{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ITE7WI4JK5UAH33TKX6PML3JRT","short_pith_number":"pith:ITE7WI4J","schema_version":"1.0","canonical_sha256":"44c9fb2389576803ef7355fcf62f698cd5ff4c6b8ed80365c99428d2e35866fd","source":{"kind":"arxiv","id":"1801.04392","version":1},"attestation_state":"computed","paper":{"title":"Certain quaternary quadratic forms of level 48 and their representation numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup Kumar Singh, B. Ramakrishnan, Brundaban Sahu","submitted_at":"2018-01-13T07:37:12Z","abstract_excerpt":"In this paper, we find a basis for the space of modular forms of weight $2$ on $\\Gamma_1(48)$. We use this basis to find formulas for the number of representations of a positive integer $n$ by certain quaternary quadratic forms of the form $\\sum_{i=1}^4 a_i x_i^2$, $\\sum_{i=1}^2 b_i(x_{2i-1}^2 + x_{2i-1}x_{2i}+x_{2i}^2)$ and $a_1x_1^2 + a_2 x_2^2 + b_1(x_3^2+x_3x_4+x_4^2)$, where $a_i$'s belong to $\\{1,2,3,4,6,12\\}$ and $b_i$'s belong to $\\{1,2,4,8,16\\}$."},"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":"1801.04392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-13T07:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"1f9e9e50bd1b5ca3412523a3f3354a3b596b88572b072bf83ddef1b49f63928f","abstract_canon_sha256":"c037bb40b1a123c7d07254c42358000ec13132d0ec187bca3ee97015e7f7ef67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:06.602855Z","signature_b64":"KkYAReNMEqzPI00Zz+7tzVjT7pZTAH1KQjA9X8OJs++Tymhzb4qAZDnOXy9phu7jDxWMrux1aA/P/RDEUkAvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c9fb2389576803ef7355fcf62f698cd5ff4c6b8ed80365c99428d2e35866fd","last_reissued_at":"2026-05-18T00:26:06.602144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:06.602144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certain quaternary quadratic forms of level 48 and their representation numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anup Kumar Singh, B. Ramakrishnan, Brundaban Sahu","submitted_at":"2018-01-13T07:37:12Z","abstract_excerpt":"In this paper, we find a basis for the space of modular forms of weight $2$ on $\\Gamma_1(48)$. We use this basis to find formulas for the number of representations of a positive integer $n$ by certain quaternary quadratic forms of the form $\\sum_{i=1}^4 a_i x_i^2$, $\\sum_{i=1}^2 b_i(x_{2i-1}^2 + x_{2i-1}x_{2i}+x_{2i}^2)$ and $a_1x_1^2 + a_2 x_2^2 + b_1(x_3^2+x_3x_4+x_4^2)$, where $a_i$'s belong to $\\{1,2,3,4,6,12\\}$ and $b_i$'s belong to $\\{1,2,4,8,16\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04392","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":"1801.04392","created_at":"2026-05-18T00:26:06.602238+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04392v1","created_at":"2026-05-18T00:26:06.602238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04392","created_at":"2026-05-18T00:26:06.602238+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITE7WI4JK5UA","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITE7WI4JK5UAH33T","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITE7WI4J","created_at":"2026-05-18T12:32:31.084164+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/ITE7WI4JK5UAH33TKX6PML3JRT","json":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT.json","graph_json":"https://pith.science/api/pith-number/ITE7WI4JK5UAH33TKX6PML3JRT/graph.json","events_json":"https://pith.science/api/pith-number/ITE7WI4JK5UAH33TKX6PML3JRT/events.json","paper":"https://pith.science/paper/ITE7WI4J"},"agent_actions":{"view_html":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT","download_json":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT.json","view_paper":"https://pith.science/paper/ITE7WI4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04392&json=true","fetch_graph":"https://pith.science/api/pith-number/ITE7WI4JK5UAH33TKX6PML3JRT/graph.json","fetch_events":"https://pith.science/api/pith-number/ITE7WI4JK5UAH33TKX6PML3JRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT/action/storage_attestation","attest_author":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT/action/author_attestation","sign_citation":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT/action/citation_signature","submit_replication":"https://pith.science/pith/ITE7WI4JK5UAH33TKX6PML3JRT/action/replication_record"}},"created_at":"2026-05-18T00:26:06.602238+00:00","updated_at":"2026-05-18T00:26:06.602238+00:00"}