{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WE6D57MQW677WM6EYYC6762V4R","short_pith_number":"pith:WE6D57MQ","canonical_record":{"source":{"id":"1406.3624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-13T08:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"736e8e8e0dbb320c601c19370f908a85e6365cfd8a3b9c5163af53556a334f60","abstract_canon_sha256":"935e30c2076fd27a4bd8faac584d685aefe7ca934408f48b6a0b7b99976c1616"},"schema_version":"1.0"},"canonical_sha256":"b13c3efd90b7bffb33c4c605effb55e470ef7a00072f217ad0556a83c9941cd4","source":{"kind":"arxiv","id":"1406.3624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3624","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3624v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3624","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"WE6D57MQW677","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WE6D57MQW677WM6E","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WE6D57MQ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WE6D57MQW677WM6EYYC6762V4R","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-13T08:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"736e8e8e0dbb320c601c19370f908a85e6365cfd8a3b9c5163af53556a334f60","abstract_canon_sha256":"935e30c2076fd27a4bd8faac584d685aefe7ca934408f48b6a0b7b99976c1616"},"schema_version":"1.0"},"canonical_sha256":"b13c3efd90b7bffb33c4c605effb55e470ef7a00072f217ad0556a83c9941cd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:45.305566Z","signature_b64":"E02whmZim1Pzt9tz85fSYdXmRIYhHFMFqDDiNBzORR+NqS1yLr/S7g+KznnZY+6EjFMLce86QdauoN+LUem/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b13c3efd90b7bffb33c4c605effb55e470ef7a00072f217ad0556a83c9941cd4","last_reissued_at":"2026-05-18T02:49:45.305177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:45.305177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3624","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UtVpK3wXJroO/MyY7oEa7GWdmuULu4j+ZYqr5wUTy47thVsuYpwxdKxTnEiRuuHA2uRwfdOmbbEXg7PooyAIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:41:11.753169Z"},"content_sha256":"3630962b87c68daf8b0421c07a0ea297a57c3a57b315679da791a6577e8c2906","schema_version":"1.0","event_id":"sha256:3630962b87c68daf8b0421c07a0ea297a57c3a57b315679da791a6577e8c2906"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WE6D57MQW677WM6EYYC6762V4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Fixed Points Approach to stability of the Pexider Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Bouikhalene, E. Elqorachi, John M. Rassias","submitted_at":"2014-06-13T08:40:59Z","abstract_excerpt":"Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$\\frac{1}{\\mid K\\mid}\\sum_{k\\in K}f(x+k\\cdot y)=g(x)+h(y),\\;\\;x,y\\in E$$ from a normed space $E$ into a complete $\\beta$-normed space $F$, where $K$ is a finite abelian subgroup of the automorphism group of the group $(E,+)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3624","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kh7cuiMa6Na09o4Mcj0+KbQZpCJZQwNVJ93zMuQQO/lz+Kwas26wdn9EC/MrxHwO6WIreCrLNqQHB4lsoCyQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:41:11.753621Z"},"content_sha256":"6eba181deb6d7f0e7786bd29f683d18875ce8c1bd74a25cc874dc8d0dc4a6e2d","schema_version":"1.0","event_id":"sha256:6eba181deb6d7f0e7786bd29f683d18875ce8c1bd74a25cc874dc8d0dc4a6e2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WE6D57MQW677WM6EYYC6762V4R/bundle.json","state_url":"https://pith.science/pith/WE6D57MQW677WM6EYYC6762V4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WE6D57MQW677WM6EYYC6762V4R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T16:41:11Z","links":{"resolver":"https://pith.science/pith/WE6D57MQW677WM6EYYC6762V4R","bundle":"https://pith.science/pith/WE6D57MQW677WM6EYYC6762V4R/bundle.json","state":"https://pith.science/pith/WE6D57MQW677WM6EYYC6762V4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WE6D57MQW677WM6EYYC6762V4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WE6D57MQW677WM6EYYC6762V4R","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":"935e30c2076fd27a4bd8faac584d685aefe7ca934408f48b6a0b7b99976c1616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-13T08:40:59Z","title_canon_sha256":"736e8e8e0dbb320c601c19370f908a85e6365cfd8a3b9c5163af53556a334f60"},"schema_version":"1.0","source":{"id":"1406.3624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3624","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3624v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3624","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"WE6D57MQW677","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WE6D57MQW677WM6E","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WE6D57MQ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:6eba181deb6d7f0e7786bd29f683d18875ce8c1bd74a25cc874dc8d0dc4a6e2d","target":"graph","created_at":"2026-05-18T02:49:45Z","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":"Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$\\frac{1}{\\mid K\\mid}\\sum_{k\\in K}f(x+k\\cdot y)=g(x)+h(y),\\;\\;x,y\\in E$$ from a normed space $E$ into a complete $\\beta$-normed space $F$, where $K$ is a finite abelian subgroup of the automorphism group of the group $(E,+)$.","authors_text":"B. Bouikhalene, E. Elqorachi, John M. Rassias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-13T08:40:59Z","title":"A Fixed Points Approach to stability of the Pexider Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3624","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":"sha256:3630962b87c68daf8b0421c07a0ea297a57c3a57b315679da791a6577e8c2906","target":"record","created_at":"2026-05-18T02:49:45Z","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":"935e30c2076fd27a4bd8faac584d685aefe7ca934408f48b6a0b7b99976c1616","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-06-13T08:40:59Z","title_canon_sha256":"736e8e8e0dbb320c601c19370f908a85e6365cfd8a3b9c5163af53556a334f60"},"schema_version":"1.0","source":{"id":"1406.3624","kind":"arxiv","version":1}},"canonical_sha256":"b13c3efd90b7bffb33c4c605effb55e470ef7a00072f217ad0556a83c9941cd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b13c3efd90b7bffb33c4c605effb55e470ef7a00072f217ad0556a83c9941cd4","first_computed_at":"2026-05-18T02:49:45.305177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:45.305177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E02whmZim1Pzt9tz85fSYdXmRIYhHFMFqDDiNBzORR+NqS1yLr/S7g+KznnZY+6EjFMLce86QdauoN+LUem/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:45.305566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3630962b87c68daf8b0421c07a0ea297a57c3a57b315679da791a6577e8c2906","sha256:6eba181deb6d7f0e7786bd29f683d18875ce8c1bd74a25cc874dc8d0dc4a6e2d"],"state_sha256":"9cdb60c3010171758e66271e654b3950f04cebeae4a666962d361f19db44fcc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yU95i1ynVDaXc7wxs6g7lPM6DcNIHrqEomYWnTRJk8694CocT8oQRx3cmdJ8AM7ei2urx8MfkfJoeqOe392JDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:41:11.756492Z","bundle_sha256":"7b2cdb36a3d301414ebcf9fa97abd829734b257e22d52b5ba7f34f3338b3d217"}}