{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5QMXJDEBDTQEDK7QWVSTJYTH67","short_pith_number":"pith:5QMXJDEB","canonical_record":{"source":{"id":"0907.2566","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-15T11:53:12Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"088e7ce1a1ac47545f223cd7b6ef2c60fcafd2199c27f4eeb24dc41b9eb2d761","abstract_canon_sha256":"154bdae7eb22f9f47b3524a0fce3dff51b44c44c5d6f8ee420e5215ee75d4ced"},"schema_version":"1.0"},"canonical_sha256":"ec19748c811ce041abf0b56534e267f7eb8fc2910fba76f98116f38ae890222e","source":{"kind":"arxiv","id":"0907.2566","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2566","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2566v3","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2566","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"5QMXJDEBDTQE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5QMXJDEBDTQEDK7Q","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5QMXJDEB","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5QMXJDEBDTQEDK7QWVSTJYTH67","target":"record","payload":{"canonical_record":{"source":{"id":"0907.2566","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-15T11:53:12Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"088e7ce1a1ac47545f223cd7b6ef2c60fcafd2199c27f4eeb24dc41b9eb2d761","abstract_canon_sha256":"154bdae7eb22f9f47b3524a0fce3dff51b44c44c5d6f8ee420e5215ee75d4ced"},"schema_version":"1.0"},"canonical_sha256":"ec19748c811ce041abf0b56534e267f7eb8fc2910fba76f98116f38ae890222e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:10.552739Z","signature_b64":"xV0r3Ep/5UqUqD1tRbRXP0SyaIpD4AOohz7x/JsHaQRpdjD704E9yEcvKDBt7+OiJ1TQJ5MlJW23m4InWb3uAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec19748c811ce041abf0b56534e267f7eb8fc2910fba76f98116f38ae890222e","last_reissued_at":"2026-05-18T00:44:10.552087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:10.552087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.2566","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDpTZdX/bQrZqDBXmp02LIWQpViGVH1BgYekwbA5OuQaPPkO+4e7KNVsTc68Dum382SITXZCrsuaXn8gru9KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:00:16.490810Z"},"content_sha256":"1746568841bd0e94238e7430458a064477fc88624a9a39e212395ce05de97c64","schema_version":"1.0","event_id":"sha256:1746568841bd0e94238e7430458a064477fc88624a9a39e212395ce05de97c64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5QMXJDEBDTQEDK7QWVSTJYTH67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.CT","authors_text":"Joao Faria Martins, Roger Picken","submitted_at":"2009-07-15T11:53:12Z","abstract_excerpt":"We define the thin fundamental Gray 3-groupoid $S_3(M)$ of a smooth manifold $M$ and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps $S_3(M) \\to C(H)$, where $H$ is a 2-crossed module of Lie groups and $C(H)$ is the Gray 3-groupoid naturally constructed from $H$. As an application, we define Wilson 3-sphere observables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2566","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMMOA/R2roEhKKHygmCLQdNfJ2+pllQkcKAbYtoWYBnjCI/2Ysjc6SzT2OEt7mF9riI7njBa7UbearWYsAKWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:00:16.491283Z"},"content_sha256":"8c4b5561d7b7bc5e0a04bdbfa41e2b67d35bf139eef66172caf1be8be7391f2a","schema_version":"1.0","event_id":"sha256:8c4b5561d7b7bc5e0a04bdbfa41e2b67d35bf139eef66172caf1be8be7391f2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/bundle.json","state_url":"https://pith.science/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T03:00:16Z","links":{"resolver":"https://pith.science/pith/5QMXJDEBDTQEDK7QWVSTJYTH67","bundle":"https://pith.science/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/bundle.json","state":"https://pith.science/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QMXJDEBDTQEDK7QWVSTJYTH67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5QMXJDEBDTQEDK7QWVSTJYTH67","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":"154bdae7eb22f9f47b3524a0fce3dff51b44c44c5d6f8ee420e5215ee75d4ced","cross_cats_sorted":["hep-th","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-15T11:53:12Z","title_canon_sha256":"088e7ce1a1ac47545f223cd7b6ef2c60fcafd2199c27f4eeb24dc41b9eb2d761"},"schema_version":"1.0","source":{"id":"0907.2566","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2566","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2566v3","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2566","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"5QMXJDEBDTQE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5QMXJDEBDTQEDK7Q","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5QMXJDEB","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:8c4b5561d7b7bc5e0a04bdbfa41e2b67d35bf139eef66172caf1be8be7391f2a","target":"graph","created_at":"2026-05-18T00:44:10Z","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 define the thin fundamental Gray 3-groupoid $S_3(M)$ of a smooth manifold $M$ and define (by using differential geometric data) 3-dimensional holonomies, to be smooth strict Gray 3-groupoid maps $S_3(M) \\to C(H)$, where $H$ is a 2-crossed module of Lie groups and $C(H)$ is the Gray 3-groupoid naturally constructed from $H$. As an application, we define Wilson 3-sphere observables.","authors_text":"Joao Faria Martins, Roger Picken","cross_cats":["hep-th","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-15T11:53:12Z","title":"The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2566","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":"sha256:1746568841bd0e94238e7430458a064477fc88624a9a39e212395ce05de97c64","target":"record","created_at":"2026-05-18T00:44:10Z","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":"154bdae7eb22f9f47b3524a0fce3dff51b44c44c5d6f8ee420e5215ee75d4ced","cross_cats_sorted":["hep-th","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-15T11:53:12Z","title_canon_sha256":"088e7ce1a1ac47545f223cd7b6ef2c60fcafd2199c27f4eeb24dc41b9eb2d761"},"schema_version":"1.0","source":{"id":"0907.2566","kind":"arxiv","version":3}},"canonical_sha256":"ec19748c811ce041abf0b56534e267f7eb8fc2910fba76f98116f38ae890222e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec19748c811ce041abf0b56534e267f7eb8fc2910fba76f98116f38ae890222e","first_computed_at":"2026-05-18T00:44:10.552087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:10.552087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xV0r3Ep/5UqUqD1tRbRXP0SyaIpD4AOohz7x/JsHaQRpdjD704E9yEcvKDBt7+OiJ1TQJ5MlJW23m4InWb3uAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:10.552739Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2566","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1746568841bd0e94238e7430458a064477fc88624a9a39e212395ce05de97c64","sha256:8c4b5561d7b7bc5e0a04bdbfa41e2b67d35bf139eef66172caf1be8be7391f2a"],"state_sha256":"03b6e55f721fc97cf8a7b2dcda6ed5b844a4c76e3c2faa21477d346d68174ca1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90JIcnEpE3JGbjnKpg1j16Xu4jBxd3iIniXFxytbe8b2vmYEJfBe5VHtdCTbo6xXsGJ+bPNiINcp1ep5w9m0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:00:16.493987Z","bundle_sha256":"c13a1f438cfd307a8ab5118a2a008d1ef97d214a3ce3d6b931b389fdebe9c3d2"}}