{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ODVJN4KM5VMGUQI5TDIHQAITEO","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":"afae474fb13951794cdb73116d16ee01f1fa49be7122dfbabb4b14751ee9a4b5","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-07-30T12:18:54Z","title_canon_sha256":"babd83fdcd3318697bc401a631fa745adb9c16d6bfc9530008793de93462c344"},"schema_version":"1.0","source":{"id":"0807.4848","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4848","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4848v3","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4848","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"ODVJN4KM5VMG","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"ODVJN4KM5VMGUQI5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"ODVJN4KM","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e4e2a51a9f5973fe644b3738415cee5e9d86237dc3ac1ed9886ad1e180a4e174","target":"graph","created_at":"2026-05-18T04:16:32Z","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":"Several notions of sheaf on various types of quantale have been proposed and studied in the last twenty five years. It is fairly standard that for an involutive quantale Q satisfying mild algebraic properties the sheaves on Q can be defined to be the idempotent self-adjoint Q-valued matrices. These can be thought of as Q-valued equivalence relations, and, accordingly, the morphisms of sheaves are the Q-valued functional relations. Few concrete examples of such sheaves are known, however, and in this paper we provide a new one by showing that the category of equivariant sheaves on a localic eta","authors_text":"Pedro Resende","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-07-30T12:18:54Z","title":"Groupoid sheaves as quantale sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4848","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":"sha256:529288a3231b6bb50dde01f8a1420385a683dc710dd91fee1242a61ab5c30818","target":"record","created_at":"2026-05-18T04:16:32Z","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":"afae474fb13951794cdb73116d16ee01f1fa49be7122dfbabb4b14751ee9a4b5","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-07-30T12:18:54Z","title_canon_sha256":"babd83fdcd3318697bc401a631fa745adb9c16d6bfc9530008793de93462c344"},"schema_version":"1.0","source":{"id":"0807.4848","kind":"arxiv","version":3}},"canonical_sha256":"70ea96f14ced586a411d98d0780113238528f14214fc105b6bd0b054f51686b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70ea96f14ced586a411d98d0780113238528f14214fc105b6bd0b054f51686b0","first_computed_at":"2026-05-18T04:16:32.497974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:32.497974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GtjPyZc34W/l6UepJLdmflVokptZ6E+WS8FD6yJAkqLHQW1apxt7geimjjtlCdJbZqYQZA+KkQbC+lB8FQu0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:32.498375Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.4848","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:529288a3231b6bb50dde01f8a1420385a683dc710dd91fee1242a61ab5c30818","sha256:e4e2a51a9f5973fe644b3738415cee5e9d86237dc3ac1ed9886ad1e180a4e174"],"state_sha256":"1cf090d81f0ac53703e83562f376df7b8e35ecb35b497325c69729ff53cd11a7"}