{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4LTM36SGUKFWYCMG22MNVS5DRZ","short_pith_number":"pith:4LTM36SG","canonical_record":{"source":{"id":"1511.03022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T08:48:16Z","cross_cats_sorted":[],"title_canon_sha256":"eeeac0ae968a9ca2adf26f1e2ea97ba2ebe6110d1419a37a6b2dde0f15bbc280","abstract_canon_sha256":"e8caf571960b4432f968c475f7cbb63681b5c1df48b53aa4ea132c54fcbcda56"},"schema_version":"1.0"},"canonical_sha256":"e2e6cdfa46a28b6c0986d698dacba38e7805d2bfa9dafa5b4b3ead24e1da8259","source":{"kind":"arxiv","id":"1511.03022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03022","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03022v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03022","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"4LTM36SGUKFW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4LTM36SGUKFWYCMG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4LTM36SG","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4LTM36SGUKFWYCMG22MNVS5DRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T08:48:16Z","cross_cats_sorted":[],"title_canon_sha256":"eeeac0ae968a9ca2adf26f1e2ea97ba2ebe6110d1419a37a6b2dde0f15bbc280","abstract_canon_sha256":"e8caf571960b4432f968c475f7cbb63681b5c1df48b53aa4ea132c54fcbcda56"},"schema_version":"1.0"},"canonical_sha256":"e2e6cdfa46a28b6c0986d698dacba38e7805d2bfa9dafa5b4b3ead24e1da8259","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:17.179305Z","signature_b64":"pT6HQa7iQZEqsgGrVpdRoT9fZ6BhmrL4PsgTURFRUIFxlmNN4qNwfRXXitdZa+91jR0BKqiVEITAVUo/rhTrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2e6cdfa46a28b6c0986d698dacba38e7805d2bfa9dafa5b4b3ead24e1da8259","last_reissued_at":"2026-05-18T01:27:17.178756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:17.178756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03022","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vopOnZI+eH0U/jsU+1nUW/G3ZFiE9AGF3oGwtneoZfTbuXpd9BwCtveoU/5zkIbx9LG7IujY5/YNdeJua5sDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:00:59.422385Z"},"content_sha256":"482445c48183bad996a284f5145f7d2528b678964a2a74643ff5693a2a6f6c7f","schema_version":"1.0","event_id":"sha256:482445c48183bad996a284f5145f7d2528b678964a2a74643ff5693a2a6f6c7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4LTM36SGUKFWYCMG22MNVS5DRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tannakian twists of quadratic forms and orthogonal Nori motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baptiste Morin, Philippe Cassou-Nogu\\`es","submitted_at":"2015-11-10T08:48:16Z","abstract_excerpt":"We revisit classical results of Serre, Fr\\\"ohlich and Saito in the theory of quadratic forms. Given a neutral Tannakian category $(\\mathcal{T},\\omega)$ over a field $k$ of characteristic $\\neq 2$, another fiber functor $\\eta$ over a $k$-scheme $X$ and an orthogonal object $(M,q)$ in $\\mathcal{T}$, we show formulas relating the torsor $\\bf{Isom}^{\\otimes}(\\omega,\\eta)$ to Hasse-Witt invariants of the quadratic space $\\omega(M,q)$ and the symmetric bundle $\\eta(M,q)$. We apply this result to various neutral Tannakian categories arising in different contexts. We first consider Nori's Tannakian ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03022","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnOCOHu5IsKgJK7ServzYCaMirAVDvSeRCvSHHTsKqGe5a01cb1b9ROArFwh/qfAHD2op8oiTKMw37eon1oDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:00:59.423061Z"},"content_sha256":"bbc50fa4f25c7fc09e1d6e12e2aa69b56f163c585729eb0f29fdf1caebd8ef99","schema_version":"1.0","event_id":"sha256:bbc50fa4f25c7fc09e1d6e12e2aa69b56f163c585729eb0f29fdf1caebd8ef99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/bundle.json","state_url":"https://pith.science/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T11:00:59Z","links":{"resolver":"https://pith.science/pith/4LTM36SGUKFWYCMG22MNVS5DRZ","bundle":"https://pith.science/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/bundle.json","state":"https://pith.science/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4LTM36SGUKFWYCMG22MNVS5DRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4LTM36SGUKFWYCMG22MNVS5DRZ","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":"e8caf571960b4432f968c475f7cbb63681b5c1df48b53aa4ea132c54fcbcda56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T08:48:16Z","title_canon_sha256":"eeeac0ae968a9ca2adf26f1e2ea97ba2ebe6110d1419a37a6b2dde0f15bbc280"},"schema_version":"1.0","source":{"id":"1511.03022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03022","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03022v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03022","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"4LTM36SGUKFW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4LTM36SGUKFWYCMG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4LTM36SG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:bbc50fa4f25c7fc09e1d6e12e2aa69b56f163c585729eb0f29fdf1caebd8ef99","target":"graph","created_at":"2026-05-18T01:27:17Z","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 revisit classical results of Serre, Fr\\\"ohlich and Saito in the theory of quadratic forms. Given a neutral Tannakian category $(\\mathcal{T},\\omega)$ over a field $k$ of characteristic $\\neq 2$, another fiber functor $\\eta$ over a $k$-scheme $X$ and an orthogonal object $(M,q)$ in $\\mathcal{T}$, we show formulas relating the torsor $\\bf{Isom}^{\\otimes}(\\omega,\\eta)$ to Hasse-Witt invariants of the quadratic space $\\omega(M,q)$ and the symmetric bundle $\\eta(M,q)$. We apply this result to various neutral Tannakian categories arising in different contexts. We first consider Nori's Tannakian ca","authors_text":"Baptiste Morin, Philippe Cassou-Nogu\\`es","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T08:48:16Z","title":"Tannakian twists of quadratic forms and orthogonal Nori motives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03022","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":"sha256:482445c48183bad996a284f5145f7d2528b678964a2a74643ff5693a2a6f6c7f","target":"record","created_at":"2026-05-18T01:27:17Z","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":"e8caf571960b4432f968c475f7cbb63681b5c1df48b53aa4ea132c54fcbcda56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T08:48:16Z","title_canon_sha256":"eeeac0ae968a9ca2adf26f1e2ea97ba2ebe6110d1419a37a6b2dde0f15bbc280"},"schema_version":"1.0","source":{"id":"1511.03022","kind":"arxiv","version":1}},"canonical_sha256":"e2e6cdfa46a28b6c0986d698dacba38e7805d2bfa9dafa5b4b3ead24e1da8259","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2e6cdfa46a28b6c0986d698dacba38e7805d2bfa9dafa5b4b3ead24e1da8259","first_computed_at":"2026-05-18T01:27:17.178756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:17.178756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pT6HQa7iQZEqsgGrVpdRoT9fZ6BhmrL4PsgTURFRUIFxlmNN4qNwfRXXitdZa+91jR0BKqiVEITAVUo/rhTrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:17.179305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:482445c48183bad996a284f5145f7d2528b678964a2a74643ff5693a2a6f6c7f","sha256:bbc50fa4f25c7fc09e1d6e12e2aa69b56f163c585729eb0f29fdf1caebd8ef99"],"state_sha256":"27fd79cca7317e11d01a8717555ead3b5d6f50898b35b75ff9c3c17c0c6baabf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FB/6Btc5os2yv2x6EvMVeFExMcEdqUCyt2VmKvlM2HVYJ+f6prpZZHVDJy5OdT1kJGxhZtvZYhe7wqbk99cxDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:00:59.426472Z","bundle_sha256":"d506e9b6e29dc7072cd3fad33e4b8f1d53176c7e383cd2bcb665223c9677e1ac"}}