{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ITE7WI4JK5UAH33TKX6PML3JRT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c037bb40b1a123c7d07254c42358000ec13132d0ec187bca3ee97015e7f7ef67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-13T07:37:12Z","title_canon_sha256":"1f9e9e50bd1b5ca3412523a3f3354a3b596b88572b072bf83ddef1b49f63928f"},"schema_version":"1.0","source":{"id":"1801.04392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04392","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04392v1","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04392","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"ITE7WI4JK5UA","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ITE7WI4JK5UAH33T","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ITE7WI4J","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:80f6b70cfb172ccd592a203d1ee11fefcbdf1f652066cc2321ffa7f2cdc0dc23","target":"graph","created_at":"2026-05-18T00:26:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\{1,2,4,8,16\\}$.","authors_text":"Anup Kumar Singh, B. Ramakrishnan, Brundaban Sahu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-13T07:37:12Z","title":"Certain quaternary quadratic forms of level 48 and their representation numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04392","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5cb4071bfa2580d2f48cc35f325e1c06f782b3f3cc13da3be7b8629c9a3c138f","target":"record","created_at":"2026-05-18T00:26:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c037bb40b1a123c7d07254c42358000ec13132d0ec187bca3ee97015e7f7ef67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-13T07:37:12Z","title_canon_sha256":"1f9e9e50bd1b5ca3412523a3f3354a3b596b88572b072bf83ddef1b49f63928f"},"schema_version":"1.0","source":{"id":"1801.04392","kind":"arxiv","version":1}},"canonical_sha256":"44c9fb2389576803ef7355fcf62f698cd5ff4c6b8ed80365c99428d2e35866fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44c9fb2389576803ef7355fcf62f698cd5ff4c6b8ed80365c99428d2e35866fd","first_computed_at":"2026-05-18T00:26:06.602144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:06.602144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KkYAReNMEqzPI00Zz+7tzVjT7pZTAH1KQjA9X8OJs++Tymhzb4qAZDnOXy9phu7jDxWMrux1aA/P/RDEUkAvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:06.602855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cb4071bfa2580d2f48cc35f325e1c06f782b3f3cc13da3be7b8629c9a3c138f","sha256:80f6b70cfb172ccd592a203d1ee11fefcbdf1f652066cc2321ffa7f2cdc0dc23"],"state_sha256":"9c34a11ad0455d2abb3368a383c376ab861fbd2fc68812af296360e7ee40b795"}