{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:W7B7YJLUT3TTS3MIOZJNVZFAGU","short_pith_number":"pith:W7B7YJLU","schema_version":"1.0","canonical_sha256":"b7c3fc25749ee7396d887652dae4a03508440d335de17c794ea41efe2d219d38","source":{"kind":"arxiv","id":"2606.28539","version":1},"attestation_state":"computed","paper":{"title":"Extremal ranks of unlabeled multifurcating rooted trees in a bijective encoding by the positive integers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alessandra R. P. Maranca, Michael R. Doboli, Noah A. Rosenberg","submitted_at":"2026-06-26T18:44:50Z","abstract_excerpt":"Maranca and Rosenberg (2024) devised a ranking scheme for unlabeled multifurcating rooted trees, in which the trees are bijectively associated with the positive integers. Here, generalizing earlier results for bifurcating trees, we determine, for trees with a fixed number of leaves, which multifurcating trees obtain the maximal and minimal ranks. We identify these maximizing and minimizing trees for each of two sets of unlabeled multifurcating rooted trees: strictly $k$-furcating trees, in which each internal node possesses exactly $k$ descendants, and at-most-$k$-furcating trees, in which int"},"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":"2606.28539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-26T18:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"da9c3053c517a7a6d075bd7e22155e88e1548ee6508eea17c2a64e2b84374294","abstract_canon_sha256":"74b61ae08f6de2dcef0aca3bf16694b3f276548cc6fe358911414a62231369c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T00:15:17.472002Z","signature_b64":"onsEDZY9+zDM7WMT+Sqw3fsFCo085GVk8ZOpG0KeHcX0DkRLci6aJV2cWsZz9jC6LQa4iMU9EBRxBKV2JvOrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c3fc25749ee7396d887652dae4a03508440d335de17c794ea41efe2d219d38","last_reissued_at":"2026-06-30T00:15:17.471632Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T00:15:17.471632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal ranks of unlabeled multifurcating rooted trees in a bijective encoding by the positive integers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alessandra R. P. Maranca, Michael R. Doboli, Noah A. Rosenberg","submitted_at":"2026-06-26T18:44:50Z","abstract_excerpt":"Maranca and Rosenberg (2024) devised a ranking scheme for unlabeled multifurcating rooted trees, in which the trees are bijectively associated with the positive integers. Here, generalizing earlier results for bifurcating trees, we determine, for trees with a fixed number of leaves, which multifurcating trees obtain the maximal and minimal ranks. We identify these maximizing and minimizing trees for each of two sets of unlabeled multifurcating rooted trees: strictly $k$-furcating trees, in which each internal node possesses exactly $k$ descendants, and at-most-$k$-furcating trees, in which int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28539","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/2606.28539/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":"2606.28539","created_at":"2026-06-30T00:15:17.471686+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28539v1","created_at":"2026-06-30T00:15:17.471686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28539","created_at":"2026-06-30T00:15:17.471686+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7B7YJLUT3TT","created_at":"2026-06-30T00:15:17.471686+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7B7YJLUT3TTS3MI","created_at":"2026-06-30T00:15:17.471686+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7B7YJLU","created_at":"2026-06-30T00:15:17.471686+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/W7B7YJLUT3TTS3MIOZJNVZFAGU","json":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU.json","graph_json":"https://pith.science/api/pith-number/W7B7YJLUT3TTS3MIOZJNVZFAGU/graph.json","events_json":"https://pith.science/api/pith-number/W7B7YJLUT3TTS3MIOZJNVZFAGU/events.json","paper":"https://pith.science/paper/W7B7YJLU"},"agent_actions":{"view_html":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU","download_json":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU.json","view_paper":"https://pith.science/paper/W7B7YJLU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28539&json=true","fetch_graph":"https://pith.science/api/pith-number/W7B7YJLUT3TTS3MIOZJNVZFAGU/graph.json","fetch_events":"https://pith.science/api/pith-number/W7B7YJLUT3TTS3MIOZJNVZFAGU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU/action/storage_attestation","attest_author":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU/action/author_attestation","sign_citation":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU/action/citation_signature","submit_replication":"https://pith.science/pith/W7B7YJLUT3TTS3MIOZJNVZFAGU/action/replication_record"}},"created_at":"2026-06-30T00:15:17.471686+00:00","updated_at":"2026-06-30T00:15:17.471686+00:00"}