{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5DDS2YNLKWTA3XHHPJERYX6EA6","short_pith_number":"pith:5DDS2YNL","canonical_record":{"source":{"id":"1711.06585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-17T15:16:44Z","cross_cats_sorted":[],"title_canon_sha256":"70954da38afe2741cf082b6440fff266e08f836eca34f59aac001061074251b3","abstract_canon_sha256":"dfa4ce6d81166931762361bfaac0f194bd0e1ce989373b4939d1bf14ad85d81f"},"schema_version":"1.0"},"canonical_sha256":"e8c72d61ab55a60ddce77a491c5fc40798cb6b24c76c654b2dad79a1de95e077","source":{"kind":"arxiv","id":"1711.06585","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06585","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06585v2","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06585","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"5DDS2YNLKWTA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5DDS2YNLKWTA3XHH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5DDS2YNL","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5DDS2YNLKWTA3XHHPJERYX6EA6","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-17T15:16:44Z","cross_cats_sorted":[],"title_canon_sha256":"70954da38afe2741cf082b6440fff266e08f836eca34f59aac001061074251b3","abstract_canon_sha256":"dfa4ce6d81166931762361bfaac0f194bd0e1ce989373b4939d1bf14ad85d81f"},"schema_version":"1.0"},"canonical_sha256":"e8c72d61ab55a60ddce77a491c5fc40798cb6b24c76c654b2dad79a1de95e077","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:53.351079Z","signature_b64":"PsIw5r5ZQ0p5PPPaeLaALOTBRkPu2uL1OOSmEP24NAALxLgtoy9Gyec2HFSJenW2e7sUjTPUfRLGSA3vZaxwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c72d61ab55a60ddce77a491c5fc40798cb6b24c76c654b2dad79a1de95e077","last_reissued_at":"2026-05-18T00:19:53.350277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:53.350277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06585","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5qgYxl94dFBUxKWvzit8MKB6An2MrSY7oaEljHpgDXyK3Mlo8ux7FivI/B/zuTjGxEd3oFwIegtmwohgTqffBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:10:49.539189Z"},"content_sha256":"c38cf3a79fb5d79c4279726f972a41dcf155207b4da2e624f4bc5215e8d16228","schema_version":"1.0","event_id":"sha256:c38cf3a79fb5d79c4279726f972a41dcf155207b4da2e624f4bc5215e8d16228"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5DDS2YNLKWTA3XHHPJERYX6EA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splitting families in Galois cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cyril Demarche, Mathieu Florence","submitted_at":"2017-11-17T15:16:44Z","abstract_excerpt":"Let $k$ be a field, with absolute Galois group $\\Gamma$. Let $A/k$ be a finite \\'etale group scheme of multiplicative type, i.e. a discrete $\\Gamma$-module. Let $n \\geq 2$ be an integer, and let $x \\in H^n(k,A)$ be a cohomology class. We show that there exists a countable set $I$, and a familiy $(X_i)_{i \\in I}$ of (smooth, geometrically integral) $k$-varieties, such that the following holds. For any field extension $l/k$, the restriction of $x$ vanishes in $H^n(l,A)$ if and only if (at least) one of the $X_i$'s has an $l$-point. We moreover show that the $X_i$'s can be made into an ind-variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06585","kind":"arxiv","version":2},"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":"2026-05-18T00:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2uJT0g3YxkYVWDF9+Z2j9CHwEw5WcVati1517+YgkVhhLsGm01glAjyTiK8o4oe3idOsf3dfsy9lrprbSwaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:10:49.539854Z"},"content_sha256":"89c2cf615679138154be514fc7030e949fe63b7b184cdcac6e39a3d748a04e1e","schema_version":"1.0","event_id":"sha256:89c2cf615679138154be514fc7030e949fe63b7b184cdcac6e39a3d748a04e1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/bundle.json","state_url":"https://pith.science/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/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":"2026-06-04T07:10:49Z","links":{"resolver":"https://pith.science/pith/5DDS2YNLKWTA3XHHPJERYX6EA6","bundle":"https://pith.science/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/bundle.json","state":"https://pith.science/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DDS2YNLKWTA3XHHPJERYX6EA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5DDS2YNLKWTA3XHHPJERYX6EA6","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":"dfa4ce6d81166931762361bfaac0f194bd0e1ce989373b4939d1bf14ad85d81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-17T15:16:44Z","title_canon_sha256":"70954da38afe2741cf082b6440fff266e08f836eca34f59aac001061074251b3"},"schema_version":"1.0","source":{"id":"1711.06585","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06585","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06585v2","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06585","created_at":"2026-05-18T00:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"5DDS2YNLKWTA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5DDS2YNLKWTA3XHH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5DDS2YNL","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:89c2cf615679138154be514fc7030e949fe63b7b184cdcac6e39a3d748a04e1e","target":"graph","created_at":"2026-05-18T00:19:53Z","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":"Let $k$ be a field, with absolute Galois group $\\Gamma$. Let $A/k$ be a finite \\'etale group scheme of multiplicative type, i.e. a discrete $\\Gamma$-module. Let $n \\geq 2$ be an integer, and let $x \\in H^n(k,A)$ be a cohomology class. We show that there exists a countable set $I$, and a familiy $(X_i)_{i \\in I}$ of (smooth, geometrically integral) $k$-varieties, such that the following holds. For any field extension $l/k$, the restriction of $x$ vanishes in $H^n(l,A)$ if and only if (at least) one of the $X_i$'s has an $l$-point. We moreover show that the $X_i$'s can be made into an ind-variet","authors_text":"Cyril Demarche, Mathieu Florence","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-17T15:16:44Z","title":"Splitting families in Galois cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06585","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:c38cf3a79fb5d79c4279726f972a41dcf155207b4da2e624f4bc5215e8d16228","target":"record","created_at":"2026-05-18T00:19:53Z","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":"dfa4ce6d81166931762361bfaac0f194bd0e1ce989373b4939d1bf14ad85d81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-17T15:16:44Z","title_canon_sha256":"70954da38afe2741cf082b6440fff266e08f836eca34f59aac001061074251b3"},"schema_version":"1.0","source":{"id":"1711.06585","kind":"arxiv","version":2}},"canonical_sha256":"e8c72d61ab55a60ddce77a491c5fc40798cb6b24c76c654b2dad79a1de95e077","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c72d61ab55a60ddce77a491c5fc40798cb6b24c76c654b2dad79a1de95e077","first_computed_at":"2026-05-18T00:19:53.350277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:53.350277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsIw5r5ZQ0p5PPPaeLaALOTBRkPu2uL1OOSmEP24NAALxLgtoy9Gyec2HFSJenW2e7sUjTPUfRLGSA3vZaxwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:53.351079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06585","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c38cf3a79fb5d79c4279726f972a41dcf155207b4da2e624f4bc5215e8d16228","sha256:89c2cf615679138154be514fc7030e949fe63b7b184cdcac6e39a3d748a04e1e"],"state_sha256":"e21017d5050861cc0408f5634c4e9f9d1c921bb3c3e87d897353950a4a24b74e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kh6kPeVvF3aJw4ONkXugvlAPXZXbP5V4WxuLsCuhSXcnwLbyCcfig2X0G/xRflcx537RdlfzknrxL9aOS3a1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T07:10:49.543139Z","bundle_sha256":"c1ae919de00ff6b1adb4c02598ab499d1c1aee0a753fc11dd33afe43e7c1355f"}}