{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QC3ATJM6A452LUHJTLTXE6J3CN","short_pith_number":"pith:QC3ATJM6","canonical_record":{"source":{"id":"1301.6874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-29T09:44:17Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7f7d4208f4309c61312c471f88b39a8ae7feb354c84a95d31009565873d4a071","abstract_canon_sha256":"423f39799ba9dde7537558ddbe7214a45724831a9167d47a7df7ae1eb429ca8a"},"schema_version":"1.0"},"canonical_sha256":"80b609a59e073ba5d0e99ae772793b13736a15cfbb5cafd08f029d6b103a1752","source":{"kind":"arxiv","id":"1301.6874","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6874","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6874v1","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6874","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"pith_short_12","alias_value":"QC3ATJM6A452","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QC3ATJM6A452LUHJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QC3ATJM6","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QC3ATJM6A452LUHJTLTXE6J3CN","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-29T09:44:17Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7f7d4208f4309c61312c471f88b39a8ae7feb354c84a95d31009565873d4a071","abstract_canon_sha256":"423f39799ba9dde7537558ddbe7214a45724831a9167d47a7df7ae1eb429ca8a"},"schema_version":"1.0"},"canonical_sha256":"80b609a59e073ba5d0e99ae772793b13736a15cfbb5cafd08f029d6b103a1752","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:12.075190Z","signature_b64":"+AzGW10+kLI/s6q0i69LiOyUuPnGAZN14VPOqpUGnzzAo0T+IySZjy/X09Beu1LVbfT0dr5kxrvDyf7n9W7jBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80b609a59e073ba5d0e99ae772793b13736a15cfbb5cafd08f029d6b103a1752","last_reissued_at":"2026-05-18T03:35:12.074463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:12.074463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6874","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":"2026-05-18T03:35:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vGZQ+86JMUFZjuRvBuI1a2HEkmZB7VDMF08kc1MMqb/OrqcJTYLWg8MHyClnK1YKw9lRWgiUwA1YmYF+lMgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:04:18.312239Z"},"content_sha256":"ccda4bb442b6812275beba3918cb83659a42253485b062b7c4fd0c4d5ed2bf48","schema_version":"1.0","event_id":"sha256:ccda4bb442b6812275beba3918cb83659a42253485b062b7c4fd0c4d5ed2bf48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QC3ATJM6A452LUHJTLTXE6J3CN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On local property of absolute summability of factored Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Dansheng Yu, H\\\"usey\\.in Bor, Ping Zhou","submitted_at":"2013-01-29T09:44:17Z","abstract_excerpt":"We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\\left\\vert A,\\alpha_{n}\\right\\vert _{k}$ summability, and the class $\\mathcal{S}\\left( \\alpha_{n},\\phi_{n}\\right) $, which generalize some well known results and can be applied to improve many classical absolute summability methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6874","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":"2026-05-18T03:35:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPDtC+OOra7ttNbZwpLsLqw/sL4BUX2iFOvTOs9k4ehFvzvoADo0mvE54zFF7Z3E9PzFaF6xt1wRTXKVlGNGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:04:18.312922Z"},"content_sha256":"56a9c69891efc95d3ba188cc25c79890c6bd6f2610299f9ac68a0b5056406d72","schema_version":"1.0","event_id":"sha256:56a9c69891efc95d3ba188cc25c79890c6bd6f2610299f9ac68a0b5056406d72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QC3ATJM6A452LUHJTLTXE6J3CN/bundle.json","state_url":"https://pith.science/pith/QC3ATJM6A452LUHJTLTXE6J3CN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QC3ATJM6A452LUHJTLTXE6J3CN/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":"2026-05-27T00:04:18Z","links":{"resolver":"https://pith.science/pith/QC3ATJM6A452LUHJTLTXE6J3CN","bundle":"https://pith.science/pith/QC3ATJM6A452LUHJTLTXE6J3CN/bundle.json","state":"https://pith.science/pith/QC3ATJM6A452LUHJTLTXE6J3CN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QC3ATJM6A452LUHJTLTXE6J3CN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QC3ATJM6A452LUHJTLTXE6J3CN","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":"423f39799ba9dde7537558ddbe7214a45724831a9167d47a7df7ae1eb429ca8a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-29T09:44:17Z","title_canon_sha256":"7f7d4208f4309c61312c471f88b39a8ae7feb354c84a95d31009565873d4a071"},"schema_version":"1.0","source":{"id":"1301.6874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6874","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6874v1","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6874","created_at":"2026-05-18T03:35:12Z"},{"alias_kind":"pith_short_12","alias_value":"QC3ATJM6A452","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QC3ATJM6A452LUHJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QC3ATJM6","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:56a9c69891efc95d3ba188cc25c79890c6bd6f2610299f9ac68a0b5056406d72","target":"graph","created_at":"2026-05-18T03:35:12Z","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":"We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\\left\\vert A,\\alpha_{n}\\right\\vert _{k}$ summability, and the class $\\mathcal{S}\\left( \\alpha_{n},\\phi_{n}\\right) $, which generalize some well known results and can be applied to improve many classical absolute summability methods.","authors_text":"Dansheng Yu, H\\\"usey\\.in Bor, Ping Zhou","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-29T09:44:17Z","title":"On local property of absolute summability of factored Fourier series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6874","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:ccda4bb442b6812275beba3918cb83659a42253485b062b7c4fd0c4d5ed2bf48","target":"record","created_at":"2026-05-18T03:35:12Z","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":"423f39799ba9dde7537558ddbe7214a45724831a9167d47a7df7ae1eb429ca8a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-29T09:44:17Z","title_canon_sha256":"7f7d4208f4309c61312c471f88b39a8ae7feb354c84a95d31009565873d4a071"},"schema_version":"1.0","source":{"id":"1301.6874","kind":"arxiv","version":1}},"canonical_sha256":"80b609a59e073ba5d0e99ae772793b13736a15cfbb5cafd08f029d6b103a1752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80b609a59e073ba5d0e99ae772793b13736a15cfbb5cafd08f029d6b103a1752","first_computed_at":"2026-05-18T03:35:12.074463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:12.074463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+AzGW10+kLI/s6q0i69LiOyUuPnGAZN14VPOqpUGnzzAo0T+IySZjy/X09Beu1LVbfT0dr5kxrvDyf7n9W7jBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:12.075190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccda4bb442b6812275beba3918cb83659a42253485b062b7c4fd0c4d5ed2bf48","sha256:56a9c69891efc95d3ba188cc25c79890c6bd6f2610299f9ac68a0b5056406d72"],"state_sha256":"1d9c4c1623aeab007349b4f17d3d328e68079ceb5c7a7c4d1fced799008932ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqD/5w5+iSe7UGStS2dl6tXC+Z3jygoZ6a8OZJXRrpY8CMFpF0ohMCgHOGxypfTwjqeD4ipde5K3HBy5AtzyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:04:18.316675Z","bundle_sha256":"b610bbdcbf576ef787e9275b6a3075abb98fd9a82010d857d853b31ab1c2dcd4"}}