{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:45JTQ7LXLOGXUA3VNPS7JRBNGZ","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":"d8abc52b83edf7d2badc151a6412c69d2462090fe0206a3266bfb89732eaa547","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-05T01:04:46Z","title_canon_sha256":"497237e871b56a1cc84b531c27777ce841f93cbfad5696ef8e7f40965894a9e8"},"schema_version":"1.0","source":{"id":"1404.1417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1417","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1417v1","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1417","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"45JTQ7LXLOGX","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"45JTQ7LXLOGXUA3V","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"45JTQ7LX","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:2ad7315ef73e72ef61d309deaab52f05db5db240b7d9b1b7fdfd35ef15e9a963","target":"graph","created_at":"2026-05-18T01:10:54Z","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":"Let F be a homotopy functor with values in the category of spectra. We show that partially stabilized cross-effects of F have an action of a certain operad. For functors from based spaces to spectra, it is the Koszul dual of the little discs operad. For functors from spectra to spectra it is a desuspension of the commutative operad. It follows that the Goodwillie derivatives of F are a right module over a certain `pro-operad'. For functors from spaces to spectra, the pro-operad is a resolution of the topological Lie operad. For functors from spectra to spectra, it is a resolution of the trivia","authors_text":"Gregory Arone, Michael Ching","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-05T01:04:46Z","title":"Cross-effects and the classification of Taylor towers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1417","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":"sha256:034f6ca6670a2143302673f4c56fefaa1e36b199941b35ebc7ca86b521b5da92","target":"record","created_at":"2026-05-18T01:10:54Z","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":"d8abc52b83edf7d2badc151a6412c69d2462090fe0206a3266bfb89732eaa547","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-05T01:04:46Z","title_canon_sha256":"497237e871b56a1cc84b531c27777ce841f93cbfad5696ef8e7f40965894a9e8"},"schema_version":"1.0","source":{"id":"1404.1417","kind":"arxiv","version":1}},"canonical_sha256":"e753387d775b8d7a03756be5f4c42d3646def15e3d769754217e9e6ba9eed941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e753387d775b8d7a03756be5f4c42d3646def15e3d769754217e9e6ba9eed941","first_computed_at":"2026-05-18T01:10:54.725639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:54.725639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nNTY9DDiayLfvqRaDicAvQWBbyrlxG5I01MvMc2U+sBb/mDw+3VCqXnwG2X6AFVV5KJxShy8SiR84olX35CgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:54.726271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:034f6ca6670a2143302673f4c56fefaa1e36b199941b35ebc7ca86b521b5da92","sha256:2ad7315ef73e72ef61d309deaab52f05db5db240b7d9b1b7fdfd35ef15e9a963"],"state_sha256":"2f1301d1158d54d5c48ced0888e6d65b14df5eed8be784e64b7f7f064e27c40b"}