{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CSAMAGDYJPT6BU2WXPMIILYSS4","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":"e989c206770ad69840ad8e3f3d312e8b35f2b03ecbdcbeeee1a17dbf06637e5c","cross_cats_sorted":["math.AC","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-11-25T09:51:04Z","title_canon_sha256":"a805b6302859bf23b8a1d26ea75a0643fd4e31769454f3a4aaf49604716e138a"},"schema_version":"1.0","source":{"id":"2411.16235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16235","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16235v1","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16235","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"CSAMAGDYJPT6","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_16","alias_value":"CSAMAGDYJPT6BU2W","created_at":"2026-07-05T09:40:06Z"},{"alias_kind":"pith_short_8","alias_value":"CSAMAGDY","created_at":"2026-07-05T09:40:06Z"}],"graph_snapshots":[{"event_id":"sha256:554716c9db8e14f3b7980bcd648a042108183b1f16c0465779b2b76f43b4264e","target":"graph","created_at":"2026-07-05T09:40:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.16235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By utilizing domain theory, we generalize the notion of an ephemeral module to the so-called continuous posets. We investigate the quotient category of persistence modules by the Serre subcategory of ephemeral modules and show that it is equivalent to the category of sheaves on the Scott topology. Furthermore, we study the metric properties of persistence modules via this equivalence.","authors_text":"Eero Hyry, Manu Harsu","cross_cats":["math.AC","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-11-25T09:51:04Z","title":"Ephemeral Modules and Scott Sheaves on a Continuous Poset"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16235","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":"sha256:9b98956463b1eb8bc922424ddaa4cf944fd39883da87a78d510f8cbd00df3c6f","target":"record","created_at":"2026-07-05T09:40:06Z","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":"e989c206770ad69840ad8e3f3d312e8b35f2b03ecbdcbeeee1a17dbf06637e5c","cross_cats_sorted":["math.AC","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-11-25T09:51:04Z","title_canon_sha256":"a805b6302859bf23b8a1d26ea75a0643fd4e31769454f3a4aaf49604716e138a"},"schema_version":"1.0","source":{"id":"2411.16235","kind":"arxiv","version":1}},"canonical_sha256":"1480c018784be7e0d356bbd8842f1297191846b8f1e9483721159b5224f41361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1480c018784be7e0d356bbd8842f1297191846b8f1e9483721159b5224f41361","first_computed_at":"2026-07-05T09:40:06.361211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:06.361211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jamO70f4ir6Tt0jaR9zq/qcg18wxry3dGB729WXnW3gepNpOT+dCGzr2xakHp88jNMcoX5F5Qo3ZsNa7PNRYCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:06.361689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b98956463b1eb8bc922424ddaa4cf944fd39883da87a78d510f8cbd00df3c6f","sha256:554716c9db8e14f3b7980bcd648a042108183b1f16c0465779b2b76f43b4264e"],"state_sha256":"90050493b5717cf948bf70d5083183d9f2dfc9263658e3d6e1e738b036abf82a"}