{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WA7APRV2HDOWXF6A2VXZHKATLM","short_pith_number":"pith:WA7APRV2","schema_version":"1.0","canonical_sha256":"b03e07c6ba38dd6b97c0d56f93a8135b23deb1fe95cfa44eb481e88ea5444c73","source":{"kind":"arxiv","id":"2204.00462","version":1},"attestation_state":"computed","paper":{"title":"Hochschild homology, and a persistent approach via connectivity digraphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Henri Riihim\\\"aki, Luigi Caputi","submitted_at":"2022-04-01T14:18:40Z","abstract_excerpt":"We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digraphs and analyse two main examples; the first, arising from Atkin's $q$-connectivity, and the second, here called $n$-path digraphs, generalising the classical notion of line graphs. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable "},"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":"2204.00462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2022-04-01T14:18:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a66212624dbc4cd7f4848f0e45f6b1e73f859b8761f89dfe257eb42285b9b20d","abstract_canon_sha256":"a8b249c8de53443595c66b9718e45588bfb74aace800f8a89db7e2b28b4d6b15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:41:43.874074Z","signature_b64":"MRPg+BYw/XfKiNlcg097pUkwXDAI6/KRGldWyLUF7V3BC+rCVWv064FakHr76aYaM5+j1WcixJfnrsaivkAjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b03e07c6ba38dd6b97c0d56f93a8135b23deb1fe95cfa44eb481e88ea5444c73","last_reissued_at":"2026-07-05T06:41:43.873597Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:41:43.873597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hochschild homology, and a persistent approach via connectivity digraphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Henri Riihim\\\"aki, Luigi Caputi","submitted_at":"2022-04-01T14:18:40Z","abstract_excerpt":"We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digraphs and analyse two main examples; the first, arising from Atkin's $q$-connectivity, and the second, here called $n$-path digraphs, generalising the classical notion of line graphs. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00462","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/2204.00462/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":"2204.00462","created_at":"2026-07-05T06:41:43.873655+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.00462v1","created_at":"2026-07-05T06:41:43.873655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00462","created_at":"2026-07-05T06:41:43.873655+00:00"},{"alias_kind":"pith_short_12","alias_value":"WA7APRV2HDOW","created_at":"2026-07-05T06:41:43.873655+00:00"},{"alias_kind":"pith_short_16","alias_value":"WA7APRV2HDOWXF6A","created_at":"2026-07-05T06:41:43.873655+00:00"},{"alias_kind":"pith_short_8","alias_value":"WA7APRV2","created_at":"2026-07-05T06:41:43.873655+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2409.09862","citing_title":"Towards a Quantitative Theory of Digraph-Based Complexes and its Applications in Brain Network Analysis","ref_index":49,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM","json":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM.json","graph_json":"https://pith.science/api/pith-number/WA7APRV2HDOWXF6A2VXZHKATLM/graph.json","events_json":"https://pith.science/api/pith-number/WA7APRV2HDOWXF6A2VXZHKATLM/events.json","paper":"https://pith.science/paper/WA7APRV2"},"agent_actions":{"view_html":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM","download_json":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM.json","view_paper":"https://pith.science/paper/WA7APRV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.00462&json=true","fetch_graph":"https://pith.science/api/pith-number/WA7APRV2HDOWXF6A2VXZHKATLM/graph.json","fetch_events":"https://pith.science/api/pith-number/WA7APRV2HDOWXF6A2VXZHKATLM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM/action/storage_attestation","attest_author":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM/action/author_attestation","sign_citation":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM/action/citation_signature","submit_replication":"https://pith.science/pith/WA7APRV2HDOWXF6A2VXZHKATLM/action/replication_record"}},"created_at":"2026-07-05T06:41:43.873655+00:00","updated_at":"2026-07-05T06:41:43.873655+00:00"}