{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EXOXMHW7BLGHHA5IEFLQDJYAJM","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":"29a453fced5c6558e8c231c0515027e56e633ef39377c3d05da285a3aad35dff","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2007-03-29T11:58:12Z","title_canon_sha256":"41cc9182680eb1aff948fdc8788eb456437cddd87da5b65d1b25d54041799c6f"},"schema_version":"1.0","source":{"id":"math/0703877","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703877","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703877v2","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703877","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"EXOXMHW7BLGH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EXOXMHW7BLGHHA5I","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EXOXMHW7","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:d2d7d103b629a5b84498855a298c068cdea6fa57f5bacd90bf0996c333a92102","target":"graph","created_at":"2026-05-17T23:45:55Z","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":"Using the identification of sections of the Galois group of the ground field into the arithmetic fundamental group with neutral fiber functors of the category of finite connections, we define the \"packets\" in Grothendieck's section conjecture and show their properties predicted by him.","authors_text":"H\\'el\\`ene Esnault, Ph\\`ung H\\^o Hai","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-03-29T11:58:12Z","title":"Packets in Grothendieck's Section Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703877","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":"sha256:08c23f88ab603c70ff2d2f9e0247c2958cdcfc1177e29aa035b2e75c75767c8d","target":"record","created_at":"2026-05-17T23:45:55Z","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":"29a453fced5c6558e8c231c0515027e56e633ef39377c3d05da285a3aad35dff","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2007-03-29T11:58:12Z","title_canon_sha256":"41cc9182680eb1aff948fdc8788eb456437cddd87da5b65d1b25d54041799c6f"},"schema_version":"1.0","source":{"id":"math/0703877","kind":"arxiv","version":2}},"canonical_sha256":"25dd761edf0acc7383a8215701a7004b3235c50921555cc92a0712cd2b0c5196","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25dd761edf0acc7383a8215701a7004b3235c50921555cc92a0712cd2b0c5196","first_computed_at":"2026-05-17T23:45:55.694714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:55.694714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gWhc+GLPw0JDGtBm7KqJaLnIOb2n3/59N0Gg2fBX4euF7OAnmlA3VQdTs2TLQXZU98G0HpxUZLd0p38aIp/eCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:55.695746Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703877","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08c23f88ab603c70ff2d2f9e0247c2958cdcfc1177e29aa035b2e75c75767c8d","sha256:d2d7d103b629a5b84498855a298c068cdea6fa57f5bacd90bf0996c333a92102"],"state_sha256":"8282c4c227b2bf60a1ec44d870b684802eaf020f0e580f721ae546d024fd5b36"}