{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:L6GHDY55CMYA5M76B2S27JNZJF","short_pith_number":"pith:L6GHDY55","schema_version":"1.0","canonical_sha256":"5f8c71e3bd13300eb3fe0ea5afa5b9496933c537d77ddb3bb2912ee26067a5a6","source":{"kind":"arxiv","id":"2407.14048","version":3},"attestation_state":"computed","paper":{"title":"Higher-rank trees arising from polyhedral graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.OA"],"primary_cat":"math.CO","authors_text":"David Pask","submitted_at":"2024-07-19T06:03:26Z","abstract_excerpt":"We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \\cite{Lambek} and Johnstone \\cite{Johnstone} used for monoid and category emedding results. We show that they are planar $k$-trees for $2 \\le k \\le 4$. We also show that higher-rank trees differ from $1$-trees by giving examples of higher-rank trees having properties which are impossible for $1$-trees. Finally, we collect more examples of higher-rank planar trees which are not in our family."},"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":"2407.14048","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-19T06:03:26Z","cross_cats_sorted":["math.CT","math.OA"],"title_canon_sha256":"e893aa00b7be1732012d4afd2babb22c67ce30a7e8b7d3ca57174553114acae4","abstract_canon_sha256":"9081581c8634fd2d5b2905603cfeae5fca2d7234a6860b4a91d02691f2d8f760"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:04.310648Z","signature_b64":"LKBPAEP/Ss3VQN28HEmpQmy3tOXRIiY+i1k4Lbe/vbiGSsQ8gEb9qtNzeGAT89bRn2n7csrCUl0gV2ZfppfaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f8c71e3bd13300eb3fe0ea5afa5b9496933c537d77ddb3bb2912ee26067a5a6","last_reissued_at":"2026-06-02T02:04:04.310217Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:04.310217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-rank trees arising from polyhedral graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.OA"],"primary_cat":"math.CO","authors_text":"David Pask","submitted_at":"2024-07-19T06:03:26Z","abstract_excerpt":"We introduce a new family of higher-rank graphs, whose construction was inspired by the graphical techniques of Lambek \\cite{Lambek} and Johnstone \\cite{Johnstone} used for monoid and category emedding results. We show that they are planar $k$-trees for $2 \\le k \\le 4$. We also show that higher-rank trees differ from $1$-trees by giving examples of higher-rank trees having properties which are impossible for $1$-trees. Finally, we collect more examples of higher-rank planar trees which are not in our family."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.14048","kind":"arxiv","version":3},"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/2407.14048/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":"2407.14048","created_at":"2026-06-02T02:04:04.310271+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.14048v3","created_at":"2026-06-02T02:04:04.310271+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.14048","created_at":"2026-06-02T02:04:04.310271+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6GHDY55CMYA","created_at":"2026-06-02T02:04:04.310271+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6GHDY55CMYA5M76","created_at":"2026-06-02T02:04:04.310271+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6GHDY55","created_at":"2026-06-02T02:04:04.310271+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/L6GHDY55CMYA5M76B2S27JNZJF","json":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF.json","graph_json":"https://pith.science/api/pith-number/L6GHDY55CMYA5M76B2S27JNZJF/graph.json","events_json":"https://pith.science/api/pith-number/L6GHDY55CMYA5M76B2S27JNZJF/events.json","paper":"https://pith.science/paper/L6GHDY55"},"agent_actions":{"view_html":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF","download_json":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF.json","view_paper":"https://pith.science/paper/L6GHDY55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.14048&json=true","fetch_graph":"https://pith.science/api/pith-number/L6GHDY55CMYA5M76B2S27JNZJF/graph.json","fetch_events":"https://pith.science/api/pith-number/L6GHDY55CMYA5M76B2S27JNZJF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF/action/storage_attestation","attest_author":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF/action/author_attestation","sign_citation":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF/action/citation_signature","submit_replication":"https://pith.science/pith/L6GHDY55CMYA5M76B2S27JNZJF/action/replication_record"}},"created_at":"2026-06-02T02:04:04.310271+00:00","updated_at":"2026-06-02T02:04:04.310271+00:00"}