{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3OVAGRNFOFHOJKVWMEMAOBDIOC","short_pith_number":"pith:3OVAGRNF","schema_version":"1.0","canonical_sha256":"dbaa0345a5714ee4aab6611807046870bbae731ad104490d950419c2a5d4d09b","source":{"kind":"arxiv","id":"2501.10311","version":1},"attestation_state":"computed","paper":{"title":"The Pop-Stack Operator on Ornamentation Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin Defant, Khalid Ajran","submitted_at":"2025-01-17T17:27:13Z","abstract_excerpt":"Each rooted plane tree $\\mathsf{T}$ has an associated ornamentation lattice $\\mathcal{O}(\\mathsf{T})$. The ornamentation lattice of an $n$-element chain is the $n$-th Tamari lattice. We study the pop-stack operator $\\mathsf{Pop}\\colon\\mathcal{O}(\\mathsf{T})\\to\\mathcal{O}(\\mathsf{T})$, which sends each element $\\delta$ to the meet of the elements covered by or equal to $\\delta$. We compute the maximum size of a forward orbit of $\\mathsf{Pop}$ on $\\mathcal{O}(\\mathsf{T})$, generalizing a result of Defant for Tamari lattices. We also characterize the image of $\\mathsf{Pop}$ on $\\mathcal{O}(\\maths"},"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":"2501.10311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-17T17:27:13Z","cross_cats_sorted":[],"title_canon_sha256":"f5dfe70fd3d6edb0d707bc921dc4026f4017a4a92c59721b2e1718b606f18c30","abstract_canon_sha256":"a8c66b7a543bf8591fd09aa1690e37ac10803c22e847f6a328ef322bcb3258e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:20.072891Z","signature_b64":"Pk2vKrzwyspsElF6RVJGZ9TTrfD3BrWJ1hT850TX15xZtBqSGclf3o+mLcvzVJZ06IbFxUlnidYVuhn/OvAVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbaa0345a5714ee4aab6611807046870bbae731ad104490d950419c2a5d4d09b","last_reissued_at":"2026-07-05T10:02:20.072559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:20.072559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Pop-Stack Operator on Ornamentation Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin Defant, Khalid Ajran","submitted_at":"2025-01-17T17:27:13Z","abstract_excerpt":"Each rooted plane tree $\\mathsf{T}$ has an associated ornamentation lattice $\\mathcal{O}(\\mathsf{T})$. The ornamentation lattice of an $n$-element chain is the $n$-th Tamari lattice. We study the pop-stack operator $\\mathsf{Pop}\\colon\\mathcal{O}(\\mathsf{T})\\to\\mathcal{O}(\\mathsf{T})$, which sends each element $\\delta$ to the meet of the elements covered by or equal to $\\delta$. We compute the maximum size of a forward orbit of $\\mathsf{Pop}$ on $\\mathcal{O}(\\mathsf{T})$, generalizing a result of Defant for Tamari lattices. We also characterize the image of $\\mathsf{Pop}$ on $\\mathcal{O}(\\maths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10311","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.10311/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.10311","created_at":"2026-07-05T10:02:20.072614+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.10311v1","created_at":"2026-07-05T10:02:20.072614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.10311","created_at":"2026-07-05T10:02:20.072614+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OVAGRNFOFHO","created_at":"2026-07-05T10:02:20.072614+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OVAGRNFOFHOJKVW","created_at":"2026-07-05T10:02:20.072614+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OVAGRNF","created_at":"2026-07-05T10:02:20.072614+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.01606","citing_title":"Ornamentation lattices and intreeval hypergraphic lattices","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC","json":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC.json","graph_json":"https://pith.science/api/pith-number/3OVAGRNFOFHOJKVWMEMAOBDIOC/graph.json","events_json":"https://pith.science/api/pith-number/3OVAGRNFOFHOJKVWMEMAOBDIOC/events.json","paper":"https://pith.science/paper/3OVAGRNF"},"agent_actions":{"view_html":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC","download_json":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC.json","view_paper":"https://pith.science/paper/3OVAGRNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.10311&json=true","fetch_graph":"https://pith.science/api/pith-number/3OVAGRNFOFHOJKVWMEMAOBDIOC/graph.json","fetch_events":"https://pith.science/api/pith-number/3OVAGRNFOFHOJKVWMEMAOBDIOC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC/action/storage_attestation","attest_author":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC/action/author_attestation","sign_citation":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC/action/citation_signature","submit_replication":"https://pith.science/pith/3OVAGRNFOFHOJKVWMEMAOBDIOC/action/replication_record"}},"created_at":"2026-07-05T10:02:20.072614+00:00","updated_at":"2026-07-05T10:02:20.072614+00:00"}