{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F6K6G5K6BVYDOR4QSKFDGT3E7Y","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":"6aae98c6e94e999b7cafc5c1b3ab7a35de345b039fc4df6797527b7723cfef65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-24T23:50:44Z","title_canon_sha256":"aed6bb1c212b44dd03c5fe359dabfa7805291455145434e9dd271802ca655d82"},"schema_version":"1.0","source":{"id":"1908.09233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09233","created_at":"2026-07-04T23:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09233v1","created_at":"2026-07-04T23:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09233","created_at":"2026-07-04T23:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"F6K6G5K6BVYD","created_at":"2026-07-04T23:59:37Z"},{"alias_kind":"pith_short_16","alias_value":"F6K6G5K6BVYDOR4Q","created_at":"2026-07-04T23:59:37Z"},{"alias_kind":"pith_short_8","alias_value":"F6K6G5K6","created_at":"2026-07-04T23:59:37Z"}],"graph_snapshots":[{"event_id":"sha256:986c90f70803bb0dd4ecb344cb3c5c034712983a6fb549f93fcef2aa8e04ef35","target":"graph","created_at":"2026-07-04T23:59:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.09233/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When $X$ is an associative H-space, the bar spectral sequence computes the homology of the delooping, $H_{*}(BX)$. If $X$ is an $n$-fold loop space for $n\\geq2$ this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on $H_{*}(BX)$, and so it is moreover a spectral sequence of Poisson algebras. Through the bracket on the spectral sequence, we establish a connection between the degree $n-1$ bracket on $H_{*}(X)$ and the degree $n-2$ bracket on $H_{*}(BX)$. This generalizes a result ","authors_text":"Xianglong Ni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-24T23:50:44Z","title":"The Bracket in the Bar Spectral Sequence for an Iterated Loop Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09233","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":"sha256:1ee0651adc89bfecf0b7ffd93d7176ce056d3e6becf057d743e832c107f61d55","target":"record","created_at":"2026-07-04T23:59:37Z","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":"6aae98c6e94e999b7cafc5c1b3ab7a35de345b039fc4df6797527b7723cfef65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-24T23:50:44Z","title_canon_sha256":"aed6bb1c212b44dd03c5fe359dabfa7805291455145434e9dd271802ca655d82"},"schema_version":"1.0","source":{"id":"1908.09233","kind":"arxiv","version":1}},"canonical_sha256":"2f95e3755e0d70374790928a334f64fe1f82c6196a47ffd6488b41ae18ce849e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f95e3755e0d70374790928a334f64fe1f82c6196a47ffd6488b41ae18ce849e","first_computed_at":"2026-07-04T23:59:37.906565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:37.906565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PAvBqrdig0TPctuJuPSQvN7f3rEJDX6ouzsANbXOvUZYgrTbjcXVOEQkMwr8sdxNy7JgMcqvUvHhDaTxf3wFBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:37.906983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ee0651adc89bfecf0b7ffd93d7176ce056d3e6becf057d743e832c107f61d55","sha256:986c90f70803bb0dd4ecb344cb3c5c034712983a6fb549f93fcef2aa8e04ef35"],"state_sha256":"e0d93c1122af6f5a52c60c24a4381f3886ceda91abdbed304bb6e563e26b40d4"}