{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3VVMELQTMDDQNSDGW5AWEAYNKW","short_pith_number":"pith:3VVMELQT","canonical_record":{"source":{"id":"1403.3525","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"360ec3231c6c41949d8963fe933ad685ec1c7fe06229ac8f1e0c622fc3c029e2","abstract_canon_sha256":"c91e657a81f28d346970fe6988122f3d6054dca6c38babf751c4cbea4edca9de"},"schema_version":"1.0"},"canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","source":{"kind":"arxiv","id":"1403.3525","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3525","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3525v1","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3525","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"pith_short_12","alias_value":"3VVMELQTMDDQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VVMELQTMDDQNSDG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VVMELQT","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3VVMELQTMDDQNSDGW5AWEAYNKW","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3525","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"360ec3231c6c41949d8963fe933ad685ec1c7fe06229ac8f1e0c622fc3c029e2","abstract_canon_sha256":"c91e657a81f28d346970fe6988122f3d6054dca6c38babf751c4cbea4edca9de"},"schema_version":"1.0"},"canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:20.236277Z","signature_b64":"G7k7gYM2QDqmZMe82aWJ4OaCDQYjodJdrTYq2SMyHajpi4xWs420xOWvr6zILDc/44784m01zO/HBgdlKT4QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","last_reissued_at":"2026-05-18T02:56:20.235552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:20.235552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3525","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":"2026-05-18T02:56:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9q7H3yqqPlVBf8LjSv9qN0NwbHVgy1/4vsCVCFgsxp0bbKU5IwXV8ivUGIdLJ7Cvt4HuLW2f7hkxNWPu/v41Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:45:26.820677Z"},"content_sha256":"29b3194c4b116d0ce2d0b62b624977a1d426b9ba0cbea1cde7c756ddb5456a34","schema_version":"1.0","event_id":"sha256:29b3194c4b116d0ce2d0b62b624977a1d426b9ba0cbea1cde7c756ddb5456a34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3VVMELQTMDDQNSDGW5AWEAYNKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Additive solvability and linear independence of the solutions of a system of functional equations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AC","authors_text":"Eszter Gselmann, Zsolt P\\'ales","submitted_at":"2014-03-14T10:47:39Z","abstract_excerpt":"The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \\[d_{k}(xy)=\\sum_{i=0}^{k}\\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \\qquad (x,y\\in \\R,\\,k\\in\\{0,\\ldots,n\\}) \\] is studied, where $\\Delta_n:=\\big\\{(i,j)\\in\\Z\\times\\Z\\mid 0\\leq i,j\\mbox{and}i+j\\leq n\\big\\}$ and $\\Gamma\\colon\\Delta_n\\to\\R$ is a symmetric function such that $\\Gamma(i,j)=1$ whenever $i\\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\\dots,d_{n}\\colon \\R\\to\\R$ of the above system of equations is characterized. As a consequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3525","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":"2026-05-18T02:56:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ubt+vrGu5LAe+GLl33ivKBtO5GKRWy2QaZkVvki5HOkmQGRq2x38wx85arRTUgzH0vCpqcSxLmcFXNg/1YYcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:45:26.821307Z"},"content_sha256":"dc639e895ca85a6f9ed6816f4c8453d4cc8add4ca654add4a6918b866ea06083","schema_version":"1.0","event_id":"sha256:dc639e895ca85a6f9ed6816f4c8453d4cc8add4ca654add4a6918b866ea06083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/bundle.json","state_url":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/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":"2026-06-06T16:45:26Z","links":{"resolver":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW","bundle":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/bundle.json","state":"https://pith.science/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VVMELQTMDDQNSDGW5AWEAYNKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3VVMELQTMDDQNSDGW5AWEAYNKW","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":"c91e657a81f28d346970fe6988122f3d6054dca6c38babf751c4cbea4edca9de","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","title_canon_sha256":"360ec3231c6c41949d8963fe933ad685ec1c7fe06229ac8f1e0c622fc3c029e2"},"schema_version":"1.0","source":{"id":"1403.3525","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3525","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3525v1","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3525","created_at":"2026-05-18T02:56:20Z"},{"alias_kind":"pith_short_12","alias_value":"3VVMELQTMDDQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VVMELQTMDDQNSDG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VVMELQT","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:dc639e895ca85a6f9ed6816f4c8453d4cc8add4ca654add4a6918b866ea06083","target":"graph","created_at":"2026-05-18T02:56:20Z","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":"The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \\[d_{k}(xy)=\\sum_{i=0}^{k}\\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \\qquad (x,y\\in \\R,\\,k\\in\\{0,\\ldots,n\\}) \\] is studied, where $\\Delta_n:=\\big\\{(i,j)\\in\\Z\\times\\Z\\mid 0\\leq i,j\\mbox{and}i+j\\leq n\\big\\}$ and $\\Gamma\\colon\\Delta_n\\to\\R$ is a symmetric function such that $\\Gamma(i,j)=1$ whenever $i\\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\\dots,d_{n}\\colon \\R\\to\\R$ of the above system of equations is characterized. As a consequen","authors_text":"Eszter Gselmann, Zsolt P\\'ales","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","title":"Additive solvability and linear independence of the solutions of a system of functional equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3525","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":"sha256:29b3194c4b116d0ce2d0b62b624977a1d426b9ba0cbea1cde7c756ddb5456a34","target":"record","created_at":"2026-05-18T02:56:20Z","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":"c91e657a81f28d346970fe6988122f3d6054dca6c38babf751c4cbea4edca9de","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2014-03-14T10:47:39Z","title_canon_sha256":"360ec3231c6c41949d8963fe933ad685ec1c7fe06229ac8f1e0c622fc3c029e2"},"schema_version":"1.0","source":{"id":"1403.3525","kind":"arxiv","version":1}},"canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd6ac22e1360c706c866b74162030d559e7dc03912334762b0b52fb3344299aa","first_computed_at":"2026-05-18T02:56:20.235552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:20.235552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7k7gYM2QDqmZMe82aWJ4OaCDQYjodJdrTYq2SMyHajpi4xWs420xOWvr6zILDc/44784m01zO/HBgdlKT4QBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:20.236277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3525","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29b3194c4b116d0ce2d0b62b624977a1d426b9ba0cbea1cde7c756ddb5456a34","sha256:dc639e895ca85a6f9ed6816f4c8453d4cc8add4ca654add4a6918b866ea06083"],"state_sha256":"cf8132d6b64a7d2cee7359d059bf542273c6638647fb6a0afa2b962dffe423b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boMBdeuuq3LQWBlOcZ1UFROwJHN+J1tJ4xBs16yUWTVk8Q4i3Dt2k/TIdgaTzbfUnctV83xPqpT28TAmXUWfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:45:26.824771Z","bundle_sha256":"84200634da044d7ea47354fb1b618c87228c4d4469737655c1d69f928bed006b"}}