{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OR2FBHI5H273DENAQTVEXHCD6X","short_pith_number":"pith:OR2FBHI5","canonical_record":{"source":{"id":"1203.1671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T00:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"f41904a4d7444dc50ebc70a5a67407af1e350f3f2ae0a74d430d50dc3b962d44","abstract_canon_sha256":"5f90358ce8abb30d388127d5591557ffa955fc3632980b9ff4b0dc75f26efbf9"},"schema_version":"1.0"},"canonical_sha256":"7474509d1d3ebfb191a084ea4b9c43f5d9d96acaa09e921a1fdd6092c94d9c6a","source":{"kind":"arxiv","id":"1203.1671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1671","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1671v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1671","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"OR2FBHI5H273","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OR2FBHI5H273DENA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OR2FBHI5","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OR2FBHI5H273DENAQTVEXHCD6X","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T00:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"f41904a4d7444dc50ebc70a5a67407af1e350f3f2ae0a74d430d50dc3b962d44","abstract_canon_sha256":"5f90358ce8abb30d388127d5591557ffa955fc3632980b9ff4b0dc75f26efbf9"},"schema_version":"1.0"},"canonical_sha256":"7474509d1d3ebfb191a084ea4b9c43f5d9d96acaa09e921a1fdd6092c94d9c6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:37.302380Z","signature_b64":"MZqZVvxb6D7AMD/wAIGhRl1i9uvKCCQ+PiH7NAT+ulxKS2/oG+0YyrOFC3OO58A6Cze+1POFZ9oV4/HJIwuxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7474509d1d3ebfb191a084ea4b9c43f5d9d96acaa09e921a1fdd6092c94d9c6a","last_reissued_at":"2026-05-18T04:00:37.301810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:37.301810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1671","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onL5X7MTqQTroTzp9JVCWdusE/K+CovjBGPYrg69m/pw4g25L78BSNPdb3FL++bFQg3hvnIHPD0z+z5dAvE+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:11:42.417445Z"},"content_sha256":"e1cf32574f8a07d6813a80a593859d0cdd99c8b3b8eac51ebecf782947f27836","schema_version":"1.0","event_id":"sha256:e1cf32574f8a07d6813a80a593859d0cdd99c8b3b8eac51ebecf782947f27836"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OR2FBHI5H273DENAQTVEXHCD6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge-decomposition of graphs into copies of a tree with four edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D\\'aniel Gerbner, J\\'anos Bar\\'at","submitted_at":"2012-03-08T00:42:06Z","abstract_excerpt":"We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Bar\\'at and Thomassen: for each tree $T$, there exists a natural number $k_T$ such that if $G$ is a $k_T$-edge-connected graph, and $|E(T)|$ divides $|E(G)|$, then $E(G)$ has a decomposition into copies of $T$. As one of our main results it is sufficient to prove the conjecture for bipartite graphs. Let $Y$ be the unique tree with degree sequence $(1,1,1,2,3)$. We prove that if $G$ is a 191-edge-connected graph of size divisible by 4, then $G$ has a $Y$-decom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1671","kind":"arxiv","version":1},"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":"2026-05-18T04:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+uPyfeeLk5WOMjhHNGRr4HeLYYpG+BoiQGhO5dHJmDx1JpgFY8ho6FzK9HuRZe6gmS7KIGR8L/pouMwbDP9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:11:42.417788Z"},"content_sha256":"d5b64d1a3d73a99ef010e45f30501ad76e151515e12234183f37d40bd4b1e29b","schema_version":"1.0","event_id":"sha256:d5b64d1a3d73a99ef010e45f30501ad76e151515e12234183f37d40bd4b1e29b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OR2FBHI5H273DENAQTVEXHCD6X/bundle.json","state_url":"https://pith.science/pith/OR2FBHI5H273DENAQTVEXHCD6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OR2FBHI5H273DENAQTVEXHCD6X/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":"2026-06-03T03:11:42Z","links":{"resolver":"https://pith.science/pith/OR2FBHI5H273DENAQTVEXHCD6X","bundle":"https://pith.science/pith/OR2FBHI5H273DENAQTVEXHCD6X/bundle.json","state":"https://pith.science/pith/OR2FBHI5H273DENAQTVEXHCD6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OR2FBHI5H273DENAQTVEXHCD6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OR2FBHI5H273DENAQTVEXHCD6X","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":"5f90358ce8abb30d388127d5591557ffa955fc3632980b9ff4b0dc75f26efbf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T00:42:06Z","title_canon_sha256":"f41904a4d7444dc50ebc70a5a67407af1e350f3f2ae0a74d430d50dc3b962d44"},"schema_version":"1.0","source":{"id":"1203.1671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1671","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1671v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1671","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"OR2FBHI5H273","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OR2FBHI5H273DENA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OR2FBHI5","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d5b64d1a3d73a99ef010e45f30501ad76e151515e12234183f37d40bd4b1e29b","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Bar\\'at and Thomassen: for each tree $T$, there exists a natural number $k_T$ such that if $G$ is a $k_T$-edge-connected graph, and $|E(T)|$ divides $|E(G)|$, then $E(G)$ has a decomposition into copies of $T$. As one of our main results it is sufficient to prove the conjecture for bipartite graphs. Let $Y$ be the unique tree with degree sequence $(1,1,1,2,3)$. We prove that if $G$ is a 191-edge-connected graph of size divisible by 4, then $G$ has a $Y$-decom","authors_text":"D\\'aniel Gerbner, J\\'anos Bar\\'at","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T00:42:06Z","title":"Edge-decomposition of graphs into copies of a tree with four edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1671","kind":"arxiv","version":1},"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:e1cf32574f8a07d6813a80a593859d0cdd99c8b3b8eac51ebecf782947f27836","target":"record","created_at":"2026-05-18T04:00:37Z","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":"5f90358ce8abb30d388127d5591557ffa955fc3632980b9ff4b0dc75f26efbf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-08T00:42:06Z","title_canon_sha256":"f41904a4d7444dc50ebc70a5a67407af1e350f3f2ae0a74d430d50dc3b962d44"},"schema_version":"1.0","source":{"id":"1203.1671","kind":"arxiv","version":1}},"canonical_sha256":"7474509d1d3ebfb191a084ea4b9c43f5d9d96acaa09e921a1fdd6092c94d9c6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7474509d1d3ebfb191a084ea4b9c43f5d9d96acaa09e921a1fdd6092c94d9c6a","first_computed_at":"2026-05-18T04:00:37.301810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.301810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MZqZVvxb6D7AMD/wAIGhRl1i9uvKCCQ+PiH7NAT+ulxKS2/oG+0YyrOFC3OO58A6Cze+1POFZ9oV4/HJIwuxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.302380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1cf32574f8a07d6813a80a593859d0cdd99c8b3b8eac51ebecf782947f27836","sha256:d5b64d1a3d73a99ef010e45f30501ad76e151515e12234183f37d40bd4b1e29b"],"state_sha256":"f45630c60e1519d9413868394311f47a4fdd3a39418b2e6195a25ef1bfc856fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"11tS/USCNqKvUTHdk+Pc5aILnx+ssJj8e0wmoPYbH/zqYbL2Eb/o1P5nTZbXEOp9wxn4sgJJK8wCJrkgO/yICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:11:42.419742Z","bundle_sha256":"3ede096074309a3fd74a86a3d9054a5f846ef78becc08d1e9323cd0690059357"}}