{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ACHCKNGMZ5MH72JKRNDE5AV7KZ","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":"e7be3683e2c1b90b4391d59a9ff1ffa22fd8cba7f1c38b8c672293a052f6914a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-15T18:53:57Z","title_canon_sha256":"886e10de49109457138141fa5c26631165acf644be27e2c05d27cdf345ecb353"},"schema_version":"1.0","source":{"id":"1109.3424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3424","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3424v1","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3424","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"ACHCKNGMZ5MH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ACHCKNGMZ5MH72JK","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ACHCKNGM","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:b0dc3c4c7fcd0155f67989a1437453ad1514deb839fa92931ddb89d83e395190","target":"graph","created_at":"2026-05-18T04:12:56Z","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":"In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.","authors_text":"Dominic Rochon, Rajeev Kumar, Romesh Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-15T18:53:57Z","title":"The Fundamental Theorems in the framework of Bicomplex Topological Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3424","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":"sha256:59cc495942d34e4789d459989c6cff471c16625ab4a63cb07f402d87f1c87d0d","target":"record","created_at":"2026-05-18T04:12:56Z","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":"e7be3683e2c1b90b4391d59a9ff1ffa22fd8cba7f1c38b8c672293a052f6914a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-15T18:53:57Z","title_canon_sha256":"886e10de49109457138141fa5c26631165acf644be27e2c05d27cdf345ecb353"},"schema_version":"1.0","source":{"id":"1109.3424","kind":"arxiv","version":1}},"canonical_sha256":"008e2534cccf587fe92a8b464e82bf565d96ac3520a6f00656405d1f069b9dc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"008e2534cccf587fe92a8b464e82bf565d96ac3520a6f00656405d1f069b9dc1","first_computed_at":"2026-05-18T04:12:56.784807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.784807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TBUX11JRtlGtGXBGtClEBSnP5arMLfumUMLmMkRiIIj1Xqv+BVL1eoYeV/fK56+v3ATVmptVAlHB7O7Fe/tSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.785275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59cc495942d34e4789d459989c6cff471c16625ab4a63cb07f402d87f1c87d0d","sha256:b0dc3c4c7fcd0155f67989a1437453ad1514deb839fa92931ddb89d83e395190"],"state_sha256":"8b9a5a8305cdd411f8929fd46e18e430ea652a324e9abdf485151755c91428bd"}