{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:O6O7N2XQ22BX5YE3P5MECRBB6U","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":"a9d68d41b2a7595509d6e6eaafe0702e782a6c7d41187c7d0defc58541b32102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-02T01:37:24Z","title_canon_sha256":"ccc4786637088d4bee8b788975d348f0cad211601c070489979fe005ae1c8a90"},"schema_version":"1.0","source":{"id":"0806.0198","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.0198","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"0806.0198v3","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0198","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"O6O7N2XQ22BX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"O6O7N2XQ22BX5YE3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"O6O7N2XQ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:d838c5f5004f0405e28ce5ec34cc360b7b85534cae87be156409ad0a2eb29fc9","target":"graph","created_at":"2026-05-18T04:24:04Z","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 compute the Grothendieck and Picard groups of a complete smooth toric Deligne-Mumford stack by using a suitable category of graded modules over a polynomial ring.","authors_text":"S. Paul Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-02T01:37:24Z","title":"The Grothendieck and Picard groups of a complete toric DM stack"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0198","kind":"arxiv","version":3},"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:ee973b2ebdfd1fe1f002e1bbafb3f96dc1abcf204af4d102106cb81a638c1e15","target":"record","created_at":"2026-05-18T04:24:04Z","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":"a9d68d41b2a7595509d6e6eaafe0702e782a6c7d41187c7d0defc58541b32102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-02T01:37:24Z","title_canon_sha256":"ccc4786637088d4bee8b788975d348f0cad211601c070489979fe005ae1c8a90"},"schema_version":"1.0","source":{"id":"0806.0198","kind":"arxiv","version":3}},"canonical_sha256":"779df6eaf0d6837ee09b7f58414421f53e4d80863a1cdfd69818fc2c5557cf57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"779df6eaf0d6837ee09b7f58414421f53e4d80863a1cdfd69818fc2c5557cf57","first_computed_at":"2026-05-18T04:24:04.416439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.416439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMqxni7XEw/+YTxVWUbSmH0mPkeT7q0x/9TgUcVM/Dz5wdAT09z45wgTDDI0dzBm76BI7mYxfZ3zSJcUFFhXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.417031Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.0198","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee973b2ebdfd1fe1f002e1bbafb3f96dc1abcf204af4d102106cb81a638c1e15","sha256:d838c5f5004f0405e28ce5ec34cc360b7b85534cae87be156409ad0a2eb29fc9"],"state_sha256":"1a52095225b25755c6a6ab3da0d1e7c17205302ed56bf700666ad269a64e8d86"}