{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G4NZ5BUQAVVRCXWYQI4RHHDUI3","short_pith_number":"pith:G4NZ5BUQ","canonical_record":{"source":{"id":"1302.0638","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-02-04T10:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"a113b43561719f7959a3031b19418e4adf9d528b25d6c3c0ed9553170f07cee1","abstract_canon_sha256":"893ac38efadb0c03aa25511c05a7d928d01385235bf333a6261c2fc966b41d2d"},"schema_version":"1.0"},"canonical_sha256":"371b9e8690056b115ed88239139c7446f4e6bcef328b2156ff6259e11abb8726","source":{"kind":"arxiv","id":"1302.0638","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0638","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0638v4","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0638","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"G4NZ5BUQAVVR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G4NZ5BUQAVVRCXWY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G4NZ5BUQ","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G4NZ5BUQAVVRCXWYQI4RHHDUI3","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0638","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-02-04T10:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"a113b43561719f7959a3031b19418e4adf9d528b25d6c3c0ed9553170f07cee1","abstract_canon_sha256":"893ac38efadb0c03aa25511c05a7d928d01385235bf333a6261c2fc966b41d2d"},"schema_version":"1.0"},"canonical_sha256":"371b9e8690056b115ed88239139c7446f4e6bcef328b2156ff6259e11abb8726","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:35.587262Z","signature_b64":"mAY7/8eHKdsVjcbkusQRgdcH2dshW5JDwvXHvSQ57erDdDh6htxVtYWrU/xluUmICcyZ03Sunj+D/RtLxjZhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"371b9e8690056b115ed88239139c7446f4e6bcef328b2156ff6259e11abb8726","last_reissued_at":"2026-05-18T01:28:35.586748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:35.586748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0638","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tvmi+k89YZXeDebmwBxqCloQqUyBKtq8r4Kz2d1mraAOYufaZOTW2sDqHqut+3S2dTIXnHaaiEmsohgTOGFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:23:24.117575Z"},"content_sha256":"bb2fe85c43d3c060d670e6dbe1402f55e6b5c8191d27c84d54ab6037dc5b4485","schema_version":"1.0","event_id":"sha256:bb2fe85c43d3c060d670e6dbe1402f55e6b5c8191d27c84d54ab6037dc5b4485"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G4NZ5BUQAVVRCXWYQI4RHHDUI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A spectral sequence for the homology of a finite algebraic delooping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Birgit Richter, Stephanie Ziegenhagen","submitted_at":"2013-02-04T10:34:20Z","abstract_excerpt":"In the world of chain complexes E_n-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic E_n-homology of an E_n-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0638","kind":"arxiv","version":4},"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":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"er/ThsxZuo/MNneZ6rhFEtj5/mxBvPio4HSd12TV+YBie/6CyDfEPHfEtwS3Rc8arZoleOXw1RD/AGyxhcNRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:23:24.117939Z"},"content_sha256":"e1142143e0865989a43268ed413ba338d6ca7ee46eed7fadbec21c382301d15b","schema_version":"1.0","event_id":"sha256:e1142143e0865989a43268ed413ba338d6ca7ee46eed7fadbec21c382301d15b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/bundle.json","state_url":"https://pith.science/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/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":"2026-06-27T06:23:24Z","links":{"resolver":"https://pith.science/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3","bundle":"https://pith.science/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/bundle.json","state":"https://pith.science/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4NZ5BUQAVVRCXWYQI4RHHDUI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G4NZ5BUQAVVRCXWYQI4RHHDUI3","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":"893ac38efadb0c03aa25511c05a7d928d01385235bf333a6261c2fc966b41d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-02-04T10:34:20Z","title_canon_sha256":"a113b43561719f7959a3031b19418e4adf9d528b25d6c3c0ed9553170f07cee1"},"schema_version":"1.0","source":{"id":"1302.0638","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0638","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0638v4","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0638","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"G4NZ5BUQAVVR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G4NZ5BUQAVVRCXWY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G4NZ5BUQ","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:e1142143e0865989a43268ed413ba338d6ca7ee46eed7fadbec21c382301d15b","target":"graph","created_at":"2026-05-18T01:28:35Z","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":"In the world of chain complexes E_n-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic E_n-homology of an E_n-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher order ","authors_text":"Birgit Richter, Stephanie Ziegenhagen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-02-04T10:34:20Z","title":"A spectral sequence for the homology of a finite algebraic delooping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0638","kind":"arxiv","version":4},"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:bb2fe85c43d3c060d670e6dbe1402f55e6b5c8191d27c84d54ab6037dc5b4485","target":"record","created_at":"2026-05-18T01:28:35Z","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":"893ac38efadb0c03aa25511c05a7d928d01385235bf333a6261c2fc966b41d2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-02-04T10:34:20Z","title_canon_sha256":"a113b43561719f7959a3031b19418e4adf9d528b25d6c3c0ed9553170f07cee1"},"schema_version":"1.0","source":{"id":"1302.0638","kind":"arxiv","version":4}},"canonical_sha256":"371b9e8690056b115ed88239139c7446f4e6bcef328b2156ff6259e11abb8726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371b9e8690056b115ed88239139c7446f4e6bcef328b2156ff6259e11abb8726","first_computed_at":"2026-05-18T01:28:35.586748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:35.586748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mAY7/8eHKdsVjcbkusQRgdcH2dshW5JDwvXHvSQ57erDdDh6htxVtYWrU/xluUmICcyZ03Sunj+D/RtLxjZhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:35.587262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0638","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb2fe85c43d3c060d670e6dbe1402f55e6b5c8191d27c84d54ab6037dc5b4485","sha256:e1142143e0865989a43268ed413ba338d6ca7ee46eed7fadbec21c382301d15b"],"state_sha256":"d524baecee000452628cff33dc034e4394e8e8d8e1ca30bf3acc5c78031bcbfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUK/b+RN0UP2laym5iJsHmYwW1y4m5FSN/ERcj2m5fQRBXwxp9f8v/zIRD7cQsOsfXudtIq+Hj1z212uV109Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:23:24.119987Z","bundle_sha256":"60e84a1d81721818159f6d5d2f6f457464266bf768bec25796e4489137b0a25c"}}