{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QH45ONRVJG6D6EU66JGXX67ELG","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":"87322e79af0826cd8c5ea6dfefcfa4aae080ff5e0ddb4ccdf0fc7c5d4e81f25c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T18:03:53Z","title_canon_sha256":"e20e94da299e1aac2d82d115e9c3d08f00863c0bad3f7eff79a3d62646adca5f"},"schema_version":"1.0","source":{"id":"1611.07907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07907","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07907v1","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07907","created_at":"2026-05-18T00:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"QH45ONRVJG6D","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QH45ONRVJG6D6EU6","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QH45ONRV","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:5814d59511ebbbd7ec3823c7dbe705cf6ffa26258e80a1ecec3cec5f15f2498d","target":"graph","created_at":"2026-05-18T00:56:59Z","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 article we introduce and study the lacunary arithmetic convergent sequence space $AC_{\\theta}$. Using the idea of strong Ces\\`{a}ro summable sequence and arithmetic convergence we define $AC_{\\sigma_1}$ and study the relations between $AC_{\\theta}$ and $AC_{\\sigma_1}$. Finally using modulus function we define $AC_{\\theta}(f)$ and study some interesting results.","authors_text":"Bipan Hazarika, Taja Yaying","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T18:03:53Z","title":"Lacunary Arithmetic convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07907","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:e1ec7a6ac1ca94e96337c8be18aaae9d666b6e6acc0aeeb465e66032dad36f30","target":"record","created_at":"2026-05-18T00:56:59Z","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":"87322e79af0826cd8c5ea6dfefcfa4aae080ff5e0ddb4ccdf0fc7c5d4e81f25c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-20T18:03:53Z","title_canon_sha256":"e20e94da299e1aac2d82d115e9c3d08f00863c0bad3f7eff79a3d62646adca5f"},"schema_version":"1.0","source":{"id":"1611.07907","kind":"arxiv","version":1}},"canonical_sha256":"81f9d7363549bc3f129ef24d7bfbe459b30a6bc5da595bc853b48b7c75d0df40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81f9d7363549bc3f129ef24d7bfbe459b30a6bc5da595bc853b48b7c75d0df40","first_computed_at":"2026-05-18T00:56:59.586395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:59.586395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VijGbg7/VkGlWgVBdquKJUigsTDr/6e2TB2LG6ueTxqXc5pVjdpCrshhKe0HS3NqKtwWpsIsGaDxmg/HxlAwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:59.586838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1ec7a6ac1ca94e96337c8be18aaae9d666b6e6acc0aeeb465e66032dad36f30","sha256:5814d59511ebbbd7ec3823c7dbe705cf6ffa26258e80a1ecec3cec5f15f2498d"],"state_sha256":"02626895bf09be462033bbab1dfbb13b7b88da4d296256680213e399381d4abc"}