{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:T4AB6GJ6H55G7SXWCRA2445FSJ","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":"ff246e64ca275e9cbf3454fac06e4fecc8e4a15b087f1c9591d2ab50ffa49fed","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2005-02-09T16:09:10Z","title_canon_sha256":"c268b7673382bc3c55d49852e99d38e81cffad33fe28c9deef4af598b9c7f239"},"schema_version":"1.0","source":{"id":"math/0502195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502195","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502195v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502195","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"T4AB6GJ6H55G","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"T4AB6GJ6H55G7SXW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"T4AB6GJ6","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:51530e2918a5c7831f640fcd7c23b9d5448e9d7f3b6244fbf91c6df29281b3a2","target":"graph","created_at":"2026-05-18T02:41:32Z","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":"The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show, under a flatness assumption, that this makes the Boekstedt spectral sequence converging to the mod p homology of THH(R) into a Hopf algebra spectral sequence. We then apply this additional structure to the study of some interesting examples, including the commutative S-algebras ku, ko, tmf, ju and j, and to calculate the homotopy groups of THH(ku) and THH(ko) af","authors_text":"John Rognes, Vigleik Angeltveit","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-02-09T16:09:10Z","title":"Hopf algebra structure on topological Hochschild homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502195","kind":"arxiv","version":2},"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:f51856eb84135fe26bb43a336776d1a70773268cceba7c2a6cdd4f15689208a4","target":"record","created_at":"2026-05-18T02:41:32Z","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":"ff246e64ca275e9cbf3454fac06e4fecc8e4a15b087f1c9591d2ab50ffa49fed","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2005-02-09T16:09:10Z","title_canon_sha256":"c268b7673382bc3c55d49852e99d38e81cffad33fe28c9deef4af598b9c7f239"},"schema_version":"1.0","source":{"id":"math/0502195","kind":"arxiv","version":2}},"canonical_sha256":"9f001f193e3f7a6fcaf61441ae73a5926c38c1e746ac7a5f7b2377205bb93d97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f001f193e3f7a6fcaf61441ae73a5926c38c1e746ac7a5f7b2377205bb93d97","first_computed_at":"2026-05-18T02:41:32.102378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.102378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GmRYb+RtII9svXf0ncnPiQIgQLvAE3SSsLn4tLMOMexA5CrpRrS0KsTZ61px6SIicI9nVx7d9WcQLxy6GT4oDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.102808Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f51856eb84135fe26bb43a336776d1a70773268cceba7c2a6cdd4f15689208a4","sha256:51530e2918a5c7831f640fcd7c23b9d5448e9d7f3b6244fbf91c6df29281b3a2"],"state_sha256":"cf6e5eba35dafeedff9f78dffa757497e20da8fb583782c41fd910048798cb35"}