{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OXRN63KV2L47RPK6CBLIKGLDPM","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":"7ec59cc9be7112717bb93444b310ef65ae839484457b3675f0b22336e4a345a3","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2022-08-12T15:08:19Z","title_canon_sha256":"b6d45dabea12cdbf6783e9ec65693aa624038015d0a1d8319e78162accf03114"},"schema_version":"1.0","source":{"id":"2208.06319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.06319","created_at":"2026-07-05T04:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"2208.06319v1","created_at":"2026-07-05T04:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.06319","created_at":"2026-07-05T04:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"OXRN63KV2L47","created_at":"2026-07-05T04:48:03Z"},{"alias_kind":"pith_short_16","alias_value":"OXRN63KV2L47RPK6","created_at":"2026-07-05T04:48:03Z"},{"alias_kind":"pith_short_8","alias_value":"OXRN63KV","created_at":"2026-07-05T04:48:03Z"}],"graph_snapshots":[{"event_id":"sha256:603370c89d6e3bc2fa7e5e39dfee0eda940861080349b79ef1004dfab80b2e96","target":"graph","created_at":"2026-07-05T04:48:03Z","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/2208.06319/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider Gauss sums associated to functions $T\\to \\mathbb R/\\mathbb Z$ which satisfy some sort of quadratic property and investigate their elementary properties. These properties and a Gauss sum formula from the nineteenth century due to Dirichlet give the Milgram Gauss sum formula computing the signature mod $8$ of a non-singular bilinear form over $\\mathbb Q$. Brown derived some results on the signature mod 8 of non-singular integral forms. Kirby and Melvin gave a formula for a generalization of this invariant to possibly non-singular forms and we further generalize it here. The Milgram G","authors_text":"Laurence R. Taylor","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2022-08-12T15:08:19Z","title":"Gauss Sums in Algebra and Topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.06319","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:bb61793548cd05c421fcc64e43cd865f3da5cf1634ce55ab796004c34cd8836a","target":"record","created_at":"2026-07-05T04:48:03Z","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":"7ec59cc9be7112717bb93444b310ef65ae839484457b3675f0b22336e4a345a3","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2022-08-12T15:08:19Z","title_canon_sha256":"b6d45dabea12cdbf6783e9ec65693aa624038015d0a1d8319e78162accf03114"},"schema_version":"1.0","source":{"id":"2208.06319","kind":"arxiv","version":1}},"canonical_sha256":"75e2df6d55d2f9f8bd5e10568519637b308fc213de6d8233dcc3237525bd9be0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75e2df6d55d2f9f8bd5e10568519637b308fc213de6d8233dcc3237525bd9be0","first_computed_at":"2026-07-05T04:48:03.468640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:03.468640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mD8sDf3uFf7gn5Q5cFpvWo1Dx7czUfhYENxgfRocC7tZe9sc7lJuFglIGwFufcdRXEeQMus86uJg146gcwakAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:03.468986Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.06319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb61793548cd05c421fcc64e43cd865f3da5cf1634ce55ab796004c34cd8836a","sha256:603370c89d6e3bc2fa7e5e39dfee0eda940861080349b79ef1004dfab80b2e96"],"state_sha256":"7a2ec49ab3198886d488817d0568c83a299c19916f956fa3d3d1beb966264cf2"}