{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4KYTAL3K2VR6M5ULREN3VWPFM7","short_pith_number":"pith:4KYTAL3K","canonical_record":{"source":{"id":"1504.06026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","cross_cats_sorted":[],"title_canon_sha256":"ba6550f5131ad7cb998c05031159596faa5ed29299617dc2ea20c717c33428b3","abstract_canon_sha256":"026d43725e8b6897504f551ba777627720e616db606963b2890b4bf018d0158d"},"schema_version":"1.0"},"canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","source":{"kind":"arxiv","id":"1504.06026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06026","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06026v1","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06026","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"4KYTAL3K2VR6","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KYTAL3K2VR6M5UL","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KYTAL3K","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4KYTAL3K2VR6M5ULREN3VWPFM7","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","cross_cats_sorted":[],"title_canon_sha256":"ba6550f5131ad7cb998c05031159596faa5ed29299617dc2ea20c717c33428b3","abstract_canon_sha256":"026d43725e8b6897504f551ba777627720e616db606963b2890b4bf018d0158d"},"schema_version":"1.0"},"canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:02.851769Z","signature_b64":"g6eZzRB0tl8CbU030/ldAVPuPZiTHqBbopryBUVBvj6LYXhnEEecLDbL6XZHorcZ8L4N0t/dmZyXoCnwgcWuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","last_reissued_at":"2026-05-18T02:18:02.851106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:02.851106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06026","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":"2026-05-18T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXzSq0lSAY6Lx9Sudjh2XkpwLFa7WkuuWCX16lYshvxf13OYBynuL2yOUhKGq5Yevv9vuwxOexLqb06gzgDaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:14.038933Z"},"content_sha256":"c2daf86bd9a1a4341d14be0bd9b924e859eaacb0a50b74102949f54e92c48d86","schema_version":"1.0","event_id":"sha256:c2daf86bd9a1a4341d14be0bd9b924e859eaacb0a50b74102949f54e92c48d86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4KYTAL3K2VR6M5ULREN3VWPFM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphical Fermat's Principle and Triangle-Free Graph Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Han Liu, Junwei Lu","submitted_at":"2015-04-23T02:28:16Z","abstract_excerpt":"We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06026","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":"2026-05-18T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37NdR3s3kxlo+L9UlFYu8mp14ydsdlVq91U/fIU2KvpBrhe5jU20GHGTbB3B0e9Ia3TMsFGIBP9TZsu9OedFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:14.039719Z"},"content_sha256":"f7bcf505ce34924c905973447dda2cf05ff9725dfa95ba36da5564c23297ac69","schema_version":"1.0","event_id":"sha256:f7bcf505ce34924c905973447dda2cf05ff9725dfa95ba36da5564c23297ac69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/bundle.json","state_url":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/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":"2026-05-26T13:14:14Z","links":{"resolver":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7","bundle":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/bundle.json","state":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4KYTAL3K2VR6M5ULREN3VWPFM7","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":"026d43725e8b6897504f551ba777627720e616db606963b2890b4bf018d0158d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","title_canon_sha256":"ba6550f5131ad7cb998c05031159596faa5ed29299617dc2ea20c717c33428b3"},"schema_version":"1.0","source":{"id":"1504.06026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06026","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06026v1","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06026","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"4KYTAL3K2VR6","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KYTAL3K2VR6M5UL","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KYTAL3K","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:f7bcf505ce34924c905973447dda2cf05ff9725dfa95ba36da5564c23297ac69","target":"graph","created_at":"2026-05-18T02:18:02Z","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":"We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover ","authors_text":"Han Liu, Junwei Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","title":"Graphical Fermat's Principle and Triangle-Free Graph Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06026","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:c2daf86bd9a1a4341d14be0bd9b924e859eaacb0a50b74102949f54e92c48d86","target":"record","created_at":"2026-05-18T02:18:02Z","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":"026d43725e8b6897504f551ba777627720e616db606963b2890b4bf018d0158d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","title_canon_sha256":"ba6550f5131ad7cb998c05031159596faa5ed29299617dc2ea20c717c33428b3"},"schema_version":"1.0","source":{"id":"1504.06026","kind":"arxiv","version":1}},"canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","first_computed_at":"2026-05-18T02:18:02.851106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:02.851106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g6eZzRB0tl8CbU030/ldAVPuPZiTHqBbopryBUVBvj6LYXhnEEecLDbL6XZHorcZ8L4N0t/dmZyXoCnwgcWuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:02.851769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2daf86bd9a1a4341d14be0bd9b924e859eaacb0a50b74102949f54e92c48d86","sha256:f7bcf505ce34924c905973447dda2cf05ff9725dfa95ba36da5564c23297ac69"],"state_sha256":"1f899ecdf15e6d5858bcffdc254cebe559b2c3766b5a1b396762d89773d5a85e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ThbAh5NClmgBGhkr8xgYZydXRMPW2sRfYrlyRVBqp4FFoA1qCbfDuK8NrSzI1kyo+v2R3m8PtI9/ox1hSIJ0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:14:14.043649Z","bundle_sha256":"b69a50ba2a63410019eb7a89aeb72afdf6dd2b2b79926339b678eabccfdea241"}}