{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZK7YCJ5ENSMMAFZKHCITY7HTQI","short_pith_number":"pith:ZK7YCJ5E","schema_version":"1.0","canonical_sha256":"cabf8127a46c98c0172a38913c7cf382211218618705c4817750e43bf8737f2b","source":{"kind":"arxiv","id":"1109.5345","version":1},"attestation_state":"computed","paper":{"title":"Cacti and filtered distributive laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"James Griffin, Vladimir Dotsenko","submitted_at":"2011-09-25T11:33:23Z","abstract_excerpt":"Motivated by the second author's construction of a classifying space for the group of pure symmetric automorphisms of a free product, we introduce and study a family of topological operads, the operads of based cacti, defined for every pointed topological space $(Y,\\bullet)$. These operads also admit linear versions, which are defined for every augmented graded cocommutative coalgebra $C$. We show that the homology of the topological operad of based $Y$-cacti is the linear operad of based $H_*(Y)$-cacti. In addition, we show that for every coalgebra $C$ the operad of based $C$-cacti is Koszul."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.5345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-25T11:33:23Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ebfb7999785c0e667c164fa7113534940708d84333b9b70114f27c88ae7c98c9","abstract_canon_sha256":"9cddb445e2ffebaea4e5f4537c3ef692e3bdbf735aeb0aeeebaa4fe4e11cb261"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.739971Z","signature_b64":"UCC/whXt5fCUZeLyUwP1ppbZ3Pb87L+51pIsuvNfC0+xDAeqbFMbD7WPTTUnnVng9+3s54F178iZIIZxuZ3qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cabf8127a46c98c0172a38913c7cf382211218618705c4817750e43bf8737f2b","last_reissued_at":"2026-05-18T02:03:38.739205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.739205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cacti and filtered distributive laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"James Griffin, Vladimir Dotsenko","submitted_at":"2011-09-25T11:33:23Z","abstract_excerpt":"Motivated by the second author's construction of a classifying space for the group of pure symmetric automorphisms of a free product, we introduce and study a family of topological operads, the operads of based cacti, defined for every pointed topological space $(Y,\\bullet)$. These operads also admit linear versions, which are defined for every augmented graded cocommutative coalgebra $C$. We show that the homology of the topological operad of based $Y$-cacti is the linear operad of based $H_*(Y)$-cacti. In addition, we show that for every coalgebra $C$ the operad of based $C$-cacti is Koszul."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5345","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.5345","created_at":"2026-05-18T02:03:38.739334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5345v1","created_at":"2026-05-18T02:03:38.739334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5345","created_at":"2026-05-18T02:03:38.739334+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZK7YCJ5ENSMM","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZK7YCJ5ENSMMAFZK","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZK7YCJ5E","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI","json":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI.json","graph_json":"https://pith.science/api/pith-number/ZK7YCJ5ENSMMAFZKHCITY7HTQI/graph.json","events_json":"https://pith.science/api/pith-number/ZK7YCJ5ENSMMAFZKHCITY7HTQI/events.json","paper":"https://pith.science/paper/ZK7YCJ5E"},"agent_actions":{"view_html":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI","download_json":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI.json","view_paper":"https://pith.science/paper/ZK7YCJ5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5345&json=true","fetch_graph":"https://pith.science/api/pith-number/ZK7YCJ5ENSMMAFZKHCITY7HTQI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZK7YCJ5ENSMMAFZKHCITY7HTQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI/action/storage_attestation","attest_author":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI/action/author_attestation","sign_citation":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI/action/citation_signature","submit_replication":"https://pith.science/pith/ZK7YCJ5ENSMMAFZKHCITY7HTQI/action/replication_record"}},"created_at":"2026-05-18T02:03:38.739334+00:00","updated_at":"2026-05-18T02:03:38.739334+00:00"}