{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YK4KR44QL4PPCCX3V6MRBQQZOX","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":"5cd306590d9f8114aa0e1379adb1d22f24f240b211458ac7c8713633aa84c8ea","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-11T17:42:44Z","title_canon_sha256":"04cb16a7eb787caad34e9ae61422dc99800ae8767a0b57397cfdd3553c5ee647"},"schema_version":"1.0","source":{"id":"1702.03445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03445","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03445v1","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03445","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"YK4KR44QL4PP","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YK4KR44QL4PPCCX3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YK4KR44Q","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:16ee0d6c30cb9ab1437afd5bc435535fca76c39986dd1439aca197bf9c3170b4","target":"graph","created_at":"2026-05-18T00:50:53Z","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":"We present a largely self contained account on the K-theory of a weighted smooth projective curve over an algebraically closed field. In particular, we discuss the weighted version of divisor theory, Euler form, and Riemann-Roch theorem. This includes a treatment of the orbifold Euler characteristic.","authors_text":"Helmut Lenzing","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-11T17:42:44Z","title":"On the K-theory of weighted projective curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03445","kind":"arxiv","version":1},"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":"sha256:9013925304b0d5468d42eb5c57f2a375e566788f9570ff3086ccf766515aea4a","target":"record","created_at":"2026-05-18T00:50:53Z","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":"5cd306590d9f8114aa0e1379adb1d22f24f240b211458ac7c8713633aa84c8ea","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-11T17:42:44Z","title_canon_sha256":"04cb16a7eb787caad34e9ae61422dc99800ae8767a0b57397cfdd3553c5ee647"},"schema_version":"1.0","source":{"id":"1702.03445","kind":"arxiv","version":1}},"canonical_sha256":"c2b8a8f3905f1ef10afbaf9910c21975d7e517813a150312839eeb6231546304","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2b8a8f3905f1ef10afbaf9910c21975d7e517813a150312839eeb6231546304","first_computed_at":"2026-05-18T00:50:53.754293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:53.754293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"POw+U7HdWoqLE641fWU+E6fNYWCktu44Rrbywsl6lBOgB0Tmuby7F1ihN5bCkxiAHcf/FanCi+2q8z+JUJP0AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:53.754802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9013925304b0d5468d42eb5c57f2a375e566788f9570ff3086ccf766515aea4a","sha256:16ee0d6c30cb9ab1437afd5bc435535fca76c39986dd1439aca197bf9c3170b4"],"state_sha256":"9ebd91c6f17b8b1e8f4f93c37eafc0e1fece51c22f9561c2e6173ed920ff7d94"}