{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","short_pith_number":"pith:ZRDTPEN3","canonical_record":{"source":{"id":"2605.03827","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-05-05T14:54:42Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"5f6bf641806f98b2006179745d043a0cc772c42e6124efe1f5de760f3309e5d7","abstract_canon_sha256":"c85f8581032cc348e5c50839371618ab322403715336699bcf8cf3b5b8a1a834"},"schema_version":"1.0"},"canonical_sha256":"cc473791bbffc997639dc5136d92e6b24646225d2b7721c00a07665e3a368de9","source":{"kind":"arxiv","id":"2605.03827","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03827","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03827v3","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03827","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZRDTPEN377EZ","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_16","alias_value":"ZRDTPEN377EZOY45","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_8","alias_value":"ZRDTPEN3","created_at":"2026-08-07T00:51:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.03827","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-05-05T14:54:42Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"5f6bf641806f98b2006179745d043a0cc772c42e6124efe1f5de760f3309e5d7","abstract_canon_sha256":"c85f8581032cc348e5c50839371618ab322403715336699bcf8cf3b5b8a1a834"},"schema_version":"1.0"},"canonical_sha256":"cc473791bbffc997639dc5136d92e6b24646225d2b7721c00a07665e3a368de9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:51:38.195972Z","signature_b64":"ao3M+j8ZJTykwKwu6DIJbbM5LrG7xLWL7GFzNA6gthYNv9c+gx1bKUNMOIKq7+buZhCriX7Vf8XO2ZOgbQeeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc473791bbffc997639dc5136d92e6b24646225d2b7721c00a07665e3a368de9","last_reissued_at":"2026-08-07T00:51:38.194639Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:51:38.194639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.03827","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":"2026-08-07T00:51:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGc4qarDljMaLAa6b82TVJaaGpCMFHOOwpNrfjTg7LSdKQZJb9ymwGRXCnnjNA7eO+OLLKulmzboC/9wKVbZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:09:51.132902Z"},"content_sha256":"a95683a4db93c7730f3bd96f3c697ac8f2562e2e34390c894bcd262f14d84d81","schema_version":"1.0","event_id":"sha256:a95683a4db93c7730f3bd96f3c697ac8f2562e2e34390c894bcd262f14d84d81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inferring Phylogenetic Networks from Required and Forbidden LCA-Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms.","cross_cats":["q-bio.PE"],"primary_cat":"cs.DM","authors_text":"Marc Hellmuth, Patricia A. Ebert","submitted_at":"2026-05-05T14:54:42Z","abstract_excerpt":"Least common ancestor (LCA) constraints encode relative-order information in directed acyclic graphs (DAGs) and give rise to a natural constraint-realization problem. Phylogenetic networks provide an important class of DAGs in which such constraints are used to represent local information about evolutionary histories. In this paper, we study the inference of DAGs and phylogenetic networks from LCA-constraints, which specify relative positions of the LCAs associated with pairs of leaves. While previous work has characterized when a set of required LCA-constraints can be realized by a DAG or phy"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For each of them, we characterize exactly when there exists a phylogenetic network that realizes all constraints in R while avoiding all constraints in F in the respective sense. Based on these characterizations, we derive polynomial-time algorithms that decide the existence of such networks and construct one whenever it exists.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The three formalizations of avoiding a forbidden LCA constraint are the natural and complete ways to interpret avoidance; the characterizations assume standard definitions of phylogenetic networks and LCA relations on a fixed set of taxa.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact characterizations and polynomial-time algorithms are given for realizing phylogenetic networks from required and forbidden LCA constraints under three variants of avoidance.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bf5b129fd43f56fa6960d8c22f0ed279500ffc0dbe53f9d40e58b46d6be5ddbe"},"source":{"id":"2605.03827","kind":"arxiv","version":3},"verdict":{"id":"0bc37cd0-59bf-4fcd-95e7-c898e454c379","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:06:58.160629Z","strongest_claim":"For each of them, we characterize exactly when there exists a phylogenetic network that realizes all constraints in R while avoiding all constraints in F in the respective sense. Based on these characterizations, we derive polynomial-time algorithms that decide the existence of such networks and construct one whenever it exists.","one_line_summary":"Exact characterizations and polynomial-time algorithms are given for realizing phylogenetic networks from required and forbidden LCA constraints under three variants of avoidance.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The three formalizations of avoiding a forbidden LCA constraint are the natural and complete ways to interpret avoidance; the characterizations assume standard definitions of phylogenetic networks and LCA relations on a fixed set of taxa.","pith_extraction_headline":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms."},"integrity":{"clean":false,"summary":{"advisory":0,"critical":3,"by_detector":{"doi_compliance":{"total":3,"advisory":0,"critical":3,"informational":0}},"informational":0},"endpoint":"/pith/2605.03827/integrity.json","findings":[{"note":"DOI '10.26021/15536' as printed in the bibliography is syntactically invalid and cannot resolve.","detector":"doi_compliance","severity":"critical","ref_index":22,"audited_at":"2026-05-19T15:00:33.716540Z","detected_doi":"10.26021/15536","finding_type":"broken_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null},{"note":"DOI '10.26021/2479' as printed in the bibliography is syntactically invalid and cannot resolve.","detector":"doi_compliance","severity":"critical","ref_index":3,"audited_at":"2026-05-19T15:00:33.716540Z","detected_doi":"10.26021/2479","finding_type":"broken_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null},{"note":"DOI '10.1073/pnas' as printed in the bibliography is syntactically invalid and cannot resolve.","detector":"doi_compliance","severity":"critical","ref_index":13,"audited_at":"2026-05-19T15:00:33.716540Z","detected_doi":"10.1073/pnas","finding_type":"broken_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null}],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T13:33:34.774014Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:21.966583Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:00:33.716540Z","status":"completed","version":"1.0.0","findings_count":3}],"snapshot_sha256":"bbd9784a62259112dac76f64cb749442c401ea7e59315f15f3f9873df0f9a8f1"},"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":"0bc37cd0-59bf-4fcd-95e7-c898e454c379"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-07T00:51:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUYnkDhH3F9MRxsL9TbLBDvnOP+9Ucel8QxQOcq8RiDiJJAB3bPV6SZnDny56+MQlw+OOmbZiVQVb/CA1MLkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:09:51.133721Z"},"content_sha256":"9d37b2983e116a60f84d3e2396b02a98b27deea6221407a21874e8d1e636ef21","schema_version":"1.0","event_id":"sha256:9d37b2983e116a60f84d3e2396b02a98b27deea6221407a21874e8d1e636ef21"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","target":"integrity","payload":{"note":"DOI '10.26021/15536' as printed in the bibliography is syntactically invalid and cannot resolve.","snippet":"Levy M (2024) Triplet matroids and closure in phylogenetics. Master’s thesis, University of Canterbury, DOI 10.26021/15536","arxiv_id":"2605.03827","detector":"doi_compliance","evidence":{"ref_index":22,"raw_excerpt":"Levy M (2024) Triplet matroids and closure in phylogenetics. Master’s thesis, University of Canterbury, DOI 10.26021/15536","verdict_class":"incontrovertible","doi_as_printed":"10.26021/15536"},"severity":"critical","ref_index":22,"audited_at":"2026-05-19T15:00:33.716540Z","event_type":"pith.integrity.v1","detected_doi":"10.26021/15536","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"broken_identifier","evidence_hash":"74ecccf3da23ffc3b7be26e71408c70f64c7d211f477544eed7340d517731631","paper_version":2,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":1756,"payload_sha256":"3f7b4ac45c99a35cfb45ecee3cf77553f634f575b3cf55d2b4427d1a4c2e1a49","signature_b64":"kw5K75hnIj42vnImhcnju7TeGVa7kuSrgv7WsWraQVgbmsQWQbxU2c+LF5LxDvWCnv/GXgHtpUPIVDLPCTNWDQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T15:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAonYn/aTORekvHRBWiHyHWZ2vb3zAE/lwf7anrKl0qLgowy2lPEjjOlkHAMARxAerFqJDq1LiHHE+LttK7xDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:09:51.137117Z"},"content_sha256":"229cff81fdfbbe091e4a7e355e4e308026d466f4db9e80a17a2c59882b24aaf7","schema_version":"1.0","event_id":"sha256:229cff81fdfbbe091e4a7e355e4e308026d466f4db9e80a17a2c59882b24aaf7"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","target":"integrity","payload":{"note":"DOI '10.1073/pnas' as printed in the bibliography is syntactically invalid and cannot resolve.","snippet":"Hellmuth M, Wieseke N, Lechner M, Lenhof HP, Middendorf M, Stadler PF (2015) Phylogenomics with paralogs. Proceedings of the National Academy of Sciences 112(7):2058–2063, DOI 10.1073/pnas. 1412770112 20","arxiv_id":"2605.03827","detector":"doi_compliance","evidence":{"ref_index":13,"raw_excerpt":"Hellmuth M, Wieseke N, Lechner M, Lenhof HP, Middendorf M, Stadler PF (2015) Phylogenomics with paralogs. Proceedings of the National Academy of Sciences 112(7):2058–2063, DOI 10.1073/pnas. 1412770112 20","verdict_class":"incontrovertible","doi_as_printed":"10.1073/pnas"},"severity":"critical","ref_index":13,"audited_at":"2026-05-19T15:00:33.716540Z","event_type":"pith.integrity.v1","detected_doi":"10.1073/pnas","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"broken_identifier","evidence_hash":"a05b5e23e6bdfc845f29995564f727434207185139b24bc45faa6e8d6e47fdbe","paper_version":2,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":1755,"payload_sha256":"986efe45059032f71c0435c8eef8689c16e431788f507425326ee26cfca61b2c","signature_b64":"pbUIk6wSu9WCIdU/CIHtMNb3Ly3HAPLM6J3EPNpj3CJ8+kqx1RCA1TJEi7XNdtW6NjiljZPH8i9ICtTkpMlRCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T15:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8/d9SXLGiW5PsI5VU0e/245fwK8QI+7RjnAZoQKjA/4dVMpDRaw1M/j/GlCw+9LQbZbBXfanVUZ8D9toXBDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:09:51.137468Z"},"content_sha256":"221acc42c8f39ac694797db0cded624bf86860779ed01dd7733d0044d9ec8e70","schema_version":"1.0","event_id":"sha256:221acc42c8f39ac694797db0cded624bf86860779ed01dd7733d0044d9ec8e70"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","target":"integrity","payload":{"note":"DOI '10.26021/2479' as printed in the bibliography is syntactically invalid and cannot resolve.","snippet":"Bryant D (1997) Building trees, hunting for trees, and comparing trees. theory and methods in phyloge- netic analysis. PhD thesis, University of Canterbury, DOI 10.26021/2479","arxiv_id":"2605.03827","detector":"doi_compliance","evidence":{"ref_index":3,"raw_excerpt":"Bryant D (1997) Building trees, hunting for trees, and comparing trees. theory and methods in phyloge- netic analysis. PhD thesis, University of Canterbury, DOI 10.26021/2479","verdict_class":"incontrovertible","doi_as_printed":"10.26021/2479"},"severity":"critical","ref_index":3,"audited_at":"2026-05-19T15:00:33.716540Z","event_type":"pith.integrity.v1","detected_doi":"10.26021/2479","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"broken_identifier","evidence_hash":"0483607463d29ffa9656447840398cdc25967ead371187fca13c930fa7874e43","paper_version":2,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":1754,"payload_sha256":"56331311889c7e763bf85a28b68465553890cb721f098bdc393839f10dbba9dd","signature_b64":"DPPWx6dBg9oKEDmnSB1Ebg/QhKAI/ZBEZNkiQPrgiW1PEr+gNN8D1x5T3A0Lq5T9bfnfos/1UplbeFbn+lhMCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T15:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zOdI4v3Mz+QQoaTA+seKc/BezNMlrnRE11a9K3QkTDbp3K/zziQa3mX9HMekNb1+F/qc2O1mrGlbUEy618mXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T01:09:51.137769Z"},"content_sha256":"04485f2203390bb1e0b257888829ad1e4c271a7a4e1db7cab2af101abc46d7b2","schema_version":"1.0","event_id":"sha256:04485f2203390bb1e0b257888829ad1e4c271a7a4e1db7cab2af101abc46d7b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/bundle.json","state_url":"https://pith.science/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/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":"2026-08-14T01:09:51Z","links":{"resolver":"https://pith.science/pith/ZRDTPEN377EZOY45YUJW3EXGWJ","bundle":"https://pith.science/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/bundle.json","state":"https://pith.science/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRDTPEN377EZOY45YUJW3EXGWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZRDTPEN377EZOY45YUJW3EXGWJ","merge_version":"pith-open-graph-merge-v1","event_count":5,"valid_event_count":5,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c85f8581032cc348e5c50839371618ab322403715336699bcf8cf3b5b8a1a834","cross_cats_sorted":["q-bio.PE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-05-05T14:54:42Z","title_canon_sha256":"5f6bf641806f98b2006179745d043a0cc772c42e6124efe1f5de760f3309e5d7"},"schema_version":"1.0","source":{"id":"2605.03827","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.03827","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"arxiv_version","alias_value":"2605.03827v3","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03827","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZRDTPEN377EZ","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_16","alias_value":"ZRDTPEN377EZOY45","created_at":"2026-08-07T00:51:38Z"},{"alias_kind":"pith_short_8","alias_value":"ZRDTPEN3","created_at":"2026-08-07T00:51:38Z"}],"graph_snapshots":[{"event_id":"sha256:9d37b2983e116a60f84d3e2396b02a98b27deea6221407a21874e8d1e636ef21","target":"graph","created_at":"2026-08-07T00:51:38Z","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":"For each of them, we characterize exactly when there exists a phylogenetic network that realizes all constraints in R while avoiding all constraints in F in the respective sense. Based on these characterizations, we derive polynomial-time algorithms that decide the existence of such networks and construct one whenever it exists."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The three formalizations of avoiding a forbidden LCA constraint are the natural and complete ways to interpret avoidance; the characterizations assume standard definitions of phylogenetic networks and LCA relations on a fixed set of taxa."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Exact characterizations and polynomial-time algorithms are given for realizing phylogenetic networks from required and forbidden LCA constraints under three variants of avoidance."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms."}],"snapshot_sha256":"bf5b129fd43f56fa6960d8c22f0ed279500ffc0dbe53f9d40e58b46d6be5ddbe"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":false,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T13:33:34.774014Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:21.966583Z","status":"completed","version":"1.0.0"},{"findings_count":3,"name":"doi_compliance","ran_at":"2026-05-19T15:00:33.716540Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.03827/integrity.json","findings":[{"audited_at":"2026-05-19T15:00:33.716540Z","detected_arxiv_id":null,"detected_doi":"10.26021/15536","detector":"doi_compliance","finding_type":"broken_identifier","note":"DOI '10.26021/15536' as printed in the bibliography is syntactically invalid and cannot resolve.","ref_index":22,"severity":"critical","verdict_class":"incontrovertible"},{"audited_at":"2026-05-19T15:00:33.716540Z","detected_arxiv_id":null,"detected_doi":"10.26021/2479","detector":"doi_compliance","finding_type":"broken_identifier","note":"DOI '10.26021/2479' as printed in the bibliography is syntactically invalid and cannot resolve.","ref_index":3,"severity":"critical","verdict_class":"incontrovertible"},{"audited_at":"2026-05-19T15:00:33.716540Z","detected_arxiv_id":null,"detected_doi":"10.1073/pnas","detector":"doi_compliance","finding_type":"broken_identifier","note":"DOI '10.1073/pnas' as printed in the bibliography is syntactically invalid and cannot resolve.","ref_index":13,"severity":"critical","verdict_class":"incontrovertible"}],"snapshot_sha256":"bbd9784a62259112dac76f64cb749442c401ea7e59315f15f3f9873df0f9a8f1","summary":{"advisory":0,"by_detector":{"doi_compliance":{"advisory":0,"critical":3,"informational":0,"total":3}},"critical":3,"informational":0}},"paper":{"abstract_excerpt":"Least common ancestor (LCA) constraints encode relative-order information in directed acyclic graphs (DAGs) and give rise to a natural constraint-realization problem. Phylogenetic networks provide an important class of DAGs in which such constraints are used to represent local information about evolutionary histories. In this paper, we study the inference of DAGs and phylogenetic networks from LCA-constraints, which specify relative positions of the LCAs associated with pairs of leaves. While previous work has characterized when a set of required LCA-constraints can be realized by a DAG or phy","authors_text":"Marc Hellmuth, Patricia A. Ebert","cross_cats":["q-bio.PE"],"headline":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-05-05T14:54:42Z","title":"Inferring Phylogenetic Networks from Required and Forbidden LCA-Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.03827","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-12T03:06:58.160629Z","id":"0bc37cd0-59bf-4fcd-95e7-c898e454c379","model_set":{"reader":"grok-4.3"},"one_line_summary":"Exact characterizations and polynomial-time algorithms are given for realizing phylogenetic networks from required and forbidden LCA constraints under three variants of avoidance.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Exact characterizations determine when phylogenetic networks realize required LCA constraints while avoiding forbidden ones under three avoidance variants, and these yield polynomial-time decision and construction algorithms.","strongest_claim":"For each of them, we characterize exactly when there exists a phylogenetic network that realizes all constraints in R while avoiding all constraints in F in the respective sense. Based on these characterizations, we derive polynomial-time algorithms that decide the existence of such networks and construct one whenever it exists.","weakest_assumption":"The three formalizations of avoiding a forbidden LCA constraint are the natural and complete ways to interpret avoidance; the characterizations assume standard definitions of phylogenetic networks and LCA relations on a fixed set of taxa."}},"verdict_id":"0bc37cd0-59bf-4fcd-95e7-c898e454c379"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a95683a4db93c7730f3bd96f3c697ac8f2562e2e34390c894bcd262f14d84d81","target":"record","created_at":"2026-08-07T00:51:38Z","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":"c85f8581032cc348e5c50839371618ab322403715336699bcf8cf3b5b8a1a834","cross_cats_sorted":["q-bio.PE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-05-05T14:54:42Z","title_canon_sha256":"5f6bf641806f98b2006179745d043a0cc772c42e6124efe1f5de760f3309e5d7"},"schema_version":"1.0","source":{"id":"2605.03827","kind":"arxiv","version":3}},"canonical_sha256":"cc473791bbffc997639dc5136d92e6b24646225d2b7721c00a07665e3a368de9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc473791bbffc997639dc5136d92e6b24646225d2b7721c00a07665e3a368de9","first_computed_at":"2026-08-07T00:51:38.194639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:51:38.194639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ao3M+j8ZJTykwKwu6DIJbbM5LrG7xLWL7GFzNA6gthYNv9c+gx1bKUNMOIKq7+buZhCriX7Vf8XO2ZOgbQeeAg==","signature_status":"signed_v1","signed_at":"2026-08-07T00:51:38.195972Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.03827","source_kind":"arxiv","source_version":3}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:04485f2203390bb1e0b257888829ad1e4c271a7a4e1db7cab2af101abc46d7b2","sha256:221acc42c8f39ac694797db0cded624bf86860779ed01dd7733d0044d9ec8e70","sha256:229cff81fdfbbe091e4a7e355e4e308026d466f4db9e80a17a2c59882b24aaf7"]}],"invalid_events":[],"applied_event_ids":["sha256:a95683a4db93c7730f3bd96f3c697ac8f2562e2e34390c894bcd262f14d84d81","sha256:9d37b2983e116a60f84d3e2396b02a98b27deea6221407a21874e8d1e636ef21"],"state_sha256":"6247b62ca0fde15a670a7ab47543b06a6597f54ab65df42f3bf2ffd14bd90b20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bT7yD96iMk/G3LtIxx9VOUUqB89QANhPXGOZcitOByCuxZJL8y2q5i9E1TtjfXuTJWbEQOGet4N8ZqOkq4hsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T01:09:51.141463Z","bundle_sha256":"12e1de193def31b59565ffc1f1bdeb0d47c4a05d1e83fdeb35263fffc05cc869"}}