{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SFC7MKP4ZDANVMIRCWH2PQ5QP3","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":"5bc6984192015ae35bcc2b537e8e665932ebd9233f8d7a02678a44100c8f95de","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T19:27:54Z","title_canon_sha256":"73270dee64af279250bf2c0822610e94822aca02e0db6517135e9ad2190cd1d8"},"schema_version":"1.0","source":{"id":"1309.1451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1451","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1451v2","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1451","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"SFC7MKP4ZDAN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SFC7MKP4ZDANVMIR","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SFC7MKP4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c30238472026677b111b91fb20cfe6136dc2ddce286767a618ba25a7933054a4","target":"graph","created_at":"2026-05-18T02:48:46Z","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":"We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide a survey on possible applications in general relativity in light of the limitations of distribution theory.","authors_text":"Clemens S\\\"amann, Eduard A. Nigsch","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T19:27:54Z","title":"Global algebras of nonlinear generalized functions with applications in general relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1451","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":"sha256:6c680a7aa5350a07efceead17ed2f49294a3d405ecd222e6d9353ed275ce45f2","target":"record","created_at":"2026-05-18T02:48:46Z","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":"5bc6984192015ae35bcc2b537e8e665932ebd9233f8d7a02678a44100c8f95de","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-05T19:27:54Z","title_canon_sha256":"73270dee64af279250bf2c0822610e94822aca02e0db6517135e9ad2190cd1d8"},"schema_version":"1.0","source":{"id":"1309.1451","kind":"arxiv","version":2}},"canonical_sha256":"9145f629fcc8c0dab111158fa7c3b07eced57267bb18294c69a89f1461787e33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9145f629fcc8c0dab111158fa7c3b07eced57267bb18294c69a89f1461787e33","first_computed_at":"2026-05-18T02:48:46.834516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:46.834516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7iNCxH8IQkFTMUhaGFnavBv5INNVruxjot7ZHjQ4r/8Zi5uqv88+gbbOzNURCdH3BiJG2a7Ppsbs4ZpGFoysAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:46.835349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c680a7aa5350a07efceead17ed2f49294a3d405ecd222e6d9353ed275ce45f2","sha256:c30238472026677b111b91fb20cfe6136dc2ddce286767a618ba25a7933054a4"],"state_sha256":"f0fc07df94616e3198260eff4a578d8970b47dbf10750f0d52c0f650a3eda988"}