{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QWLQMFINW5TYKMPIBDFEVDJF6G","short_pith_number":"pith:QWLQMFIN","canonical_record":{"source":{"id":"2511.07965","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-11T08:20:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"7c687a444050a846ed5e2ff9ab75728fc42c2d7d547bd97de821bd8d2a0df5e7","abstract_canon_sha256":"7d63ce29ec25e9959d92dd91221ebd7c6722076aa62b0ea6a57df3a2b7de7ec6"},"schema_version":"1.0"},"canonical_sha256":"859706150db7678531e808ca4a8d25f1a3b4faec4009b7600d42dabdf89523eb","source":{"kind":"arxiv","id":"2511.07965","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.07965","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"2511.07965v3","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.07965","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"QWLQMFINW5TY","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_16","alias_value":"QWLQMFINW5TYKMPI","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_8","alias_value":"QWLQMFIN","created_at":"2026-06-01T01:02:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QWLQMFINW5TYKMPIBDFEVDJF6G","target":"record","payload":{"canonical_record":{"source":{"id":"2511.07965","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-11T08:20:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"7c687a444050a846ed5e2ff9ab75728fc42c2d7d547bd97de821bd8d2a0df5e7","abstract_canon_sha256":"7d63ce29ec25e9959d92dd91221ebd7c6722076aa62b0ea6a57df3a2b7de7ec6"},"schema_version":"1.0"},"canonical_sha256":"859706150db7678531e808ca4a8d25f1a3b4faec4009b7600d42dabdf89523eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:25.217055Z","signature_b64":"K2qu7F2yfGJOE4aVS1f8303Dn7gBgBzoeHU3JhmBGhlzLnUTxJph9H6JH8gaTlXMFVUMD8LYphBMMop0ZWmEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"859706150db7678531e808ca4a8d25f1a3b4faec4009b7600d42dabdf89523eb","last_reissued_at":"2026-06-01T01:02:25.216090Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:25.216090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2511.07965","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":"2026-06-01T01:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/x+YOKnLKud2JszTLnaAmpKhn8D0qfQF914H3L80oR2H+FZzDSUcihEvH6XLTATGm2+cmdgq/yY0JJ+ckTdoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:18:44.263183Z"},"content_sha256":"a1835ddc18285008e7967f32862aced2bdfebcae2f1483ceafe0289003eaff70","schema_version":"1.0","event_id":"sha256:a1835ddc18285008e7967f32862aced2bdfebcae2f1483ceafe0289003eaff70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QWLQMFINW5TYKMPIBDFEVDJF6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inferring DAGs and Phylogenetic Networks from Least Common Ancestors","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them.","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anna Lindeberg, Anton Alfonsson, Guillaume E. Scholz, Marc Hellmuth, Vincent Moulton","submitted_at":"2025-11-11T08:20:31Z","abstract_excerpt":"A least common ancestor (LCA) of two leaves in a directed acyclic graph (DAG) is a vertex that is an ancestor of both leaves and has no proper descendant that is also their common ancestor. LCAs capture hierarchical relationships in rooted trees and, more generally, in DAGs. In 1981, Aho et al. introduced the problem of determining whether a set of pairwise LCA constraints on a set $X$, of the form $(i,j)<(k,l)$ with $i,j,k,l\\in X$, can be realized by a rooted tree whose leaf set is $X$, such that whenever $(i,j)<(k,l)$, the LCA of $i,j$ is a descendant of that of $k,l$. They also presented a "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that R is DAG-realizable if and only if it is realized by G_R. We further adapt this construction to phylogenetic networks, defining a canonical network N_R and prove that it is regular.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input collection R of LCA constraints is assumed to be presented in a form that permits efficient computation of the plus-closure and the canonical graph without hidden inconsistencies in the ancestor partial order.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"82e3322bec48a38751c15211e4034626177233a56de44faf8508306fa994178b"},"source":{"id":"2511.07965","kind":"arxiv","version":3},"verdict":{"id":"34efd112-b28f-42f3-a35c-5fb780ef2eff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T00:01:45.393431Z","strongest_claim":"We prove that R is DAG-realizable if and only if it is realized by G_R. We further adapt this construction to phylogenetic networks, defining a canonical network N_R and prove that it is regular.","one_line_summary":"A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input collection R of LCA constraints is assumed to be presented in a form that permits efficient computation of the plus-closure and the canonical graph without hidden inconsistencies in the ancestor partial order.","pith_extraction_headline":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.07965/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"34efd112-b28f-42f3-a35c-5fb780ef2eff"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-01T01:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvLNt3FjtlkZ6I+CSeiKx0DdjApbHsq8NgHTsYFbRJtMtuIrz3fvNSj6KLCFVHKr1j9ru4njQ3RqkOxPA3skDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:18:44.263850Z"},"content_sha256":"b7cca31a56f2565af6c1a7a3e8a5e3b881b5179ca2b11406aa276359bbd11386","schema_version":"1.0","event_id":"sha256:b7cca31a56f2565af6c1a7a3e8a5e3b881b5179ca2b11406aa276359bbd11386"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/bundle.json","state_url":"https://pith.science/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/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":"2026-08-14T07:18:44Z","links":{"resolver":"https://pith.science/pith/QWLQMFINW5TYKMPIBDFEVDJF6G","bundle":"https://pith.science/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/bundle.json","state":"https://pith.science/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWLQMFINW5TYKMPIBDFEVDJF6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QWLQMFINW5TYKMPIBDFEVDJF6G","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":"7d63ce29ec25e9959d92dd91221ebd7c6722076aa62b0ea6a57df3a2b7de7ec6","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-11T08:20:31Z","title_canon_sha256":"7c687a444050a846ed5e2ff9ab75728fc42c2d7d547bd97de821bd8d2a0df5e7"},"schema_version":"1.0","source":{"id":"2511.07965","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.07965","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"2511.07965v3","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.07965","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"QWLQMFINW5TY","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_16","alias_value":"QWLQMFINW5TYKMPI","created_at":"2026-06-01T01:02:25Z"},{"alias_kind":"pith_short_8","alias_value":"QWLQMFIN","created_at":"2026-06-01T01:02:25Z"}],"graph_snapshots":[{"event_id":"sha256:b7cca31a56f2565af6c1a7a3e8a5e3b881b5179ca2b11406aa276359bbd11386","target":"graph","created_at":"2026-06-01T01:02:25Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that R is DAG-realizable if and only if it is realized by G_R. We further adapt this construction to phylogenetic networks, defining a canonical network N_R and prove that it is regular."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The input collection R of LCA constraints is assumed to be presented in a form that permits efficient computation of the plus-closure and the canonical graph without hidden inconsistencies in the ancestor partial order."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them."}],"snapshot_sha256":"82e3322bec48a38751c15211e4034626177233a56de44faf8508306fa994178b"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.07965/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A least common ancestor (LCA) of two leaves in a directed acyclic graph (DAG) is a vertex that is an ancestor of both leaves and has no proper descendant that is also their common ancestor. LCAs capture hierarchical relationships in rooted trees and, more generally, in DAGs. In 1981, Aho et al. introduced the problem of determining whether a set of pairwise LCA constraints on a set $X$, of the form $(i,j)<(k,l)$ with $i,j,k,l\\in X$, can be realized by a rooted tree whose leaf set is $X$, such that whenever $(i,j)<(k,l)$, the LCA of $i,j$ is a descendant of that of $k,l$. They also presented a ","authors_text":"Anna Lindeberg, Anton Alfonsson, Guillaume E. Scholz, Marc Hellmuth, Vincent Moulton","cross_cats":["cs.DM"],"headline":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-11T08:20:31Z","title":"Inferring DAGs and Phylogenetic Networks from Least Common Ancestors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.07965","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-18T00:01:45.393431Z","id":"34efd112-b28f-42f3-a35c-5fb780ef2eff","model_set":{"reader":"grok-4.3"},"one_line_summary":"A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A set of least common ancestor constraints on leaves is realizable by some DAG exactly when the canonical DAG built from their plus-closure realizes them.","strongest_claim":"We prove that R is DAG-realizable if and only if it is realized by G_R. We further adapt this construction to phylogenetic networks, defining a canonical network N_R and prove that it is regular.","weakest_assumption":"The input collection R of LCA constraints is assumed to be presented in a form that permits efficient computation of the plus-closure and the canonical graph without hidden inconsistencies in the ancestor partial order."}},"verdict_id":"34efd112-b28f-42f3-a35c-5fb780ef2eff"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a1835ddc18285008e7967f32862aced2bdfebcae2f1483ceafe0289003eaff70","target":"record","created_at":"2026-06-01T01:02:25Z","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":"7d63ce29ec25e9959d92dd91221ebd7c6722076aa62b0ea6a57df3a2b7de7ec6","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-11T08:20:31Z","title_canon_sha256":"7c687a444050a846ed5e2ff9ab75728fc42c2d7d547bd97de821bd8d2a0df5e7"},"schema_version":"1.0","source":{"id":"2511.07965","kind":"arxiv","version":3}},"canonical_sha256":"859706150db7678531e808ca4a8d25f1a3b4faec4009b7600d42dabdf89523eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"859706150db7678531e808ca4a8d25f1a3b4faec4009b7600d42dabdf89523eb","first_computed_at":"2026-06-01T01:02:25.216090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:02:25.216090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2qu7F2yfGJOE4aVS1f8303Dn7gBgBzoeHU3JhmBGhlzLnUTxJph9H6JH8gaTlXMFVUMD8LYphBMMop0ZWmEDw==","signature_status":"signed_v1","signed_at":"2026-06-01T01:02:25.217055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.07965","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1835ddc18285008e7967f32862aced2bdfebcae2f1483ceafe0289003eaff70","sha256:b7cca31a56f2565af6c1a7a3e8a5e3b881b5179ca2b11406aa276359bbd11386"],"state_sha256":"21b0d0720ef6315f58718ae4d874802722d3711503cae383618ae75e554ec202"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lHZrq516Mu3erVW2m7gaogtgs0XquIqjuOHi5C2t2Et6bwhnOLQterKqbwQ4ah1/uRIBZIwyH43F/RfQnAp6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T07:18:44.268232Z","bundle_sha256":"0be53a48da1f4cabfdbe8b2c8580598a60a22bd8e680b257eb5d4f0a495cf30e"}}