{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AXIOIHIPQYNEFJCGFCRA4XP4HJ","short_pith_number":"pith:AXIOIHIP","schema_version":"1.0","canonical_sha256":"05d0e41d0f861a42a44628a20e5dfc3a6d60cac279f64f92a576eb082719f173","source":{"kind":"arxiv","id":"1507.05816","version":1},"attestation_state":"computed","paper":{"title":"Topological Bicomplex Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Heera Saini, Romesh Kumar","submitted_at":"2015-07-21T13:07:13Z","abstract_excerpt":"In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions under which topological bicomplex modules and locally bicomplex convex modules become hyperbolic normable and hyperbolic metrizable respectively."},"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":"1507.05816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T13:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"a890c8cb5c190399320996c8378c4439bd70752a5f294abde927d4b23f37c33e","abstract_canon_sha256":"423c2df6e22385b07c943812e56168e4d1ad141526fec234ac09a41a76d89e61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:32.361430Z","signature_b64":"RBMhCmYtGQCZWwyV1g/ZfcJ66AZDy7XS+f2CygF8IqBaW3GykTu2iOkfOomTY91XNmUWRUVgqe4m/4jbwNrnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d0e41d0f861a42a44628a20e5dfc3a6d60cac279f64f92a576eb082719f173","last_reissued_at":"2026-05-18T01:36:32.360842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:32.360842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Bicomplex Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Heera Saini, Romesh Kumar","submitted_at":"2015-07-21T13:07:13Z","abstract_excerpt":"In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions under which topological bicomplex modules and locally bicomplex convex modules become hyperbolic normable and hyperbolic metrizable respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05816","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":"1507.05816","created_at":"2026-05-18T01:36:32.360925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05816v1","created_at":"2026-05-18T01:36:32.360925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05816","created_at":"2026-05-18T01:36:32.360925+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXIOIHIPQYNE","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXIOIHIPQYNEFJCG","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXIOIHIP","created_at":"2026-05-18T12:29:10.953037+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/AXIOIHIPQYNEFJCGFCRA4XP4HJ","json":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ.json","graph_json":"https://pith.science/api/pith-number/AXIOIHIPQYNEFJCGFCRA4XP4HJ/graph.json","events_json":"https://pith.science/api/pith-number/AXIOIHIPQYNEFJCGFCRA4XP4HJ/events.json","paper":"https://pith.science/paper/AXIOIHIP"},"agent_actions":{"view_html":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ","download_json":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ.json","view_paper":"https://pith.science/paper/AXIOIHIP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05816&json=true","fetch_graph":"https://pith.science/api/pith-number/AXIOIHIPQYNEFJCGFCRA4XP4HJ/graph.json","fetch_events":"https://pith.science/api/pith-number/AXIOIHIPQYNEFJCGFCRA4XP4HJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ/action/storage_attestation","attest_author":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ/action/author_attestation","sign_citation":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ/action/citation_signature","submit_replication":"https://pith.science/pith/AXIOIHIPQYNEFJCGFCRA4XP4HJ/action/replication_record"}},"created_at":"2026-05-18T01:36:32.360925+00:00","updated_at":"2026-05-18T01:36:32.360925+00:00"}