{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4LC7AAHOOVH3UNPHOOGKGRXWHY","short_pith_number":"pith:4LC7AAHO","canonical_record":{"source":{"id":"1308.1113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-05T20:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"ce1e4cb5b245e229e6e43656a22daca9835fc6c35e3ba832d909001103b2b355","abstract_canon_sha256":"3812b4f74d4f2483f39972f2315a469165dc5721c74580771f24efe389cb2c92"},"schema_version":"1.0"},"canonical_sha256":"e2c5f000ee754fba35e7738ca346f63e35665fa3e85eaebe71267da5025d2f14","source":{"kind":"arxiv","id":"1308.1113","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1113","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1113v3","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1113","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"4LC7AAHOOVH3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4LC7AAHOOVH3UNPH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4LC7AAHO","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4LC7AAHOOVH3UNPHOOGKGRXWHY","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-05T20:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"ce1e4cb5b245e229e6e43656a22daca9835fc6c35e3ba832d909001103b2b355","abstract_canon_sha256":"3812b4f74d4f2483f39972f2315a469165dc5721c74580771f24efe389cb2c92"},"schema_version":"1.0"},"canonical_sha256":"e2c5f000ee754fba35e7738ca346f63e35665fa3e85eaebe71267da5025d2f14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.836922Z","signature_b64":"Xm6/lE+yQeZzHakewJNNzzLLAGN3Cqsy4jvTorkL1Vs7kZ33AVFbE8wwiyZ8Va0BeBpdHygvYVJMuIgt6cp4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2c5f000ee754fba35e7738ca346f63e35665fa3e85eaebe71267da5025d2f14","last_reissued_at":"2026-05-18T01:25:47.836303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.836303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1113","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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tQpAmv4Fj2rBp5zLnAqyoYT8doBslu6nqEWU3XrKwGJOoXiLyHMmx30Wnqep6KNoWBhhBA7vCpf/zAc7GNzHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:34:55.179553Z"},"content_sha256":"8d16fd0f2497cb7584ad07f07b9f6a5fafb2981c118c3813a3b14a6c6fab9234","schema_version":"1.0","event_id":"sha256:8d16fd0f2497cb7584ad07f07b9f6a5fafb2981c118c3813a3b14a6c6fab9234"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4LC7AAHOOVH3UNPHOOGKGRXWHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Descent for n-Bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jesse Wolfson","submitted_at":"2013-08-05T20:38:00Z","abstract_excerpt":"Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U of X, specifying a transition cocycle on the cover, and descending the trivialized bundle along the cover. We demonstrate the existence of an analogous construction for local n-bundles for general n. We establish analogues for simplicial Lie groups of Moore's results on simplicial groups; these imply that bundles for strict Lie n-groups arise from local n-bundles. Our construction leads to simple finite dimensional models of Lie 2-groups such as String(n)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1113","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":"2026-05-18T01:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKPL4Bat3sKQLq960Nylk4gHox5KE4vIukOtlrGwGgF/lF8tMM7sKeE3aIgfYEoRXQmgMjRzE6qEvU7Y32aWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:34:55.180179Z"},"content_sha256":"855e262e27e796bf17a99cd6b729d5c8b72a20e041657552112433dadffa18c2","schema_version":"1.0","event_id":"sha256:855e262e27e796bf17a99cd6b729d5c8b72a20e041657552112433dadffa18c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/bundle.json","state_url":"https://pith.science/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/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":"2026-05-27T05:34:55Z","links":{"resolver":"https://pith.science/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY","bundle":"https://pith.science/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/bundle.json","state":"https://pith.science/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4LC7AAHOOVH3UNPHOOGKGRXWHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4LC7AAHOOVH3UNPHOOGKGRXWHY","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":"3812b4f74d4f2483f39972f2315a469165dc5721c74580771f24efe389cb2c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-05T20:38:00Z","title_canon_sha256":"ce1e4cb5b245e229e6e43656a22daca9835fc6c35e3ba832d909001103b2b355"},"schema_version":"1.0","source":{"id":"1308.1113","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1113","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1113v3","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1113","created_at":"2026-05-18T01:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"4LC7AAHOOVH3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4LC7AAHOOVH3UNPH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4LC7AAHO","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:855e262e27e796bf17a99cd6b729d5c8b72a20e041657552112433dadffa18c2","target":"graph","created_at":"2026-05-18T01:25:47Z","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":"Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U of X, specifying a transition cocycle on the cover, and descending the trivialized bundle along the cover. We demonstrate the existence of an analogous construction for local n-bundles for general n. We establish analogues for simplicial Lie groups of Moore's results on simplicial groups; these imply that bundles for strict Lie n-groups arise from local n-bundles. Our construction leads to simple finite dimensional models of Lie 2-groups such as String(n).","authors_text":"Jesse Wolfson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-05T20:38:00Z","title":"Descent for n-Bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1113","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":"sha256:8d16fd0f2497cb7584ad07f07b9f6a5fafb2981c118c3813a3b14a6c6fab9234","target":"record","created_at":"2026-05-18T01:25:47Z","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":"3812b4f74d4f2483f39972f2315a469165dc5721c74580771f24efe389cb2c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-05T20:38:00Z","title_canon_sha256":"ce1e4cb5b245e229e6e43656a22daca9835fc6c35e3ba832d909001103b2b355"},"schema_version":"1.0","source":{"id":"1308.1113","kind":"arxiv","version":3}},"canonical_sha256":"e2c5f000ee754fba35e7738ca346f63e35665fa3e85eaebe71267da5025d2f14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2c5f000ee754fba35e7738ca346f63e35665fa3e85eaebe71267da5025d2f14","first_computed_at":"2026-05-18T01:25:47.836303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:47.836303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xm6/lE+yQeZzHakewJNNzzLLAGN3Cqsy4jvTorkL1Vs7kZ33AVFbE8wwiyZ8Va0BeBpdHygvYVJMuIgt6cp4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:47.836922Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1113","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d16fd0f2497cb7584ad07f07b9f6a5fafb2981c118c3813a3b14a6c6fab9234","sha256:855e262e27e796bf17a99cd6b729d5c8b72a20e041657552112433dadffa18c2"],"state_sha256":"aab84f5c5a7da819ccd503a4e3e153dd9bdc7b142c9b34113eb226502e2966f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w22FbDZfzNnQl7yRmTi8tcqqSPRbTmPP2mVQmp2ZVDCtIgW9DaE7/mkLcLySOENeUGUgm+xWW3hwjXvDs5beCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:34:55.183535Z","bundle_sha256":"4afcce6df7014c14d6f93003e9616f28a3ec242b5e68b8e4e94f79102cbc20f3"}}