{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IMVWKDQPDKW5ONEUT4OQUNG25L","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":"fcfab67de80b90aa3848068cfa55a1c04ea242aaccb90d697b8ac80b052dc835","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-05-21T18:20:55Z","title_canon_sha256":"4e6190e200d4af62350867fb38bf164b8f26a846ecc855b1a06cfe4142033cdc"},"schema_version":"1.0","source":{"id":"2605.22946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22946","created_at":"2026-05-25T02:01:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22946v1","created_at":"2026-05-25T02:01:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22946","created_at":"2026-05-25T02:01:31Z"},{"alias_kind":"pith_short_12","alias_value":"IMVWKDQPDKW5","created_at":"2026-05-25T02:01:31Z"},{"alias_kind":"pith_short_16","alias_value":"IMVWKDQPDKW5ONEU","created_at":"2026-05-25T02:01:31Z"},{"alias_kind":"pith_short_8","alias_value":"IMVWKDQP","created_at":"2026-05-25T02:01:31Z"}],"graph_snapshots":[{"event_id":"sha256:0b705b5472f5cc77af93af6b08663e529b4916d4eb6c8daa0459d9957d3fcdd4","target":"graph","created_at":"2026-05-25T02:01:31Z","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/2605.22946/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify topological symmetric homology as the free $\\mathbb{E}_\\infty$-algebra on an $\\mathbb{E}_1$-algebra and topological braid homology as the free $\\mathbb{E}_2$-algebra on an $\\mathbb{E}_1$-algebra. In this way, topological symmetric homology and topological braid homology can be regarded as variants of $1$-dimensional representation homology. In order to identify topological braid homology as the free $\\mathbb{E}_2$-algebra on an $\\mathbb{E}_1$-algebra, we prove that the $\\mathbb{E}_2$-monoidal envelope of the associative operad can be identified with the braided crossed simplicial g","authors_text":"David Chan, Gabriel Angelini-Knoll, Maximilien P\\'eroux, Mona Merling, Teena Gerhardt","cross_cats":["math.CT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-05-21T18:20:55Z","title":"Topological symmetric and braid homologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22946","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:e452130509209ae309153f884fd50bdd0d0076643239a8e13bb839d018c64a37","target":"record","created_at":"2026-05-25T02:01:31Z","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":"fcfab67de80b90aa3848068cfa55a1c04ea242aaccb90d697b8ac80b052dc835","cross_cats_sorted":["math.CT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-05-21T18:20:55Z","title_canon_sha256":"4e6190e200d4af62350867fb38bf164b8f26a846ecc855b1a06cfe4142033cdc"},"schema_version":"1.0","source":{"id":"2605.22946","kind":"arxiv","version":1}},"canonical_sha256":"432b650e0f1aadd734949f1d0a34daeac949683f5710e0869e226374f8d9d077","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"432b650e0f1aadd734949f1d0a34daeac949683f5710e0869e226374f8d9d077","first_computed_at":"2026-05-25T02:01:31.711397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:31.711397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUwNmACZJRME3RgEqN1etT5nGUHYGR2ZajvAW+sEAABVLDMenUDjvldOMKiYNCZhYXUpk6B540dq3lQeTRyyCQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:31.712113Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e452130509209ae309153f884fd50bdd0d0076643239a8e13bb839d018c64a37","sha256:0b705b5472f5cc77af93af6b08663e529b4916d4eb6c8daa0459d9957d3fcdd4"],"state_sha256":"7c44ea3fb3003ea87525cd187f15b708e08450626e81b3178d391a669c6c290a"}