{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5S35CFEX4ET4T2X5BIW4TZ2EB5","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":"6081fbbefb6d0f2211ce801a8cc32169d26cadfe1b6b2f9367d03fadddcac1c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-31T14:20:34Z","title_canon_sha256":"73a3f98f802bfd2138a1877974f095c05bc235807d0f2e4d6ac666b02b59cb36"},"schema_version":"1.0","source":{"id":"1401.0149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0149","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0149v2","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0149","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"5S35CFEX4ET4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5S35CFEX4ET4T2X5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5S35CFEX","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:9144f98a3990bcb6f9a86877e94783fc100e2dc1dc7c8bc6fd0a610429f0e911","target":"graph","created_at":"2026-05-18T01:23:09Z","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":"Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in category-theoretic terms, where symmetry is expressed as the action of a 2-group G (equivalently, a categorical group) on a category C. It describes the construction of a transformation groupoid in diagrammatic terms, and considers this construction internal to Cat, the category of categories. The result is a double category C//G which describes the local symmetries ","authors_text":"Jeffrey C. Morton, Roger Picken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-31T14:20:34Z","title":"Transformation Double Categories Associated to 2-Group Actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0149","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:a2a065c84e20210f908d6ae83559175b70455723eb2de7990dd97a0ea950816c","target":"record","created_at":"2026-05-18T01:23:09Z","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":"6081fbbefb6d0f2211ce801a8cc32169d26cadfe1b6b2f9367d03fadddcac1c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-12-31T14:20:34Z","title_canon_sha256":"73a3f98f802bfd2138a1877974f095c05bc235807d0f2e4d6ac666b02b59cb36"},"schema_version":"1.0","source":{"id":"1401.0149","kind":"arxiv","version":2}},"canonical_sha256":"ecb7d11497e127c9eafd0a2dc9e7440f6888464050249e31c50e31cc23e8574c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecb7d11497e127c9eafd0a2dc9e7440f6888464050249e31c50e31cc23e8574c","first_computed_at":"2026-05-18T01:23:09.039637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:09.039637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"46i5uLqKtbTlAnpOY4L1w6qfPE3IduKilnN9WE6zZhG5M1E6j+j4OLVoCkpOAwDUCC1UcrBOadZUksBDJxCwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:09.040074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2a065c84e20210f908d6ae83559175b70455723eb2de7990dd97a0ea950816c","sha256:9144f98a3990bcb6f9a86877e94783fc100e2dc1dc7c8bc6fd0a610429f0e911"],"state_sha256":"b0a9b65986d5a240fc7477f3a7b3c9263fd657bc72d44cd8ccbd7648a6ff938f"}