{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FZEH2HFRDRYNTKB67D3XE2IHXW","short_pith_number":"pith:FZEH2HFR","canonical_record":{"source":{"id":"1502.06166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-22T02:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"bbae28a11842e45815b1cec2e9037ca025b39fdc2ab06ba8f798b93b1cd826a7","abstract_canon_sha256":"e77ce3498c73be1d978f725d48147002a4ba967e8fe80fad18f742f1d41b4ad9"},"schema_version":"1.0"},"canonical_sha256":"2e487d1cb11c70d9a83ef8f7726907bd9071995d2e1cf5f5584e2b4911ca9a3a","source":{"kind":"arxiv","id":"1502.06166","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06166","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06166v1","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06166","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"FZEH2HFRDRYN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZEH2HFRDRYNTKB6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZEH2HFR","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FZEH2HFRDRYNTKB67D3XE2IHXW","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-22T02:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"bbae28a11842e45815b1cec2e9037ca025b39fdc2ab06ba8f798b93b1cd826a7","abstract_canon_sha256":"e77ce3498c73be1d978f725d48147002a4ba967e8fe80fad18f742f1d41b4ad9"},"schema_version":"1.0"},"canonical_sha256":"2e487d1cb11c70d9a83ef8f7726907bd9071995d2e1cf5f5584e2b4911ca9a3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:37.907207Z","signature_b64":"Dr8L3SUhY8pZqlUzwcstFlGQRcrXYUb01w1xn27xhVvxkn3nQSIZoTw0dR1b9uAzDMVY8qTxkxk6zRyOVNvwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e487d1cb11c70d9a83ef8f7726907bd9071995d2e1cf5f5584e2b4911ca9a3a","last_reissued_at":"2026-05-18T02:26:37.906675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:37.906675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06166","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vepvZ5jMuqA7Et/OmCHP0E1j+HS2/Ns4hvCMsfUINVwWDG0QbkKHrBmQy7Gmq273AgT/2jB7s6psM71ArNOeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:17.504690Z"},"content_sha256":"08785da0a8a821ca63a94fc8c6b6a99cd58c1c4d773e5967ecbeb3185c3b55f5","schema_version":"1.0","event_id":"sha256:08785da0a8a821ca63a94fc8c6b6a99cd58c1c4d773e5967ecbeb3185c3b55f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FZEH2HFRDRYNTKB67D3XE2IHXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Membranes and higher groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mikhail Kapranov","submitted_at":"2015-02-22T02:07:10Z","abstract_excerpt":"We study the dg-Lie algebra f_n generated by the coefficients of the universal translation invariant flat dg-connection on the n-dimensional affine space. We describe its \"semiabelianization\" (in particular, the universal quotient which is a crossed module of Lie algebras) in terms of closed differential forms of arbitrary order. This generalizes the theorem of Reutenauer on the abelianization of the commutant of a free Lie algebra.\n  Semiabelian dg-Lie algebras, i.e., non-poisitively graded dg-Lie algebras with brackets of any elements of strictly negative degree being 0, are Lie algebraic an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06166","kind":"arxiv","version":1},"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":"2026-05-18T02:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hULlLe86C0yXaBfUA2UKe++8LhQfWvo+H06MAqib/x51kM7NbhKT0SORQ1bPIzI0/2R6OoOkHdn58SyixKc8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:10:17.505036Z"},"content_sha256":"9a521d3b3abdcb020792d24496faa0aebd86a8bfb12ac5c9c6021b0b93950bd5","schema_version":"1.0","event_id":"sha256:9a521d3b3abdcb020792d24496faa0aebd86a8bfb12ac5c9c6021b0b93950bd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/bundle.json","state_url":"https://pith.science/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/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":"2026-05-25T23:10:17Z","links":{"resolver":"https://pith.science/pith/FZEH2HFRDRYNTKB67D3XE2IHXW","bundle":"https://pith.science/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/bundle.json","state":"https://pith.science/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZEH2HFRDRYNTKB67D3XE2IHXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FZEH2HFRDRYNTKB67D3XE2IHXW","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":"e77ce3498c73be1d978f725d48147002a4ba967e8fe80fad18f742f1d41b4ad9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-22T02:07:10Z","title_canon_sha256":"bbae28a11842e45815b1cec2e9037ca025b39fdc2ab06ba8f798b93b1cd826a7"},"schema_version":"1.0","source":{"id":"1502.06166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06166","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06166v1","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06166","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"FZEH2HFRDRYN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FZEH2HFRDRYNTKB6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FZEH2HFR","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:9a521d3b3abdcb020792d24496faa0aebd86a8bfb12ac5c9c6021b0b93950bd5","target":"graph","created_at":"2026-05-18T02:26:37Z","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 study the dg-Lie algebra f_n generated by the coefficients of the universal translation invariant flat dg-connection on the n-dimensional affine space. We describe its \"semiabelianization\" (in particular, the universal quotient which is a crossed module of Lie algebras) in terms of closed differential forms of arbitrary order. This generalizes the theorem of Reutenauer on the abelianization of the commutant of a free Lie algebra.\n  Semiabelian dg-Lie algebras, i.e., non-poisitively graded dg-Lie algebras with brackets of any elements of strictly negative degree being 0, are Lie algebraic an","authors_text":"Mikhail Kapranov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-22T02:07:10Z","title":"Membranes and higher groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06166","kind":"arxiv","version":1},"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":"sha256:08785da0a8a821ca63a94fc8c6b6a99cd58c1c4d773e5967ecbeb3185c3b55f5","target":"record","created_at":"2026-05-18T02:26:37Z","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":"e77ce3498c73be1d978f725d48147002a4ba967e8fe80fad18f742f1d41b4ad9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-22T02:07:10Z","title_canon_sha256":"bbae28a11842e45815b1cec2e9037ca025b39fdc2ab06ba8f798b93b1cd826a7"},"schema_version":"1.0","source":{"id":"1502.06166","kind":"arxiv","version":1}},"canonical_sha256":"2e487d1cb11c70d9a83ef8f7726907bd9071995d2e1cf5f5584e2b4911ca9a3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e487d1cb11c70d9a83ef8f7726907bd9071995d2e1cf5f5584e2b4911ca9a3a","first_computed_at":"2026-05-18T02:26:37.906675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:37.906675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dr8L3SUhY8pZqlUzwcstFlGQRcrXYUb01w1xn27xhVvxkn3nQSIZoTw0dR1b9uAzDMVY8qTxkxk6zRyOVNvwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:37.907207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08785da0a8a821ca63a94fc8c6b6a99cd58c1c4d773e5967ecbeb3185c3b55f5","sha256:9a521d3b3abdcb020792d24496faa0aebd86a8bfb12ac5c9c6021b0b93950bd5"],"state_sha256":"aac9caf63caf5cb19fb92034ae9861f45378196157af24b505797d82fe60c9a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOUvHMN7F11Jzn2noRjuQjw9ThdDRJtCSHfmQvxZ/hSQs88rcPS3X057mS9VRAElOr+8G2lVqPAafjmg+QCADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:10:17.507339Z","bundle_sha256":"d18d9c9e74eba9f0f60d64716d1b3fbcbf1e26ddd161e58137e2b55655998411"}}