{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3OVAGRNFOFHOJKVWMEMAOBDIOC","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":"a8c66b7a543bf8591fd09aa1690e37ac10803c22e847f6a328ef322bcb3258e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-17T17:27:13Z","title_canon_sha256":"f5dfe70fd3d6edb0d707bc921dc4026f4017a4a92c59721b2e1718b606f18c30"},"schema_version":"1.0","source":{"id":"2501.10311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.10311","created_at":"2026-07-05T10:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"2501.10311v1","created_at":"2026-07-05T10:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.10311","created_at":"2026-07-05T10:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"3OVAGRNFOFHO","created_at":"2026-07-05T10:02:20Z"},{"alias_kind":"pith_short_16","alias_value":"3OVAGRNFOFHOJKVW","created_at":"2026-07-05T10:02:20Z"},{"alias_kind":"pith_short_8","alias_value":"3OVAGRNF","created_at":"2026-07-05T10:02:20Z"}],"graph_snapshots":[{"event_id":"sha256:cb0ee0c0a77510af61d257dc70c91f2f5cce512e6f4c0b4f1004f61d1c442b94","target":"graph","created_at":"2026-07-05T10:02:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.10311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Colin Defant, Khalid Ajran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-17T17:27:13Z","title":"The Pop-Stack Operator on Ornamentation Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10311","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:b0ad68525ec9fc5b0a84e492346208c52b449f3f9c217a6e3cb9c772f5c04eff","target":"record","created_at":"2026-07-05T10:02:20Z","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":"a8c66b7a543bf8591fd09aa1690e37ac10803c22e847f6a328ef322bcb3258e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-17T17:27:13Z","title_canon_sha256":"f5dfe70fd3d6edb0d707bc921dc4026f4017a4a92c59721b2e1718b606f18c30"},"schema_version":"1.0","source":{"id":"2501.10311","kind":"arxiv","version":1}},"canonical_sha256":"dbaa0345a5714ee4aab6611807046870bbae731ad104490d950419c2a5d4d09b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbaa0345a5714ee4aab6611807046870bbae731ad104490d950419c2a5d4d09b","first_computed_at":"2026-07-05T10:02:20.072559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:20.072559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pk2vKrzwyspsElF6RVJGZ9TTrfD3BrWJ1hT850TX15xZtBqSGclf3o+mLcvzVJZ06IbFxUlnidYVuhn/OvAVBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:20.072891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.10311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0ad68525ec9fc5b0a84e492346208c52b449f3f9c217a6e3cb9c772f5c04eff","sha256:cb0ee0c0a77510af61d257dc70c91f2f5cce512e6f4c0b4f1004f61d1c442b94"],"state_sha256":"4193f2516133851c142d692e5586721abee0758ec69e17a63fe05200ef9ed907"}