{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V46OR27QKVRRM5S3CZWQ4AFIRW","short_pith_number":"pith:V46OR27Q","canonical_record":{"source":{"id":"1706.07289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-18T10:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"c108a0a92ab7c44a229a452e4e73d52adafff71bab10fd7ce3d3e556fdd8eba9","abstract_canon_sha256":"e8f3602beb79667c04b180fe5b9a538a83d5cc7f996b90e0f8c90f193ce93761"},"schema_version":"1.0"},"canonical_sha256":"af3ce8ebf0556316765b166d0e00a88d8ebefc025f44f9b25537e717857eceb5","source":{"kind":"arxiv","id":"1706.07289","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07289","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07289v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07289","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"V46OR27QKVRR","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V46OR27QKVRRM5S3","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V46OR27Q","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V46OR27QKVRRM5S3CZWQ4AFIRW","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-18T10:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"c108a0a92ab7c44a229a452e4e73d52adafff71bab10fd7ce3d3e556fdd8eba9","abstract_canon_sha256":"e8f3602beb79667c04b180fe5b9a538a83d5cc7f996b90e0f8c90f193ce93761"},"schema_version":"1.0"},"canonical_sha256":"af3ce8ebf0556316765b166d0e00a88d8ebefc025f44f9b25537e717857eceb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:52.056554Z","signature_b64":"dlo4FlkQlh3BoPukBz5vFxw9zavpcwDeZPi1nIL4wH5jgc5Tg0OY81jUCMmvqFQSKOOXWg5XtJ/HThTAR1Y8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af3ce8ebf0556316765b166d0e00a88d8ebefc025f44f9b25537e717857eceb5","last_reissued_at":"2026-05-18T00:41:52.055729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:52.055729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07289","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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qy3mbuPkBAmgG43/s+Cgcqaw9ndUY4BE6Yj7POTfMGTMsUBxZOymHYtmi0Cjhx30Zhhxct0B7+Nnr8daO8aHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T16:16:31.599298Z"},"content_sha256":"382a1dbc20f177bdb74f607589cca9e94d3486cb153f6e9a4735b18e862349f8","schema_version":"1.0","event_id":"sha256:382a1dbc20f177bdb74f607589cca9e94d3486cb153f6e9a4735b18e862349f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V46OR27QKVRRM5S3CZWQ4AFIRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Fibonacci sequence spaces of non-absolute type derived from $\\ell_{p} $ with $(1 \\leq p \\leq \\infty)$ and Hausdorff measure of non-compactness of composition operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anupam Das, Bipan Hazarika, Feyzi Ba\\c{s}ar","submitted_at":"2017-06-18T10:08:06Z","abstract_excerpt":"The aim of the paper is to introduce the spaces $\\ell_{\\infty}^{\\lambda}(\\widehat{F})$ and $\\ell_{p}^{\\lambda}(\\widehat{F})$ derived by the composition of the two infinite matrices $\\Lambda=(\\lambda_{nk})$ and $\\widehat{F}=\\left( f_{nk} \\right),$ which are the $BK$-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the $\\alpha$-, $\\beta$-, $\\gamma$-duals of those spaces and also construct the basis for $\\ell_{p}^{\\lambda}(\\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\\ell_{\\infty}^{\\lambda}(\\widehat{F})$ and $\\ell_{p}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07289","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":"2026-05-18T00:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ykeo1RSXnIx+8sdQvz7+U3zI9Uxs1jzs7z2g8ZCD/0QjNzNulzBlvO4FgJ4fJowu5F8Q3S0DnZWwX4x+kGH+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T16:16:31.599659Z"},"content_sha256":"aaec8dfd7f5d8b051eaf3b9e5386731b746cc945b2f496199e39b4cb443b5e05","schema_version":"1.0","event_id":"sha256:aaec8dfd7f5d8b051eaf3b9e5386731b746cc945b2f496199e39b4cb443b5e05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/bundle.json","state_url":"https://pith.science/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/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":"2026-07-02T16:16:31Z","links":{"resolver":"https://pith.science/pith/V46OR27QKVRRM5S3CZWQ4AFIRW","bundle":"https://pith.science/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/bundle.json","state":"https://pith.science/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V46OR27QKVRRM5S3CZWQ4AFIRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V46OR27QKVRRM5S3CZWQ4AFIRW","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":"e8f3602beb79667c04b180fe5b9a538a83d5cc7f996b90e0f8c90f193ce93761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-18T10:08:06Z","title_canon_sha256":"c108a0a92ab7c44a229a452e4e73d52adafff71bab10fd7ce3d3e556fdd8eba9"},"schema_version":"1.0","source":{"id":"1706.07289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07289","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07289v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07289","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"V46OR27QKVRR","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V46OR27QKVRRM5S3","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V46OR27Q","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:aaec8dfd7f5d8b051eaf3b9e5386731b746cc945b2f496199e39b4cb443b5e05","target":"graph","created_at":"2026-05-18T00:41:52Z","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 the paper is to introduce the spaces $\\ell_{\\infty}^{\\lambda}(\\widehat{F})$ and $\\ell_{p}^{\\lambda}(\\widehat{F})$ derived by the composition of the two infinite matrices $\\Lambda=(\\lambda_{nk})$ and $\\widehat{F}=\\left( f_{nk} \\right),$ which are the $BK$-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the $\\alpha$-, $\\beta$-, $\\gamma$-duals of those spaces and also construct the basis for $\\ell_{p}^{\\lambda}(\\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\\ell_{\\infty}^{\\lambda}(\\widehat{F})$ and $\\ell_{p}^{","authors_text":"Anupam Das, Bipan Hazarika, Feyzi Ba\\c{s}ar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-18T10:08:06Z","title":"Some Fibonacci sequence spaces of non-absolute type derived from $\\ell_{p} $ with $(1 \\leq p \\leq \\infty)$ and Hausdorff measure of non-compactness of composition operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07289","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":"sha256:382a1dbc20f177bdb74f607589cca9e94d3486cb153f6e9a4735b18e862349f8","target":"record","created_at":"2026-05-18T00:41:52Z","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":"e8f3602beb79667c04b180fe5b9a538a83d5cc7f996b90e0f8c90f193ce93761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-18T10:08:06Z","title_canon_sha256":"c108a0a92ab7c44a229a452e4e73d52adafff71bab10fd7ce3d3e556fdd8eba9"},"schema_version":"1.0","source":{"id":"1706.07289","kind":"arxiv","version":1}},"canonical_sha256":"af3ce8ebf0556316765b166d0e00a88d8ebefc025f44f9b25537e717857eceb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af3ce8ebf0556316765b166d0e00a88d8ebefc025f44f9b25537e717857eceb5","first_computed_at":"2026-05-18T00:41:52.055729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.055729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dlo4FlkQlh3BoPukBz5vFxw9zavpcwDeZPi1nIL4wH5jgc5Tg0OY81jUCMmvqFQSKOOXWg5XtJ/HThTAR1Y8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.056554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:382a1dbc20f177bdb74f607589cca9e94d3486cb153f6e9a4735b18e862349f8","sha256:aaec8dfd7f5d8b051eaf3b9e5386731b746cc945b2f496199e39b4cb443b5e05"],"state_sha256":"7000033b8cf2c85f556d013a6bde265890fdbc87933fb240a250166d5e6b4449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RLNcE+61YMYHUnjgFQbbLq2jiAZASaMWc2KuMH/60Q/NFVERFym4pb1IpPc5963dPLP8b+TmV0du+xuV69iSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T16:16:31.601717Z","bundle_sha256":"9eb587ad5b3fecc3098bb44939126dae3f6b06fb98f720eac18a79bfb98d231d"}}