{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XDNESS2G4SRO56SLARCD7ZTYA4","short_pith_number":"pith:XDNESS2G","canonical_record":{"source":{"id":"1211.7046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-11-29T20:39:49Z","cross_cats_sorted":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"title_canon_sha256":"28cd61f29c59086ed64cabca8dbc6a3cf36da9cc1e9f64184bcbd10f2a3a0cce","abstract_canon_sha256":"508bc3c2a806603cd2013dba5127754fb68ba274c153621bc19821e90403f2d2"},"schema_version":"1.0"},"canonical_sha256":"b8da494b46e4a2eefa4b04443fe6780739c19341ec1e0b09a9f3a2753abf823e","source":{"kind":"arxiv","id":"1211.7046","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7046","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7046v2","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7046","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"XDNESS2G4SRO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XDNESS2G4SRO56SL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XDNESS2G","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XDNESS2G4SRO56SLARCD7ZTYA4","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-11-29T20:39:49Z","cross_cats_sorted":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"title_canon_sha256":"28cd61f29c59086ed64cabca8dbc6a3cf36da9cc1e9f64184bcbd10f2a3a0cce","abstract_canon_sha256":"508bc3c2a806603cd2013dba5127754fb68ba274c153621bc19821e90403f2d2"},"schema_version":"1.0"},"canonical_sha256":"b8da494b46e4a2eefa4b04443fe6780739c19341ec1e0b09a9f3a2753abf823e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:57.603013Z","signature_b64":"KvAXIf/ruwfRmnbA76JW9bd+kZeC/7hvDedGPxdRvaIIVQf5zwF34JaUBRJzH/MJxXqkiGu5YDF+okv9WLghAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8da494b46e4a2eefa4b04443fe6780739c19341ec1e0b09a9f3a2753abf823e","last_reissued_at":"2026-05-18T02:58:57.602115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:57.602115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7046","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":"2026-05-18T02:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AM2t541pPnrc4jS4Y6d6prXrgvvHdjrRs8eGEL21/S51xCiZky0FYeOwbZe0plvKX1ESsNwe8TF3grP+AiutBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:09:49.572223Z"},"content_sha256":"4f762f2f5ddfd82c393188a6574e7e6496c5f17140771c70bf3555b730100c2a","schema_version":"1.0","event_id":"sha256:4f762f2f5ddfd82c393188a6574e7e6496c5f17140771c70bf3555b730100c2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XDNESS2G4SRO56SLARCD7ZTYA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polyhedral computational geometry for averaging metric phylogenetic trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"primary_cat":"math.MG","authors_text":"Ezra Miller, J. Scott Provan, Megan Owen","submitted_at":"2012-11-29T20:39:49Z","abstract_excerpt":"This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability measures on spaces of nonpositive curvature developed by Sturm. We show that the combinatorics of geodesics with a specified fixed endpoint in tree space are determined by the location of the varying endpoint in a certain polyhedral subdivision of tree space. The variance function associated to a finite subset of tree space has a fixed $C^\\infty$ algebraic formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7046","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":"2026-05-18T02:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGvuh8yhkkldDRvJwd6E6Mh9knziaRA7QOupqauXhmQHltgL+Z9P39o4sPBviRqKgyICfvu3YT1gNPTOOtlLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:09:49.572596Z"},"content_sha256":"26d410bcf1a772a48010767d89722a7ddc8d90e2bba8c48efadae55e9bb1ec1b","schema_version":"1.0","event_id":"sha256:26d410bcf1a772a48010767d89722a7ddc8d90e2bba8c48efadae55e9bb1ec1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDNESS2G4SRO56SLARCD7ZTYA4/bundle.json","state_url":"https://pith.science/pith/XDNESS2G4SRO56SLARCD7ZTYA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDNESS2G4SRO56SLARCD7ZTYA4/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":"2026-05-28T14:09:49Z","links":{"resolver":"https://pith.science/pith/XDNESS2G4SRO56SLARCD7ZTYA4","bundle":"https://pith.science/pith/XDNESS2G4SRO56SLARCD7ZTYA4/bundle.json","state":"https://pith.science/pith/XDNESS2G4SRO56SLARCD7ZTYA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDNESS2G4SRO56SLARCD7ZTYA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XDNESS2G4SRO56SLARCD7ZTYA4","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":"508bc3c2a806603cd2013dba5127754fb68ba274c153621bc19821e90403f2d2","cross_cats_sorted":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-11-29T20:39:49Z","title_canon_sha256":"28cd61f29c59086ed64cabca8dbc6a3cf36da9cc1e9f64184bcbd10f2a3a0cce"},"schema_version":"1.0","source":{"id":"1211.7046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7046","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7046v2","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7046","created_at":"2026-05-18T02:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"XDNESS2G4SRO","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XDNESS2G4SRO56SL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XDNESS2G","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:26d410bcf1a772a48010767d89722a7ddc8d90e2bba8c48efadae55e9bb1ec1b","target":"graph","created_at":"2026-05-18T02:58:57Z","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":"This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability measures on spaces of nonpositive curvature developed by Sturm. We show that the combinatorics of geodesics with a specified fixed endpoint in tree space are determined by the location of the varying endpoint in a certain polyhedral subdivision of tree space. The variance function associated to a finite subset of tree space has a fixed $C^\\infty$ algebraic formul","authors_text":"Ezra Miller, J. Scott Provan, Megan Owen","cross_cats":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-11-29T20:39:49Z","title":"Polyhedral computational geometry for averaging metric phylogenetic trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7046","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":"sha256:4f762f2f5ddfd82c393188a6574e7e6496c5f17140771c70bf3555b730100c2a","target":"record","created_at":"2026-05-18T02:58:57Z","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":"508bc3c2a806603cd2013dba5127754fb68ba274c153621bc19821e90403f2d2","cross_cats_sorted":["cs.CG","math.CO","math.ST","q-bio.PE","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-11-29T20:39:49Z","title_canon_sha256":"28cd61f29c59086ed64cabca8dbc6a3cf36da9cc1e9f64184bcbd10f2a3a0cce"},"schema_version":"1.0","source":{"id":"1211.7046","kind":"arxiv","version":2}},"canonical_sha256":"b8da494b46e4a2eefa4b04443fe6780739c19341ec1e0b09a9f3a2753abf823e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8da494b46e4a2eefa4b04443fe6780739c19341ec1e0b09a9f3a2753abf823e","first_computed_at":"2026-05-18T02:58:57.602115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:57.602115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KvAXIf/ruwfRmnbA76JW9bd+kZeC/7hvDedGPxdRvaIIVQf5zwF34JaUBRJzH/MJxXqkiGu5YDF+okv9WLghAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:57.603013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f762f2f5ddfd82c393188a6574e7e6496c5f17140771c70bf3555b730100c2a","sha256:26d410bcf1a772a48010767d89722a7ddc8d90e2bba8c48efadae55e9bb1ec1b"],"state_sha256":"6448132cb09b2b2f0355c5f8451700954953227df94a3976c650b8423554d223"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPW4FcdoiDMthNOfle7NBTSn4y+eTo/cO/3u6c28n8M3tbJMtktu9vPjVLSdr+uofKxMWpWqn5GRrHzHqusCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:09:49.574780Z","bundle_sha256":"f5904ee0d962cef8c957cefc018426f22392ca9658e4078f4aa9c10730da758f"}}