{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O42X3PD6GL3PRRCBRHHRORLR7Y","short_pith_number":"pith:O42X3PD6","canonical_record":{"source":{"id":"1307.7287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-27T18:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"0f83b78afef9839cbe4cc9f638089cf61267c3431f046b30fb4f0412cc2dc99a","abstract_canon_sha256":"8ac71bf19b1e5a44b20581be2b649ee0dfbc0a96ebff877a2786ef69af33a868"},"schema_version":"1.0"},"canonical_sha256":"77357dbc7e32f6f8c44189cf174571fe2061c50c24578a10eb8183efefd2459e","source":{"kind":"arxiv","id":"1307.7287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7287","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7287v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7287","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"O42X3PD6GL3P","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O42X3PD6GL3PRRCB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O42X3PD6","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O42X3PD6GL3PRRCBRHHRORLR7Y","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-27T18:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"0f83b78afef9839cbe4cc9f638089cf61267c3431f046b30fb4f0412cc2dc99a","abstract_canon_sha256":"8ac71bf19b1e5a44b20581be2b649ee0dfbc0a96ebff877a2786ef69af33a868"},"schema_version":"1.0"},"canonical_sha256":"77357dbc7e32f6f8c44189cf174571fe2061c50c24578a10eb8183efefd2459e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:23.713833Z","signature_b64":"H/cABFm3JMuVtyXanJt36FJPTs5FKdAH6AJQawa6s3mhgnW7e6pD1MNoJG80WYvICzoasmc0pG7OvGOWiFJkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77357dbc7e32f6f8c44189cf174571fe2061c50c24578a10eb8183efefd2459e","last_reissued_at":"2026-05-18T03:17:23.713059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:23.713059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7287","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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUYBh0LDlfWVvyh7CxMTMs4PjQ6IIwsrwf0HoTzu+XhnXQ6XjtlL1F8RmnUHycvqhY8BlkYi2zJ2OGG3YRLkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:12:44.590392Z"},"content_sha256":"01e9737ea666e41cd267cec15628f5b54f66c2b3538beec6f46ef5e70c4bd191","schema_version":"1.0","event_id":"sha256:01e9737ea666e41cd267cec15628f5b54f66c2b3538beec6f46ef5e70c4bd191"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O42X3PD6GL3PRRCBRHHRORLR7Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A matroid associated with a phylogenetic tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andreas Dress, Katharina Huber, Mike Steel","submitted_at":"2013-07-27T18:03:00Z","abstract_excerpt":"A (pseudo-)metric $D$ on a finite set $X$ is said to be a `tree metric' if there is a finite tree with leaf set $X$ and non-negative edge weights so that, for all $x,y \\in X$, $D(x,y)$ is the path distance in the tree between $x$ and $y$. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is -- up to canonical isomorphism -- uniquely determined by $D$, and one does not even need all of the distances in order to fully (re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7287","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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9qpP9FMPd5NvCj0NeHPkA6deCkFukhmw4d3JrhEO7I7xw2wlNMmGL5Kr4x9xkt6fyzHLfjA6HZMhCCwg4rNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:12:44.591084Z"},"content_sha256":"acf10600ac4879b67b51c4850238f34d735e8e77e9472bffb2ba0d741f18d7d2","schema_version":"1.0","event_id":"sha256:acf10600ac4879b67b51c4850238f34d735e8e77e9472bffb2ba0d741f18d7d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/bundle.json","state_url":"https://pith.science/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/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":"2026-06-01T09:12:44Z","links":{"resolver":"https://pith.science/pith/O42X3PD6GL3PRRCBRHHRORLR7Y","bundle":"https://pith.science/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/bundle.json","state":"https://pith.science/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O42X3PD6GL3PRRCBRHHRORLR7Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O42X3PD6GL3PRRCBRHHRORLR7Y","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":"8ac71bf19b1e5a44b20581be2b649ee0dfbc0a96ebff877a2786ef69af33a868","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-27T18:03:00Z","title_canon_sha256":"0f83b78afef9839cbe4cc9f638089cf61267c3431f046b30fb4f0412cc2dc99a"},"schema_version":"1.0","source":{"id":"1307.7287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7287","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7287v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7287","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"O42X3PD6GL3P","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O42X3PD6GL3PRRCB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O42X3PD6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:acf10600ac4879b67b51c4850238f34d735e8e77e9472bffb2ba0d741f18d7d2","target":"graph","created_at":"2026-05-18T03:17:23Z","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":"A (pseudo-)metric $D$ on a finite set $X$ is said to be a `tree metric' if there is a finite tree with leaf set $X$ and non-negative edge weights so that, for all $x,y \\in X$, $D(x,y)$ is the path distance in the tree between $x$ and $y$. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weights and that has no vertices of degree 2, any such tree is -- up to canonical isomorphism -- uniquely determined by $D$, and one does not even need all of the distances in order to fully (re","authors_text":"Andreas Dress, Katharina Huber, Mike Steel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-27T18:03:00Z","title":"A matroid associated with a phylogenetic tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7287","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":"sha256:01e9737ea666e41cd267cec15628f5b54f66c2b3538beec6f46ef5e70c4bd191","target":"record","created_at":"2026-05-18T03:17:23Z","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":"8ac71bf19b1e5a44b20581be2b649ee0dfbc0a96ebff877a2786ef69af33a868","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-27T18:03:00Z","title_canon_sha256":"0f83b78afef9839cbe4cc9f638089cf61267c3431f046b30fb4f0412cc2dc99a"},"schema_version":"1.0","source":{"id":"1307.7287","kind":"arxiv","version":1}},"canonical_sha256":"77357dbc7e32f6f8c44189cf174571fe2061c50c24578a10eb8183efefd2459e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77357dbc7e32f6f8c44189cf174571fe2061c50c24578a10eb8183efefd2459e","first_computed_at":"2026-05-18T03:17:23.713059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:23.713059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H/cABFm3JMuVtyXanJt36FJPTs5FKdAH6AJQawa6s3mhgnW7e6pD1MNoJG80WYvICzoasmc0pG7OvGOWiFJkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:23.713833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01e9737ea666e41cd267cec15628f5b54f66c2b3538beec6f46ef5e70c4bd191","sha256:acf10600ac4879b67b51c4850238f34d735e8e77e9472bffb2ba0d741f18d7d2"],"state_sha256":"55b40f03b745c04f7b7a05f7a2c2fe16f608b85e1db4535e08aac96137bd0377"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7+pXa8xMV7LgczOgPmpCiy9ldJQiKlC06AZrJ7LhDLV2gaxgHP8JcUnh7lSFXhb9+eTzqWVhyQoy5pBUPpADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:12:44.594344Z","bundle_sha256":"2fcc376cc7959249cf1cd78e2163bc75a0c3302110dd9c128e6513523f9ccd4e"}}