{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:46GE2JZIYY2AVWVUJGNLQ4ZF5D","short_pith_number":"pith:46GE2JZI","schema_version":"1.0","canonical_sha256":"e78c4d2728c6340adab4499ab87325e8cd2d341f1c64c08a7119886004d446dc","source":{"kind":"arxiv","id":"1506.06376","version":1},"attestation_state":"computed","paper":{"title":"Solution and Stability of a Mixed Type Functional Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abasalt Bodaghi, Pasupathi Narasimman","submitted_at":"2015-06-21T15:27:23Z","abstract_excerpt":"In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the new mixed type additive and cubic functional equation $$3f(x+3y) - f(3x + y)=12[f(x+y)+f(x-y)]-16[f(x)+f(y)] + 12f(2y) - 4f(2x).$$ As some corollaries, we show that the stability of this equation can be controlled by the sum and product of powers of norms."},"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":"1506.06376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-21T15:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"6314957c1c6a752056d534854554f891439c78c33e846779d68e64effc64a0e3","abstract_canon_sha256":"c64a764f2e742b23f5a639474187aa28390b09a096f659ea278bc299f114478f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:45.355127Z","signature_b64":"868LcYVuSkbNaBfwfL1WNzs/ZDrlYBGFtwCK5dwPu2ynrrAu/t0u9rPhImURi3a4MVInGK4CJTXJgHA6gpv0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e78c4d2728c6340adab4499ab87325e8cd2d341f1c64c08a7119886004d446dc","last_reissued_at":"2026-05-18T01:41:45.354630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:45.354630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solution and Stability of a Mixed Type Functional Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abasalt Bodaghi, Pasupathi Narasimman","submitted_at":"2015-06-21T15:27:23Z","abstract_excerpt":"In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the new mixed type additive and cubic functional equation $$3f(x+3y) - f(3x + y)=12[f(x+y)+f(x-y)]-16[f(x)+f(y)] + 12f(2y) - 4f(2x).$$ As some corollaries, we show that the stability of this equation can be controlled by the sum and product of powers of norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06376","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":"1506.06376","created_at":"2026-05-18T01:41:45.354715+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06376v1","created_at":"2026-05-18T01:41:45.354715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06376","created_at":"2026-05-18T01:41:45.354715+00:00"},{"alias_kind":"pith_short_12","alias_value":"46GE2JZIYY2A","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"46GE2JZIYY2AVWVU","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"46GE2JZI","created_at":"2026-05-18T12:29:05.191682+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/46GE2JZIYY2AVWVUJGNLQ4ZF5D","json":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D.json","graph_json":"https://pith.science/api/pith-number/46GE2JZIYY2AVWVUJGNLQ4ZF5D/graph.json","events_json":"https://pith.science/api/pith-number/46GE2JZIYY2AVWVUJGNLQ4ZF5D/events.json","paper":"https://pith.science/paper/46GE2JZI"},"agent_actions":{"view_html":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D","download_json":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D.json","view_paper":"https://pith.science/paper/46GE2JZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06376&json=true","fetch_graph":"https://pith.science/api/pith-number/46GE2JZIYY2AVWVUJGNLQ4ZF5D/graph.json","fetch_events":"https://pith.science/api/pith-number/46GE2JZIYY2AVWVUJGNLQ4ZF5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D/action/storage_attestation","attest_author":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D/action/author_attestation","sign_citation":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D/action/citation_signature","submit_replication":"https://pith.science/pith/46GE2JZIYY2AVWVUJGNLQ4ZF5D/action/replication_record"}},"created_at":"2026-05-18T01:41:45.354715+00:00","updated_at":"2026-05-18T01:41:45.354715+00:00"}