{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OIAILHR6MWPDB4NTBXVGS2VOXG","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":"2c3729e2bb7b2cdf4149f9dbf325a4c7c052ee5442c975cca0739643b4dc9f40","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T13:22:59Z","title_canon_sha256":"f758fa0ef2d871ba22a5eb82b32cdb567695253b36db102c816acaca3a0fa99d"},"schema_version":"1.0","source":{"id":"1708.07390","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07390","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07390v2","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07390","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"OIAILHR6MWPD","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIAILHR6MWPDB4NT","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIAILHR6","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:130d61957e95f1689d93b641e9dcaedb9274ff13609c09b1b3f56db32967d816","target":"graph","created_at":"2026-05-17T23:43:09Z","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":"A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter family of spaces obtained from the data. In applications data often depend on several parameters, and in this case one is interested in studying the persistent homology of a multiparameter family of spaces associated to the data. While the theory of persistent homology for one-parameter families is well-understood, the situation for multiparameter families is mo","authors_text":"Hal Schenck, Heather A. Harrington, Nina Otter, Ulrike Tillmann","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T13:22:59Z","title":"Stratifying multiparameter persistent homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07390","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:fdd8eab43b7289b487a2ba8275727939b4ba43ce67ccb7bd5423a3771637d590","target":"record","created_at":"2026-05-17T23:43:09Z","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":"2c3729e2bb7b2cdf4149f9dbf325a4c7c052ee5442c975cca0739643b4dc9f40","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T13:22:59Z","title_canon_sha256":"f758fa0ef2d871ba22a5eb82b32cdb567695253b36db102c816acaca3a0fa99d"},"schema_version":"1.0","source":{"id":"1708.07390","kind":"arxiv","version":2}},"canonical_sha256":"7200859e3e659e30f1b30dea696aaeb9acd8ef2884240d711931586932ee74ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7200859e3e659e30f1b30dea696aaeb9acd8ef2884240d711931586932ee74ff","first_computed_at":"2026-05-17T23:43:09.607703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:09.607703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9SZsO2+69iOXleAAQYalsqpImvwbIirZE4wzNfD1CQNuSmi2RF2Y1rTZ0xhuBHmj+gCQ5Yg7zhwDFwTjIOSIAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:09.608255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07390","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdd8eab43b7289b487a2ba8275727939b4ba43ce67ccb7bd5423a3771637d590","sha256:130d61957e95f1689d93b641e9dcaedb9274ff13609c09b1b3f56db32967d816"],"state_sha256":"52771ffc7dea4f0a4ba224aac8262534a06a8229c8ada816eb13608e6e01998f"}