{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YE3YFY7JRKOLJ4FEG5NTADHTAU","short_pith_number":"pith:YE3YFY7J","canonical_record":{"source":{"id":"0905.4384","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-27T11:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"b7a936aa5b1a0c95e4cf315b2e330aa31a211ce7a0ec68c245bc68164686a50f","abstract_canon_sha256":"4de3c46a850edd41370641990d386bf300ed0c13dd1d6bbed3cc1673fb7c0ec6"},"schema_version":"1.0"},"canonical_sha256":"c13782e3e98a9cb4f0a4375b300cf3052ae814f39d58d67ea83601e0dc6244c9","source":{"kind":"arxiv","id":"0905.4384","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4384","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4384v4","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4384","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"YE3YFY7JRKOL","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YE3YFY7JRKOLJ4FE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YE3YFY7J","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YE3YFY7JRKOLJ4FEG5NTADHTAU","target":"record","payload":{"canonical_record":{"source":{"id":"0905.4384","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-27T11:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"b7a936aa5b1a0c95e4cf315b2e330aa31a211ce7a0ec68c245bc68164686a50f","abstract_canon_sha256":"4de3c46a850edd41370641990d386bf300ed0c13dd1d6bbed3cc1673fb7c0ec6"},"schema_version":"1.0"},"canonical_sha256":"c13782e3e98a9cb4f0a4375b300cf3052ae814f39d58d67ea83601e0dc6244c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:52.705837Z","signature_b64":"0o13oJL1UHz01uUIS7kAioZYiTm9kZ6qLeDZAzkDJribUo9QCXA5pILafm1Fb7DlcBAGDiCzcUn+6r6H2qD/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c13782e3e98a9cb4f0a4375b300cf3052ae814f39d58d67ea83601e0dc6244c9","last_reissued_at":"2026-05-18T02:17:52.705146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:52.705146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.4384","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NiUtAR/iyal10IbtPKTYbfYIDeyWsikf1nIPVpKxxuFedwiFd5J9dJZzfevTRmxS70NUroUIqb7rySCUUtD2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:02:32.695477Z"},"content_sha256":"6a9b8bd442bcd7218054c2876a48454dd33a656b7d73ce73ac2cc1aad8768cc9","schema_version":"1.0","event_id":"sha256:6a9b8bd442bcd7218054c2876a48454dd33a656b7d73ce73ac2cc1aad8768cc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YE3YFY7JRKOLJ4FEG5NTADHTAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motivic construction of cohomological invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nikita Semenov","submitted_at":"2009-05-27T11:47:05Z","abstract_excerpt":"Let G be a group of type E8 of compact type over the field of rational numbers, let K be a field of characteristic 0, and q the 5-fold Pfister form which is the sum of 32 squares. J-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that G is split over K if and only if q is hyperbolic over K?\n  In the present article we construct a cohomological invariant of degree 5 for groups of type E8 with trivial Rost invariant over any field k of characteristic 0, and putting the field of rational numbers for k answer positively this question of Serre. Aside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4384","kind":"arxiv","version":4},"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":"2026-05-18T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FX7dFdQbt6kceSqLRt6PrDQF3RbBEi/V04GJpBxg7QBn9WtBumJh/13XDHTnCWe5YSAkjzb8+j38fjEbHArBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:02:32.695834Z"},"content_sha256":"0b2beb963edd72f63dbea7b1db045a136f51d28edcfedde1fe7833ef6f325323","schema_version":"1.0","event_id":"sha256:0b2beb963edd72f63dbea7b1db045a136f51d28edcfedde1fe7833ef6f325323"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/bundle.json","state_url":"https://pith.science/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/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":"2026-06-05T08:02:32Z","links":{"resolver":"https://pith.science/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU","bundle":"https://pith.science/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/bundle.json","state":"https://pith.science/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YE3YFY7JRKOLJ4FEG5NTADHTAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YE3YFY7JRKOLJ4FEG5NTADHTAU","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":"4de3c46a850edd41370641990d386bf300ed0c13dd1d6bbed3cc1673fb7c0ec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-27T11:47:05Z","title_canon_sha256":"b7a936aa5b1a0c95e4cf315b2e330aa31a211ce7a0ec68c245bc68164686a50f"},"schema_version":"1.0","source":{"id":"0905.4384","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4384","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4384v4","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4384","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"YE3YFY7JRKOL","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YE3YFY7JRKOLJ4FE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YE3YFY7J","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:0b2beb963edd72f63dbea7b1db045a136f51d28edcfedde1fe7833ef6f325323","target":"graph","created_at":"2026-05-18T02:17:52Z","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 G be a group of type E8 of compact type over the field of rational numbers, let K be a field of characteristic 0, and q the 5-fold Pfister form which is the sum of 32 squares. J-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that G is split over K if and only if q is hyperbolic over K?\n  In the present article we construct a cohomological invariant of degree 5 for groups of type E8 with trivial Rost invariant over any field k of characteristic 0, and putting the field of rational numbers for k answer positively this question of Serre. Aside","authors_text":"Nikita Semenov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-27T11:47:05Z","title":"Motivic construction of cohomological invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4384","kind":"arxiv","version":4},"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":"sha256:6a9b8bd442bcd7218054c2876a48454dd33a656b7d73ce73ac2cc1aad8768cc9","target":"record","created_at":"2026-05-18T02:17:52Z","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":"4de3c46a850edd41370641990d386bf300ed0c13dd1d6bbed3cc1673fb7c0ec6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-27T11:47:05Z","title_canon_sha256":"b7a936aa5b1a0c95e4cf315b2e330aa31a211ce7a0ec68c245bc68164686a50f"},"schema_version":"1.0","source":{"id":"0905.4384","kind":"arxiv","version":4}},"canonical_sha256":"c13782e3e98a9cb4f0a4375b300cf3052ae814f39d58d67ea83601e0dc6244c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c13782e3e98a9cb4f0a4375b300cf3052ae814f39d58d67ea83601e0dc6244c9","first_computed_at":"2026-05-18T02:17:52.705146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:52.705146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0o13oJL1UHz01uUIS7kAioZYiTm9kZ6qLeDZAzkDJribUo9QCXA5pILafm1Fb7DlcBAGDiCzcUn+6r6H2qD/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:52.705837Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4384","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a9b8bd442bcd7218054c2876a48454dd33a656b7d73ce73ac2cc1aad8768cc9","sha256:0b2beb963edd72f63dbea7b1db045a136f51d28edcfedde1fe7833ef6f325323"],"state_sha256":"e61c0d354b185c9ee344a9c332eba58ab802fb2999902ed690e0c55d5cbb8960"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+UPpgy13e9dpSNl/HYgYyxlHjFW4JxIfTw48eGgOX7xL7FwzPZtacsyvyK6DN2XOyA7pcO9DhCgM/HjTkMIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:02:32.697690Z","bundle_sha256":"e67b5aa769c2a78f5a5ae7a40b96a7429f3ca3e7c990ebcf9e536853da1d5f8e"}}