{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X2TU3P25HMCH45GGGDLMCLG4GK","short_pith_number":"pith:X2TU3P25","canonical_record":{"source":{"id":"1704.07112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-24T09:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"ca843a7865c9a96cc7d5bff7fc3fa9cf2abfd85dfa32d78e92520f96fa596c71","abstract_canon_sha256":"aa85bfdfb2de794213353b8784be9370d766237f9ca851416504e5b15d3bae2d"},"schema_version":"1.0"},"canonical_sha256":"bea74dbf5d3b047e74c630d6c12cdc32b01a159113acaf399792c4fa71f5f3bd","source":{"kind":"arxiv","id":"1704.07112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07112","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07112v1","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07112","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"X2TU3P25HMCH","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X2TU3P25HMCH45GG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X2TU3P25","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X2TU3P25HMCH45GGGDLMCLG4GK","target":"record","payload":{"canonical_record":{"source":{"id":"1704.07112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-24T09:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"ca843a7865c9a96cc7d5bff7fc3fa9cf2abfd85dfa32d78e92520f96fa596c71","abstract_canon_sha256":"aa85bfdfb2de794213353b8784be9370d766237f9ca851416504e5b15d3bae2d"},"schema_version":"1.0"},"canonical_sha256":"bea74dbf5d3b047e74c630d6c12cdc32b01a159113acaf399792c4fa71f5f3bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:53.531706Z","signature_b64":"MhlKATESBtL/ddXPqv6jmOfLJDELAih7Up8iNjNyl7NTLXJzLg0zy8gEk9leSVvW8lQ7NhZVT+u13he3Dak6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bea74dbf5d3b047e74c630d6c12cdc32b01a159113acaf399792c4fa71f5f3bd","last_reissued_at":"2026-05-18T00:45:53.531070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:53.531070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.07112","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":"2026-05-18T00:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tnh4x+HuwLUlO1tSsEWlIeR/tXmsCBQRNLShgZKe/WI9ByDsolX7slFJG9GQrd1Tk4aw8dv/QNH1ZBcedGpCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:38:40.794105Z"},"content_sha256":"4bddc06952f87a96b725fdde693ed98aa73df280ab823dc4d35e7f632a8ebd45","schema_version":"1.0","event_id":"sha256:4bddc06952f87a96b725fdde693ed98aa73df280ab823dc4d35e7f632a8ebd45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X2TU3P25HMCH45GGGDLMCLG4GK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Packing tree degree sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Changshuo Liu, Istv\\'an Mikl\\'os, Krist\\'of B\\'erczi, Zolt\\'an Kir\\'aly","submitted_at":"2017-04-24T09:42:18Z","abstract_excerpt":"We consider special cases of the two tree degree sequences problem. We show that if two tree degree sequences do not have common leaves then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove that two tree degree sequences always have edge-disjoint realizations if each vertex is a leaf in at least one of the trees. This theorem can be extended to more trees: we show that the edge packing problem is in P for an arbitrary number of tree sequences with the property that each vertex is a non-leaf in at most one of the trees.\n  We also consider the fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07112","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":"2026-05-18T00:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rZJ0AHDiXMLFyU17e+rDApAjL2AAVuO42AwAbTpR831Xsg6U6vqRi2QMheHnt6YPskB6s00gbu7FB14DnH9sAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:38:40.794817Z"},"content_sha256":"e2542a6d250ca206c010493b970ea7d38cfa5f51b638a894986732d7d14d9fe9","schema_version":"1.0","event_id":"sha256:e2542a6d250ca206c010493b970ea7d38cfa5f51b638a894986732d7d14d9fe9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2TU3P25HMCH45GGGDLMCLG4GK/bundle.json","state_url":"https://pith.science/pith/X2TU3P25HMCH45GGGDLMCLG4GK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2TU3P25HMCH45GGGDLMCLG4GK/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":"2026-06-09T05:38:40Z","links":{"resolver":"https://pith.science/pith/X2TU3P25HMCH45GGGDLMCLG4GK","bundle":"https://pith.science/pith/X2TU3P25HMCH45GGGDLMCLG4GK/bundle.json","state":"https://pith.science/pith/X2TU3P25HMCH45GGGDLMCLG4GK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2TU3P25HMCH45GGGDLMCLG4GK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X2TU3P25HMCH45GGGDLMCLG4GK","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":"aa85bfdfb2de794213353b8784be9370d766237f9ca851416504e5b15d3bae2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-24T09:42:18Z","title_canon_sha256":"ca843a7865c9a96cc7d5bff7fc3fa9cf2abfd85dfa32d78e92520f96fa596c71"},"schema_version":"1.0","source":{"id":"1704.07112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07112","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07112v1","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07112","created_at":"2026-05-18T00:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"X2TU3P25HMCH","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X2TU3P25HMCH45GG","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X2TU3P25","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:e2542a6d250ca206c010493b970ea7d38cfa5f51b638a894986732d7d14d9fe9","target":"graph","created_at":"2026-05-18T00:45:53Z","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 consider special cases of the two tree degree sequences problem. We show that if two tree degree sequences do not have common leaves then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove that two tree degree sequences always have edge-disjoint realizations if each vertex is a leaf in at least one of the trees. This theorem can be extended to more trees: we show that the edge packing problem is in P for an arbitrary number of tree sequences with the property that each vertex is a non-leaf in at most one of the trees.\n  We also consider the fo","authors_text":"Changshuo Liu, Istv\\'an Mikl\\'os, Krist\\'of B\\'erczi, Zolt\\'an Kir\\'aly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-24T09:42:18Z","title":"Packing tree degree sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07112","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":"sha256:4bddc06952f87a96b725fdde693ed98aa73df280ab823dc4d35e7f632a8ebd45","target":"record","created_at":"2026-05-18T00:45:53Z","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":"aa85bfdfb2de794213353b8784be9370d766237f9ca851416504e5b15d3bae2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-24T09:42:18Z","title_canon_sha256":"ca843a7865c9a96cc7d5bff7fc3fa9cf2abfd85dfa32d78e92520f96fa596c71"},"schema_version":"1.0","source":{"id":"1704.07112","kind":"arxiv","version":1}},"canonical_sha256":"bea74dbf5d3b047e74c630d6c12cdc32b01a159113acaf399792c4fa71f5f3bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bea74dbf5d3b047e74c630d6c12cdc32b01a159113acaf399792c4fa71f5f3bd","first_computed_at":"2026-05-18T00:45:53.531070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:53.531070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MhlKATESBtL/ddXPqv6jmOfLJDELAih7Up8iNjNyl7NTLXJzLg0zy8gEk9leSVvW8lQ7NhZVT+u13he3Dak6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:53.531706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bddc06952f87a96b725fdde693ed98aa73df280ab823dc4d35e7f632a8ebd45","sha256:e2542a6d250ca206c010493b970ea7d38cfa5f51b638a894986732d7d14d9fe9"],"state_sha256":"6a187a1fd9395e955dfc51a4c813ec6c30a7123ece11f6269d7d93155a5e6641"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0MCWcTaveMG4k19AzlhiRSrRXi/zjyKdjJcvq6HEaCt061viqOvpJwEjEeBvn0PU3Ry1t4DuhJW7ETSV4SmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:38:40.799415Z","bundle_sha256":"e5cceddfa710b3fd01bd70cc34efcd6c320ebd30ba365066c06d547cb9e0ba2a"}}