{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QDAVXGP3GX3LUV6ZJ2I7VLOS7O","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":"5b589456431a9599b0f305525dcc395e4e44ba84931123817f00f0d336d30f66","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-11T08:46:19Z","title_canon_sha256":"003c62148d20caad22693ee5db1dc5aa46641de7ac9e5651198a9be8bb4d88d6"},"schema_version":"1.0","source":{"id":"2508.07761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07761","created_at":"2026-07-05T11:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07761v1","created_at":"2026-07-05T11:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07761","created_at":"2026-07-05T11:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"QDAVXGP3GX3L","created_at":"2026-07-05T11:51:51Z"},{"alias_kind":"pith_short_16","alias_value":"QDAVXGP3GX3LUV6Z","created_at":"2026-07-05T11:51:51Z"},{"alias_kind":"pith_short_8","alias_value":"QDAVXGP3","created_at":"2026-07-05T11:51:51Z"}],"graph_snapshots":[{"event_id":"sha256:24297616dfd8cad057cf95b25320bfc8adc2e247fb2a0c4072c14a0266958434","target":"graph","created_at":"2026-07-05T11:51:51Z","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/2508.07761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of operators arising from quadratic forms. A major conceptual perspective is the correspondence to signed Schr\\\"odinger operators unveiling the Forman curvature. The main results are criteria for essential self-adjointness via lower bounded Forman curvature and a Gaffney type result via completeness. Finally, we study spectral relations between these Laplacians","authors_text":"Matthias Keller, Philipp Bartmann","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-11T08:46:19Z","title":"On Hodge Laplacians on General Simplicial Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07761","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":"sha256:45c3305bd79247f95103de6a4a67586841bbd2b6d20914bdaf408f45679401ba","target":"record","created_at":"2026-07-05T11:51:51Z","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":"5b589456431a9599b0f305525dcc395e4e44ba84931123817f00f0d336d30f66","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-08-11T08:46:19Z","title_canon_sha256":"003c62148d20caad22693ee5db1dc5aa46641de7ac9e5651198a9be8bb4d88d6"},"schema_version":"1.0","source":{"id":"2508.07761","kind":"arxiv","version":1}},"canonical_sha256":"80c15b99fb35f6ba57d94e91faadd2fb81f12ffa9f4718ca107fcfaaa1f156cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80c15b99fb35f6ba57d94e91faadd2fb81f12ffa9f4718ca107fcfaaa1f156cc","first_computed_at":"2026-07-05T11:51:51.792939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:51:51.792939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mTTa+icvlpN7wTJZ3Gbi64KJzEhqtPFYXOKr10aKqFsUx7DwTAIbjMWpW4tbJsIbzU7HaVzTR571txEaWnkAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:51:51.793372Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.07761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45c3305bd79247f95103de6a4a67586841bbd2b6d20914bdaf408f45679401ba","sha256:24297616dfd8cad057cf95b25320bfc8adc2e247fb2a0c4072c14a0266958434"],"state_sha256":"6e609fcc82bbfc5e13a6cd037ad2ccd5d324dcc84133bdb6b99757818171dfe2"}