{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:J4EE6TCQCYWOSTPRBYNBDYD4WN","short_pith_number":"pith:J4EE6TCQ","schema_version":"1.0","canonical_sha256":"4f084f4c50162ce94df10e1a11e07cb37aff5d197ce6e3f5f703f7d2cae6914e","source":{"kind":"arxiv","id":"1709.02922","version":1},"attestation_state":"computed","paper":{"title":"Classification of Drury-Arveson-type Hilbert modules associated with certain directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deepak Kumar Pradhan, Sameer Chavan, Shailesh Trivedi","submitted_at":"2017-09-09T06:56:41Z","abstract_excerpt":"Given a directed Cartesian product $\\mathscr T$ of locally finite, leafless, rooted directed trees $\\mathscr T_1, \\ldots, \\mathscr T_d$ of finite joint branching index, one may associate with $\\mathscr T$ the Drury-Arveson-type $\\mathbb C[z_1, \\ldots, z_d]$-Hilbert module $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ of vector-valued holomorphic functions on the open unit ball $\\mathbb B^d$ in $\\mathbb C^d$, where $a >0.$ In case all directed trees under consideration are without branching vertices, $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ turns out to be the classical Drury-Arveson-type Hilbert mo"},"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":"1709.02922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-09T06:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"86342085ff8ecfeee8b445231182c8b7c37067df2f4d4a2766b0c611b51c0599","abstract_canon_sha256":"0debd79f9e68e5b2ab1d74a0502a3df22826d7a915bc5989d4372eed68c8fcd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:40.091617Z","signature_b64":"hkuQ3B68KINt8n739pKLPDtIln6U2zNccQ0yD3VGG15guneJgobEvI/gGF6+wl0WgE0ji/baBM6kkzK+xV17Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f084f4c50162ce94df10e1a11e07cb37aff5d197ce6e3f5f703f7d2cae6914e","last_reissued_at":"2026-05-18T00:35:40.091060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:40.091060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of Drury-Arveson-type Hilbert modules associated with certain directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deepak Kumar Pradhan, Sameer Chavan, Shailesh Trivedi","submitted_at":"2017-09-09T06:56:41Z","abstract_excerpt":"Given a directed Cartesian product $\\mathscr T$ of locally finite, leafless, rooted directed trees $\\mathscr T_1, \\ldots, \\mathscr T_d$ of finite joint branching index, one may associate with $\\mathscr T$ the Drury-Arveson-type $\\mathbb C[z_1, \\ldots, z_d]$-Hilbert module $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ of vector-valued holomorphic functions on the open unit ball $\\mathbb B^d$ in $\\mathbb C^d$, where $a >0.$ In case all directed trees under consideration are without branching vertices, $\\mathscr H_{\\mathfrak c_a}(\\mathscr T)$ turns out to be the classical Drury-Arveson-type Hilbert mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02922","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":""},"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":"1709.02922","created_at":"2026-05-18T00:35:40.091154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.02922v1","created_at":"2026-05-18T00:35:40.091154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02922","created_at":"2026-05-18T00:35:40.091154+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4EE6TCQCYWO","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4EE6TCQCYWOSTPR","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4EE6TCQ","created_at":"2026-05-18T12:31:21.493067+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/J4EE6TCQCYWOSTPRBYNBDYD4WN","json":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN.json","graph_json":"https://pith.science/api/pith-number/J4EE6TCQCYWOSTPRBYNBDYD4WN/graph.json","events_json":"https://pith.science/api/pith-number/J4EE6TCQCYWOSTPRBYNBDYD4WN/events.json","paper":"https://pith.science/paper/J4EE6TCQ"},"agent_actions":{"view_html":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN","download_json":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN.json","view_paper":"https://pith.science/paper/J4EE6TCQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.02922&json=true","fetch_graph":"https://pith.science/api/pith-number/J4EE6TCQCYWOSTPRBYNBDYD4WN/graph.json","fetch_events":"https://pith.science/api/pith-number/J4EE6TCQCYWOSTPRBYNBDYD4WN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN/action/storage_attestation","attest_author":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN/action/author_attestation","sign_citation":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN/action/citation_signature","submit_replication":"https://pith.science/pith/J4EE6TCQCYWOSTPRBYNBDYD4WN/action/replication_record"}},"created_at":"2026-05-18T00:35:40.091154+00:00","updated_at":"2026-05-18T00:35:40.091154+00:00"}