{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EBWR7F5UADVPJ52OWP7NO6A4C4","short_pith_number":"pith:EBWR7F5U","canonical_record":{"source":{"id":"1508.05424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-21T22:03:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1b082ca2d609ed264deeee1defb7db508e201f52258e39e402929e1ad8a31af5","abstract_canon_sha256":"28caf9e603dac15d319c16debdba523bb8927b6ed4ef262cc373740afd7118dc"},"schema_version":"1.0"},"canonical_sha256":"206d1f97b400eaf4f74eb3fed7781c170c5b15aa1a7eae83b4ed992691f63c39","source":{"kind":"arxiv","id":"1508.05424","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05424","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05424v2","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05424","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"EBWR7F5UADVP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EBWR7F5UADVPJ52O","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EBWR7F5U","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EBWR7F5UADVPJ52OWP7NO6A4C4","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-21T22:03:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1b082ca2d609ed264deeee1defb7db508e201f52258e39e402929e1ad8a31af5","abstract_canon_sha256":"28caf9e603dac15d319c16debdba523bb8927b6ed4ef262cc373740afd7118dc"},"schema_version":"1.0"},"canonical_sha256":"206d1f97b400eaf4f74eb3fed7781c170c5b15aa1a7eae83b4ed992691f63c39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:46.706783Z","signature_b64":"ywDdpZ7M1THcx+DzHb4s69NDnG1TO/Xfwsjun/qG6nXIxs7TjR95qzlSLDQcpF0lH9JI4ZyJRrwxJ1ht50x6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"206d1f97b400eaf4f74eb3fed7781c170c5b15aa1a7eae83b4ed992691f63c39","last_reissued_at":"2026-05-18T00:41:46.706254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:46.706254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05424","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDitaRlGsq/WNwxrVheqVZX6W+yTVySAoZWUsdizFs0+76BZQ2wWPtn8FoUZnJ5oT8saC8d+7Au8cX73J4AdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:17:27.530542Z"},"content_sha256":"0c3d5cd711be8093993c5cb872ef9ba19fd44e65be4d4c20bb929b04b100bcc6","schema_version":"1.0","event_id":"sha256:0c3d5cd711be8093993c5cb872ef9ba19fd44e65be4d4c20bb929b04b100bcc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EBWR7F5UADVPJ52OWP7NO6A4C4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reticulation-visible networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Charles Semple, Magnus Bordewich","submitted_at":"2015-08-21T22:03:35Z","abstract_excerpt":"Let $X$ be a finite set, $\\mathcal N$ be a reticulation-visible network on $X$, and $\\mathcal T$ be a rooted binary phylogenetic tree. We show that there is a polynomial-time algorithm for deciding whether or not $\\mathcal N$ displays $\\mathcal T$. Furthermore, for all $|X|\\ge 1$, we show that $\\mathcal N$ has at most $8|X|-7$ vertices in total and at most $3|X|-3$ reticulation vertices, and that these upper bounds are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05424","kind":"arxiv","version":2},"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":"2026-05-18T00:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/uE7BQG0ppAuLYZmDAmM9Nc0R7LMCySXizH+Rkf2JZHVSWEpOczrqU/qIvtbFs+pbXNjSX9TnK+ZgPXmDAsDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:17:27.530895Z"},"content_sha256":"8f7dcd60a14c726f4a898609568d965668d6f49bbfe667151a04bf40a65dec86","schema_version":"1.0","event_id":"sha256:8f7dcd60a14c726f4a898609568d965668d6f49bbfe667151a04bf40a65dec86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/bundle.json","state_url":"https://pith.science/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/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":"2026-06-21T09:17:27Z","links":{"resolver":"https://pith.science/pith/EBWR7F5UADVPJ52OWP7NO6A4C4","bundle":"https://pith.science/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/bundle.json","state":"https://pith.science/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBWR7F5UADVPJ52OWP7NO6A4C4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EBWR7F5UADVPJ52OWP7NO6A4C4","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":"28caf9e603dac15d319c16debdba523bb8927b6ed4ef262cc373740afd7118dc","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-21T22:03:35Z","title_canon_sha256":"1b082ca2d609ed264deeee1defb7db508e201f52258e39e402929e1ad8a31af5"},"schema_version":"1.0","source":{"id":"1508.05424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05424","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05424v2","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05424","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"EBWR7F5UADVP","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EBWR7F5UADVPJ52O","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EBWR7F5U","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:8f7dcd60a14c726f4a898609568d965668d6f49bbfe667151a04bf40a65dec86","target":"graph","created_at":"2026-05-18T00:41:46Z","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":"Let $X$ be a finite set, $\\mathcal N$ be a reticulation-visible network on $X$, and $\\mathcal T$ be a rooted binary phylogenetic tree. We show that there is a polynomial-time algorithm for deciding whether or not $\\mathcal N$ displays $\\mathcal T$. Furthermore, for all $|X|\\ge 1$, we show that $\\mathcal N$ has at most $8|X|-7$ vertices in total and at most $3|X|-3$ reticulation vertices, and that these upper bounds are sharp.","authors_text":"Charles Semple, Magnus Bordewich","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-21T22:03:35Z","title":"Reticulation-visible networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05424","kind":"arxiv","version":2},"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":"sha256:0c3d5cd711be8093993c5cb872ef9ba19fd44e65be4d4c20bb929b04b100bcc6","target":"record","created_at":"2026-05-18T00:41:46Z","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":"28caf9e603dac15d319c16debdba523bb8927b6ed4ef262cc373740afd7118dc","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-21T22:03:35Z","title_canon_sha256":"1b082ca2d609ed264deeee1defb7db508e201f52258e39e402929e1ad8a31af5"},"schema_version":"1.0","source":{"id":"1508.05424","kind":"arxiv","version":2}},"canonical_sha256":"206d1f97b400eaf4f74eb3fed7781c170c5b15aa1a7eae83b4ed992691f63c39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"206d1f97b400eaf4f74eb3fed7781c170c5b15aa1a7eae83b4ed992691f63c39","first_computed_at":"2026-05-18T00:41:46.706254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:46.706254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywDdpZ7M1THcx+DzHb4s69NDnG1TO/Xfwsjun/qG6nXIxs7TjR95qzlSLDQcpF0lH9JI4ZyJRrwxJ1ht50x6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:46.706783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c3d5cd711be8093993c5cb872ef9ba19fd44e65be4d4c20bb929b04b100bcc6","sha256:8f7dcd60a14c726f4a898609568d965668d6f49bbfe667151a04bf40a65dec86"],"state_sha256":"164481850cadb18071858bb48b477f6a93ced47bf56339ca3b4f3f6f16997ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFgVRLFx0qixlkukU0r3FjYGbt0qdFgu1muFFbDyp37qeR1QqSIa1cQg6PTqyuGQixLIpmhIjsPNf+x99nC9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:17:27.532888Z","bundle_sha256":"f4d51314b9699a09f3f81c16ef67270b60cfd63868a26ae257977806819f53ec"}}