{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T26NRZHBPWJ55V5FVH4AGSHVSC","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":"0635ac71ea934e2c683ee9031373f7632a04d70ced8ca33dd320958b60494906","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-15T23:25:15Z","title_canon_sha256":"5c5a2bbb5f76a3583297c32dc34414e44fe0f41cb335e611bc30b4b14109a5db"},"schema_version":"1.0","source":{"id":"1312.4205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4205","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4205v2","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4205","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"T26NRZHBPWJ5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T26NRZHBPWJ55V5F","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T26NRZHB","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:7f7df7001647d02410e1d1935e63b34c32d0fa83c98c967dfe6dabdf29d5b08e","target":"graph","created_at":"2026-05-18T02:44:00Z","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 prove that the $K$-group of reciprocity functors, defined by F. Ivorra and the first author, vanishes over a perfect field as soon as one of the reciprocity functors is $\\mathbb{G}_a$ and one is an abelian variety.","authors_text":"Kay R\\\"ulling, Takao Yamazaki","cross_cats":["math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-15T23:25:15Z","title":"K-Groups of reciprocity functors for G_a and abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4205","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:dd88f460c1cce51c74b688e07030f60ed9af0faf0fa851b3139b5920361126c7","target":"record","created_at":"2026-05-18T02:44:00Z","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":"0635ac71ea934e2c683ee9031373f7632a04d70ced8ca33dd320958b60494906","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-15T23:25:15Z","title_canon_sha256":"5c5a2bbb5f76a3583297c32dc34414e44fe0f41cb335e611bc30b4b14109a5db"},"schema_version":"1.0","source":{"id":"1312.4205","kind":"arxiv","version":2}},"canonical_sha256":"9ebcd8e4e17d93ded7a5a9f80348f59096aa65f1c03622cc50049e49886f1941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ebcd8e4e17d93ded7a5a9f80348f59096aa65f1c03622cc50049e49886f1941","first_computed_at":"2026-05-18T02:44:00.543658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:00.543658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zEOVdKTVXlwEG/9TOzZckcxAI6na2oF665pNL1vSiV3F0Ra5BKnv8t9h6DKBy3/Kqob4CwwX0VPlNOyLAQWDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:00.544137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd88f460c1cce51c74b688e07030f60ed9af0faf0fa851b3139b5920361126c7","sha256:7f7df7001647d02410e1d1935e63b34c32d0fa83c98c967dfe6dabdf29d5b08e"],"state_sha256":"fc0859d397d6cdfe2ae7e5f7a835c01c0fab6edea94e226019a84974264bac88"}