{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TBPB3PSN6GMDEKDQ6LBIEURLSM","short_pith_number":"pith:TBPB3PSN","canonical_record":{"source":{"id":"1511.08056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-25T13:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"df7a857cf1327b49bd9a2fb4e5956c59c19233bd0035a89c204a6e5f525f31cb","abstract_canon_sha256":"5828ac60ed2523cfbd952c6dad9e56ecf511aca150f5f7a17897370526d662f3"},"schema_version":"1.0"},"canonical_sha256":"985e1dbe4df198322870f2c282522b932dd59d591af3c451d453ac4ccd3d29a1","source":{"kind":"arxiv","id":"1511.08056","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08056","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08056v2","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08056","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"TBPB3PSN6GMD","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBPB3PSN6GMDEKDQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBPB3PSN","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TBPB3PSN6GMDEKDQ6LBIEURLSM","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-25T13:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"df7a857cf1327b49bd9a2fb4e5956c59c19233bd0035a89c204a6e5f525f31cb","abstract_canon_sha256":"5828ac60ed2523cfbd952c6dad9e56ecf511aca150f5f7a17897370526d662f3"},"schema_version":"1.0"},"canonical_sha256":"985e1dbe4df198322870f2c282522b932dd59d591af3c451d453ac4ccd3d29a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:04.779474Z","signature_b64":"1FWjocxi7XFgQEGFm8dBiVfeiDM88iT2UEyu4xPGwH053IlwK0NVUqvA/sq+AbkYYi+iErZfAOrIe0sOQWIEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"985e1dbe4df198322870f2c282522b932dd59d591af3c451d453ac4ccd3d29a1","last_reissued_at":"2026-05-18T01:02:04.778959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:04.778959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08056","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":"2026-05-18T01:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1EHm8DCoKKM6f/n19mkHrBPZGHORni2V7QHACcx8aHbxLVWQ0i4dwESRhP2KwNy/0feYTaveagqnPsfoBAAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:40.451263Z"},"content_sha256":"0f901c8167c7b66edf76d42b33a77dcd8f4b2d7aa13913dc899c1dd6fef46b32","schema_version":"1.0","event_id":"sha256:0f901c8167c7b66edf76d42b33a77dcd8f4b2d7aa13913dc899c1dd6fef46b32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TBPB3PSN6GMDEKDQ6LBIEURLSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the challenge of reconstructing level-1 phylogenetic networks from triplets and clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"K.T. Huber, P. Gambette, S. Kelk","submitted_at":"2015-11-25T13:42:26Z","abstract_excerpt":"Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network $N$ induces a triplet system $\\mathcal R(N)$ and a softwired cluster system $\\mathcal S(N)$. Since in real-world studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available it is of particular interest to understand whether subsets of $\\mathcal R(N)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08056","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":"2026-05-18T01:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnYOEzyGp4VFA8a8DuUUbxt4Pop7n2mncwtXPdnU6kmNJ9LL4G1gHWkONzV/L+rqTSEEFtvsQlDp+lOMj0E7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:48:40.452113Z"},"content_sha256":"d7fac6365b6f6e48537e1df1611a93df3144673c57fe1cda3231f216e06efb42","schema_version":"1.0","event_id":"sha256:d7fac6365b6f6e48537e1df1611a93df3144673c57fe1cda3231f216e06efb42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/bundle.json","state_url":"https://pith.science/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/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":"2026-06-11T08:48:40Z","links":{"resolver":"https://pith.science/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM","bundle":"https://pith.science/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/bundle.json","state":"https://pith.science/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TBPB3PSN6GMDEKDQ6LBIEURLSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TBPB3PSN6GMDEKDQ6LBIEURLSM","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":"5828ac60ed2523cfbd952c6dad9e56ecf511aca150f5f7a17897370526d662f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-25T13:42:26Z","title_canon_sha256":"df7a857cf1327b49bd9a2fb4e5956c59c19233bd0035a89c204a6e5f525f31cb"},"schema_version":"1.0","source":{"id":"1511.08056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08056","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08056v2","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08056","created_at":"2026-05-18T01:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"TBPB3PSN6GMD","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBPB3PSN6GMDEKDQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBPB3PSN","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:d7fac6365b6f6e48537e1df1611a93df3144673c57fe1cda3231f216e06efb42","target":"graph","created_at":"2026-05-18T01:02:04Z","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":"Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network $N$ induces a triplet system $\\mathcal R(N)$ and a softwired cluster system $\\mathcal S(N)$. Since in real-world studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available it is of particular interest to understand whether subsets of $\\mathcal R(N)","authors_text":"K.T. Huber, P. Gambette, S. Kelk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-25T13:42:26Z","title":"On the challenge of reconstructing level-1 phylogenetic networks from triplets and clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08056","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":"sha256:0f901c8167c7b66edf76d42b33a77dcd8f4b2d7aa13913dc899c1dd6fef46b32","target":"record","created_at":"2026-05-18T01:02:04Z","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":"5828ac60ed2523cfbd952c6dad9e56ecf511aca150f5f7a17897370526d662f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-25T13:42:26Z","title_canon_sha256":"df7a857cf1327b49bd9a2fb4e5956c59c19233bd0035a89c204a6e5f525f31cb"},"schema_version":"1.0","source":{"id":"1511.08056","kind":"arxiv","version":2}},"canonical_sha256":"985e1dbe4df198322870f2c282522b932dd59d591af3c451d453ac4ccd3d29a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"985e1dbe4df198322870f2c282522b932dd59d591af3c451d453ac4ccd3d29a1","first_computed_at":"2026-05-18T01:02:04.778959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:04.778959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1FWjocxi7XFgQEGFm8dBiVfeiDM88iT2UEyu4xPGwH053IlwK0NVUqvA/sq+AbkYYi+iErZfAOrIe0sOQWIEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:04.779474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f901c8167c7b66edf76d42b33a77dcd8f4b2d7aa13913dc899c1dd6fef46b32","sha256:d7fac6365b6f6e48537e1df1611a93df3144673c57fe1cda3231f216e06efb42"],"state_sha256":"4f706de578e0a388622c32f304ef9a3908093e4a890f48b4a2d607731e1528f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxOtWYD3ZDWK+Y9HAVlFNGEtny6y3rHyd1Ta2prmHttNmGgwxcm7P4JelUHaWCK7bJnNAQQQHn0Hb0tmQ3vzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:48:40.456108Z","bundle_sha256":"cac1f0071a432bbf0c6c720e0703a7ad524a3bbbf7652cd3b25b41349e3d8ed4"}}