{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:OEMB76LMNAWR3U3BQTFGWSNQ5H","short_pith_number":"pith:OEMB76LM","schema_version":"1.0","canonical_sha256":"71181ff96c682d1dd36184ca6b49b0e9ddc29fee31a7127128a99cf32c0aced8","source":{"kind":"arxiv","id":"2605.14178","version":1},"attestation_state":"computed","paper":{"title":"Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.","cross_cats":[],"primary_cat":"math.GM","authors_text":"Andr\\'e Fujita, Heitor Baldo, Koichi Sameshima, Luiz A. Baccal\\'a","submitted_at":"2026-05-13T22:58:42Z","abstract_excerpt":"Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2026-05-13T22:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"701312d20bd3140e01327a54ce65299ac16c39945837b0bb3d214af47081b8f6","abstract_canon_sha256":"792d1d78c4fa22c9e917b60d4ad0a83f33c3e2d3f740fa039618827905a3fc56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:11.280156Z","signature_b64":"nAQP3LnvW/KcRiWQzu47og+vq0bFrFTxLbkcyRggOaUPd1DVjReTh+mlq09lPy8QTYjzcJFceP0I5KE2m5etCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71181ff96c682d1dd36184ca6b49b0e9ddc29fee31a7127128a99cf32c0aced8","last_reissued_at":"2026-05-17T23:39:11.279624Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:11.279624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.","cross_cats":[],"primary_cat":"math.GM","authors_text":"Andr\\'e Fujita, Heitor Baldo, Koichi Sameshima, Luiz A. Baccal\\'a","submitted_at":"2026-05-13T22:58:42Z","abstract_excerpt":"Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their 'higher-order structures' or 'simplicial structures'), stressing the interrelations between directed cliques (their 'directed higher-order connectivities'), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That directed cliques can be consistently defined from digraphs and that their interrelations meaningfully capture higher-order directed interactions without additional assumptions on the underlying data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new formalism for directed Q-analysis using directed clique complexes to quantify and compare higher-order connectivities in digraphs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9bfbceaf7dcd1713b30bc8df735d307b8cb294a7d4c045b3e1dc0e0830d515d2"},"source":{"id":"2605.14178","kind":"arxiv","version":1},"verdict":{"id":"c1840247-71a4-4a2c-9d56-3598ab5278b4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:49:03.246253Z","strongest_claim":"we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their 'higher-order structures' or 'simplicial structures'), stressing the interrelations between directed cliques (their 'directed higher-order connectivities'), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.","one_line_summary":"A new formalism for directed Q-analysis using directed clique complexes to quantify and compare higher-order connectivities in digraphs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That directed cliques can be consistently defined from digraphs and that their interrelations meaningfully capture higher-order directed interactions without additional assumptions on the underlying data.","pith_extraction_headline":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships."},"references":{"count":300,"sample":[{"doi":"","year":null,"title":"Abdelnour, F. and Dayan, M. and Devinsky, O. and Thesen, T. and Raj, A. Estimating brain's functional graph from the structural graph's Laplacian. Proceedings of SPIE","work_id":"e91ac279-d6fe-4955-9b77-c2739217fff5","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Abdelnour, F. and Dayan, M. and Devinsky, O. and Thesen, T. and Raj, A. Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure. NeuroImage","work_id":"dedd6bc2-2d9c-4537-aad2-c85825dcf249","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Achard, S. and Bullmore, E. Efficiency and Cost of Economical Brain Functional Networks. PLoS Comput Biol","work_id":"f082db03-3131-46eb-9076-f3152f6b68f1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Aharoni, R. and Berger, E. and Meshulam, R. Eigenvalues and homology of flag complexes and vector representations of graphs. Geom. Funct. Anal","work_id":"c6c19a62-f5de-45f2-8c32-f6634348b125","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Ahmadlou, M. and Adeli, H. and Adeli, A. Graph theoretical analysis of organization of functional brain networks in ADHD. Clinical EEG and neuroscience","work_id":"7c961119-58f2-482a-8486-5ab48083644c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"566e27380f668a2aab4ce1750d33afe5e807877c9deb39dee64701be83080b00","internal_anchors":4},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8724ca9cfb4d4d602efeefe4a1ab8f14823bf9347ba3db9b044a37362042e167"},"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":"2605.14178","created_at":"2026-05-17T23:39:11.279725+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14178v1","created_at":"2026-05-17T23:39:11.279725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14178","created_at":"2026-05-17T23:39:11.279725+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEMB76LMNAWR","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEMB76LMNAWR3U3B","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEMB76LM","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H","json":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H.json","graph_json":"https://pith.science/api/pith-number/OEMB76LMNAWR3U3BQTFGWSNQ5H/graph.json","events_json":"https://pith.science/api/pith-number/OEMB76LMNAWR3U3BQTFGWSNQ5H/events.json","paper":"https://pith.science/paper/OEMB76LM"},"agent_actions":{"view_html":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H","download_json":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H.json","view_paper":"https://pith.science/paper/OEMB76LM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14178&json=true","fetch_graph":"https://pith.science/api/pith-number/OEMB76LMNAWR3U3BQTFGWSNQ5H/graph.json","fetch_events":"https://pith.science/api/pith-number/OEMB76LMNAWR3U3BQTFGWSNQ5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H/action/storage_attestation","attest_author":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H/action/author_attestation","sign_citation":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H/action/citation_signature","submit_replication":"https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H/action/replication_record"}},"created_at":"2026-05-17T23:39:11.279725+00:00","updated_at":"2026-05-17T23:39:11.279725+00:00"}