{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LLY7IEWAIV7TB53AH2KF3XKBK6","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":"22dcf2b9a89afa9884e521eb8dbd1111435c424f197418d7320284e7214baabf","cross_cats_sorted":["math.AP","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2024-11-26T21:19:41Z","title_canon_sha256":"609a88b9945e14b8d1e94b04a96eac7abfc96c5818bab6e538e9b4057e249436"},"schema_version":"1.0","source":{"id":"2411.17890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17890","created_at":"2026-07-05T09:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17890v1","created_at":"2026-07-05T09:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17890","created_at":"2026-07-05T09:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"LLY7IEWAIV7T","created_at":"2026-07-05T09:41:08Z"},{"alias_kind":"pith_short_16","alias_value":"LLY7IEWAIV7TB53A","created_at":"2026-07-05T09:41:08Z"},{"alias_kind":"pith_short_8","alias_value":"LLY7IEWA","created_at":"2026-07-05T09:41:08Z"}],"graph_snapshots":[{"event_id":"sha256:1593bd700ba2c23b2cbb6e0b548fbb1cfa9bd057092010c31fb6deb270a6b1b7","target":"graph","created_at":"2026-07-05T09:41:08Z","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/2411.17890/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a concise development of the well-studied theory of trace class operators on infinite dimensional (separable) Hilbert spaces suitable for an advanced undergraduate, as well as a construction of the inverse Laplacian on closed manifolds. With these developments acting as prerequisite, we present original trace computations involving the inverse Laplacian on the (flat) torus, generalizing computations done by R. Grady and O. Gwilliam within the context of topological quantum field theory.","authors_text":"Bryce Morrow","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2024-11-26T21:19:41Z","title":"The Inverse Laplacian: Traces in Infinite Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17890","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":"sha256:375f00bf0c8e710ed68761cfb45bbb348043bb52eefbfb9241c839ad26b4b95b","target":"record","created_at":"2026-07-05T09:41:08Z","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":"22dcf2b9a89afa9884e521eb8dbd1111435c424f197418d7320284e7214baabf","cross_cats_sorted":["math.AP","math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2024-11-26T21:19:41Z","title_canon_sha256":"609a88b9945e14b8d1e94b04a96eac7abfc96c5818bab6e538e9b4057e249436"},"schema_version":"1.0","source":{"id":"2411.17890","kind":"arxiv","version":1}},"canonical_sha256":"5af1f412c0457f30f7603e945ddd415786aae565832e64dfce35ead0a1339929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af1f412c0457f30f7603e945ddd415786aae565832e64dfce35ead0a1339929","first_computed_at":"2026-07-05T09:41:08.571422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:08.571422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VBitNY55Kiee/McegOa5mBp4VffMX1w2DPl0Cyk6UrrXpbG2YGkrkCK7SI/VUEiX/SlmleiuUjWm2Jw5iH0DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:08.571809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.17890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:375f00bf0c8e710ed68761cfb45bbb348043bb52eefbfb9241c839ad26b4b95b","sha256:1593bd700ba2c23b2cbb6e0b548fbb1cfa9bd057092010c31fb6deb270a6b1b7"],"state_sha256":"6f14df83702e8571a2c75f3372b37c949edf1c35e63ace2084e6e20d1abca8c7"}