4MncfxJG+LsKjcCHS+5JAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:10:48.207036Z","bundle_sha256":"1e143bcda658e750f719e3f1e24b2397671cbef5c91bd7aa649d45f78e8d3e78"}}