{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EHNLT65H2ELDIBWIEXMHXR6GT5","short_pith_number":"pith:EHNLT65H","canonical_record":{"source":{"id":"1603.06781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-22T13:29:45Z","cross_cats_sorted":[],"title_canon_sha256":"6e174bfdad2940036204720fea9b81f98e4580b7adfb2afbd424e4152cf17984","abstract_canon_sha256":"8fce6b11a8be5a87981eaebc583d52c4669dd509700bbcf588c989ef3c4d3ed1"},"schema_version":"1.0"},"canonical_sha256":"21dab9fba7d1163406c825d87bc7c69f75f92a302f821c538ebb586589dc00de","source":{"kind":"arxiv","id":"1603.06781","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06781","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06781v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06781","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"EHNLT65H2ELD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EHNLT65H2ELDIBWI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EHNLT65H","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EHNLT65H2ELDIBWIEXMHXR6GT5","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-22T13:29:45Z","cross_cats_sorted":[],"title_canon_sha256":"6e174bfdad2940036204720fea9b81f98e4580b7adfb2afbd424e4152cf17984","abstract_canon_sha256":"8fce6b11a8be5a87981eaebc583d52c4669dd509700bbcf588c989ef3c4d3ed1"},"schema_version":"1.0"},"canonical_sha256":"21dab9fba7d1163406c825d87bc7c69f75f92a302f821c538ebb586589dc00de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:34.744415Z","signature_b64":"8exTJDQ+9qj2xPgOPKys/R5GTT9eYF2oLBktIpveW/LPO+NQsiNKE7ZJHUqWpigbCSm4TTW6NCnhSS0lyH2zBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21dab9fba7d1163406c825d87bc7c69f75f92a302f821c538ebb586589dc00de","last_reissued_at":"2026-05-18T01:18:34.743930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:34.743930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06781","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//PejVJY44IwcWeo/Ewe+N9mc8eAvwVTlfVeUB52nqB0BXAka0zpnVGQZ0HbZqY2U0V5gOmFZIbnMnLo5VlqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:20:05.888214Z"},"content_sha256":"0c3870523dd1c030b114fc97197e5ae10e32935ba5fdf9b1c24ecb6a3174d2ad","schema_version":"1.0","event_id":"sha256:0c3870523dd1c030b114fc97197e5ae10e32935ba5fdf9b1c24ecb6a3174d2ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EHNLT65H2ELDIBWIEXMHXR6GT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new $I_\\lambda$-lacunary statistical convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adem K{\\i}l{\\i}\\c{c}man, Stuti Borgohain","submitted_at":"2016-03-22T13:29:45Z","abstract_excerpt":"In this paper, we introduce some new $I_\\lambda$-lacunary statistically convergent sequence spaces of order $\\alpha$ defined by a Musielak-Orlicz function. We study some relations between $I_\\lambda$-lacunary statistically convergence with lacunary $I_\\lambda$-summable sequences. Moreover we also study about the $I_\\lambda$-lacunary statistically convergence of sequences in topological groups and give some important inclusion theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06781","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NfwfnSt0aE0HGA5wTuXIe8mjnUfcJABWUmrxmlw//vhEaD7M2XSahUatFQeqX6X0An7alMaUaWpvwdAskr8EBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:20:05.889119Z"},"content_sha256":"a1d751f266719f4a94e0f98c7a70f6fb3a578049dcf8d6d47cf728e98b3c000f","schema_version":"1.0","event_id":"sha256:a1d751f266719f4a94e0f98c7a70f6fb3a578049dcf8d6d47cf728e98b3c000f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/bundle.json","state_url":"https://pith.science/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/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":"2026-06-11T22:20:05Z","links":{"resolver":"https://pith.science/pith/EHNLT65H2ELDIBWIEXMHXR6GT5","bundle":"https://pith.science/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/bundle.json","state":"https://pith.science/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHNLT65H2ELDIBWIEXMHXR6GT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EHNLT65H2ELDIBWIEXMHXR6GT5","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":"8fce6b11a8be5a87981eaebc583d52c4669dd509700bbcf588c989ef3c4d3ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-22T13:29:45Z","title_canon_sha256":"6e174bfdad2940036204720fea9b81f98e4580b7adfb2afbd424e4152cf17984"},"schema_version":"1.0","source":{"id":"1603.06781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06781","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06781v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06781","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"EHNLT65H2ELD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EHNLT65H2ELDIBWI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EHNLT65H","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:a1d751f266719f4a94e0f98c7a70f6fb3a578049dcf8d6d47cf728e98b3c000f","target":"graph","created_at":"2026-05-18T01:18:34Z","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 paper, we introduce some new $I_\\lambda$-lacunary statistically convergent sequence spaces of order $\\alpha$ defined by a Musielak-Orlicz function. We study some relations between $I_\\lambda$-lacunary statistically convergence with lacunary $I_\\lambda$-summable sequences. Moreover we also study about the $I_\\lambda$-lacunary statistically convergence of sequences in topological groups and give some important inclusion theorems.","authors_text":"Adem K{\\i}l{\\i}\\c{c}man, Stuti Borgohain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-22T13:29:45Z","title":"Some new $I_\\lambda$-lacunary statistical convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06781","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":"sha256:0c3870523dd1c030b114fc97197e5ae10e32935ba5fdf9b1c24ecb6a3174d2ad","target":"record","created_at":"2026-05-18T01:18:34Z","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":"8fce6b11a8be5a87981eaebc583d52c4669dd509700bbcf588c989ef3c4d3ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-22T13:29:45Z","title_canon_sha256":"6e174bfdad2940036204720fea9b81f98e4580b7adfb2afbd424e4152cf17984"},"schema_version":"1.0","source":{"id":"1603.06781","kind":"arxiv","version":1}},"canonical_sha256":"21dab9fba7d1163406c825d87bc7c69f75f92a302f821c538ebb586589dc00de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21dab9fba7d1163406c825d87bc7c69f75f92a302f821c538ebb586589dc00de","first_computed_at":"2026-05-18T01:18:34.743930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:34.743930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8exTJDQ+9qj2xPgOPKys/R5GTT9eYF2oLBktIpveW/LPO+NQsiNKE7ZJHUqWpigbCSm4TTW6NCnhSS0lyH2zBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:34.744415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c3870523dd1c030b114fc97197e5ae10e32935ba5fdf9b1c24ecb6a3174d2ad","sha256:a1d751f266719f4a94e0f98c7a70f6fb3a578049dcf8d6d47cf728e98b3c000f"],"state_sha256":"05d500d971c5b74b6be597dea799a5059aec110f30dc74f56dc47e5f8c1d6666"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txAlxEFtDNXlXC+DxZRQ6Tlc6tyKdgUFkANALUXcQlcLW5tsmBXI0FktOKLVaqlmYAhmD5WH7FZMns7ekje/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:20:05.893232Z","bundle_sha256":"de8d4cbf3baea48e6e8798ec2b9f5677548c5d21e5ee27c3b809a36fc717ab51"}}