{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:25LRPK2VDVLSS7G5OESPCGHTLE","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":"05841b79b0d86ef24d5dc0e9a460ec398e79ae55c729c43b80b4dca63e27f0a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-16T19:19:45Z","title_canon_sha256":"d06dfeb7d525491e283c55ea8e8e45d15b8cbd9c7ff64b435f8a9caa5e239baa"},"schema_version":"1.0","source":{"id":"1109.3694","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3694","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3694v3","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3694","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"25LRPK2VDVLS","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"25LRPK2VDVLSS7G5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"25LRPK2V","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:f6ad9c0d172cd8d296da9bc9292a86142911653c6dcf29f63218e33765b59b7e","target":"graph","created_at":"2026-05-18T02:41:43Z","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 spectral sequence that one obtains by applying mod 2 homology to the Goodwillie tower which sends a spectrum X to the suspension spectrum of its 0th space X_0. This converges strongly to H_*(X_0) when X is 0-connected. The E^1 term is the homology of the extended powers of X, and thus is a well known functor of H_*(X), including structure as a bigraded Hopf algebra, a right module over the mod 2 Steenrod algebra A, and a left module over the Dyer-Lashof operations.\n  Hopf algebra considerations show that all pages of the spectral sequence are primitively generated, with primitives","authors_text":"Jason B. McCarty, Nicholas J. Kuhn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-16T19:19:45Z","title":"The mod 2 homology of infinite loopspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3694","kind":"arxiv","version":3},"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":"sha256:9e6ddec4f5b02404dfcc3f4fddd6de743c03cd5ebef0954c61418eaa528f5fe4","target":"record","created_at":"2026-05-18T02:41:43Z","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":"05841b79b0d86ef24d5dc0e9a460ec398e79ae55c729c43b80b4dca63e27f0a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-16T19:19:45Z","title_canon_sha256":"d06dfeb7d525491e283c55ea8e8e45d15b8cbd9c7ff64b435f8a9caa5e239baa"},"schema_version":"1.0","source":{"id":"1109.3694","kind":"arxiv","version":3}},"canonical_sha256":"d75717ab551d57297cdd7124f118f3593db77a78c7300dda60cebb83de4bbb06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75717ab551d57297cdd7124f118f3593db77a78c7300dda60cebb83de4bbb06","first_computed_at":"2026-05-18T02:41:43.657990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:43.657990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PK1GtdD1zmTHOzp8AI6nhNF6KQiKdmmpzj35Rb7RHV6aSX3rcE176eaNMyjS4KIPcxcQMnVDYdD/hM/3+/bUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:43.658695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3694","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e6ddec4f5b02404dfcc3f4fddd6de743c03cd5ebef0954c61418eaa528f5fe4","sha256:f6ad9c0d172cd8d296da9bc9292a86142911653c6dcf29f63218e33765b59b7e"],"state_sha256":"1c6c001a2f891894f1e5f8700a56a41ab1beff7d82ac89c3f2cfa3cd7ae8c092"}