{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XEBT2JQ26BZRMYERSXXCCBW6MP","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":"191efd783ab8c44cb6ce3fbaf08f0d3259c0b5eb5523c2b3fcbe7f27a1e766a5","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-01-19T20:37:37Z","title_canon_sha256":"bf40920a92c8455a9c318e56f10e9be3cad7a16a2f1da7e058fdcf65bbf3c940"},"schema_version":"1.0","source":{"id":"1601.05072","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05072","created_at":"2026-05-17T23:40:50Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05072v2","created_at":"2026-05-17T23:40:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05072","created_at":"2026-05-17T23:40:50Z"},{"alias_kind":"pith_short_12","alias_value":"XEBT2JQ26BZR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XEBT2JQ26BZRMYER","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XEBT2JQ2","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:c956d9d3dfa67905a93c48f156310da1aaa54affc4edb8f1cbfc8b02f456f992","target":"graph","created_at":"2026-05-17T23:40:50Z","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 $Q$ be a commutative, Noetherian ring and $Z \\subseteq \\operatorname{Spec}(Q)$ a closed subset. Define $K_0^Z(Q)$ to be the Grothendieck group of those bounded complexes of finitely generated projective $Q$-modules that have homology supported on $Z$. We develop \"cyclic\" Adams operations on $K_0^Z(Q)$ and we prove these operations satisfy the four axioms used by Gillet and Soul\\'e in their paper \"Intersection Theory Using Adams Operations\". From this we recover a shorter proof of Serre's Vanishing Conjecture. We also show our cyclic Adams operations agree with the Adams operations defined ","authors_text":"Claudia Miller, Mark E. Walker, Michael K. Brown, Peder Thompson","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-01-19T20:37:37Z","title":"Cyclic Adams Operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05072","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":"sha256:1945935983fcc0d8195ef65589d3d89b1f98fcb0cc6455ed006efab4a36fe683","target":"record","created_at":"2026-05-17T23:40:50Z","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":"191efd783ab8c44cb6ce3fbaf08f0d3259c0b5eb5523c2b3fcbe7f27a1e766a5","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-01-19T20:37:37Z","title_canon_sha256":"bf40920a92c8455a9c318e56f10e9be3cad7a16a2f1da7e058fdcf65bbf3c940"},"schema_version":"1.0","source":{"id":"1601.05072","kind":"arxiv","version":2}},"canonical_sha256":"b9033d261af07316609195ee2106de63e508c9e3657fc70b08cb0ea3fedbfca3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9033d261af07316609195ee2106de63e508c9e3657fc70b08cb0ea3fedbfca3","first_computed_at":"2026-05-17T23:40:50.109211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:50.109211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04b1drYViR4hPoeIkNZj3Sr4RKhhJMuXkwKP2kru8BdO7YCHTRfq1laihf2oW+ZOOCQdz1K6NPkBehmRLBvlAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:50.109931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1945935983fcc0d8195ef65589d3d89b1f98fcb0cc6455ed006efab4a36fe683","sha256:c956d9d3dfa67905a93c48f156310da1aaa54affc4edb8f1cbfc8b02f456f992"],"state_sha256":"75b11a2c08540d6fec485580e374eef7b28d290d59410b53b981f86532c4ca3c"}