{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ORI6DEIVILRS5RFNAMDREDQV4T","short_pith_number":"pith:ORI6DEIV","canonical_record":{"source":{"id":"1401.2236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-10T06:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"579e21ce30e3072911ee352c77c1e2ac8ab11076a2078cf62d33bb4f37f5b4f0","abstract_canon_sha256":"16243baed8b2ada1b30147f492cc1c037ccd6ec7785269da212a776256ec62e1"},"schema_version":"1.0"},"canonical_sha256":"7451e1911542e32ec4ad0307120e15e4e5e22b201c7c388bc9b9fb06687f5501","source":{"kind":"arxiv","id":"1401.2236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2236","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2236v1","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2236","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ORI6DEIVILRS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"ORI6DEIVILRS5RFN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"ORI6DEIV","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ORI6DEIVILRS5RFNAMDREDQV4T","target":"record","payload":{"canonical_record":{"source":{"id":"1401.2236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-10T06:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"579e21ce30e3072911ee352c77c1e2ac8ab11076a2078cf62d33bb4f37f5b4f0","abstract_canon_sha256":"16243baed8b2ada1b30147f492cc1c037ccd6ec7785269da212a776256ec62e1"},"schema_version":"1.0"},"canonical_sha256":"7451e1911542e32ec4ad0307120e15e4e5e22b201c7c388bc9b9fb06687f5501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:45.956193Z","signature_b64":"NhEJ6y3WHQ9qnP19kmMx7xkzyxy1A87b4iKT6miyWC5SSeXgVVjjBPj3C7RN8p1+AciP+KD0QZhBEqmfmRjSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7451e1911542e32ec4ad0307120e15e4e5e22b201c7c388bc9b9fb06687f5501","last_reissued_at":"2026-05-18T03:02:45.955727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:45.955727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.2236","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":"2026-05-18T03:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"544qHsRqbdhB+zT23Ltr3XVGtST4TbKUGMbGZDSSF0CVr5ZKollpdq/OnrlEG52iZwJLQIjXR8eI9cTCAGK1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:37:21.664782Z"},"content_sha256":"e69b0bbe74fc7f0fb6c937bac83d9020d919601b5f232d7aba8cc2fe17a69dce","schema_version":"1.0","event_id":"sha256:e69b0bbe74fc7f0fb6c937bac83d9020d919601b5f232d7aba8cc2fe17a69dce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ORI6DEIVILRS5RFNAMDREDQV4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the coefficients of an expansion of $(1+1/x)^x$ related to Carleman's inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cristinel Mortici, Yue Hu","submitted_at":"2014-01-10T06:28:06Z","abstract_excerpt":"In this note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001) 651-659] and Alzer and Berg [some classes of completely monotonic functions Ann. Acad. Sci. Fennicae 27(2002) 445-460]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2236","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":"2026-05-18T03:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7KxiLfGGFXROCc6zSAjKW37s5BdxNvEum3Y8obUma4bgKjxoF9/Ja+kIQ1gHm2JkBZfS32JxEzSGopnqJibAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:37:21.665727Z"},"content_sha256":"e55e491c997cac0b7c53918dc34e27c2fa749b5677809c34113da33d4ad61412","schema_version":"1.0","event_id":"sha256:e55e491c997cac0b7c53918dc34e27c2fa749b5677809c34113da33d4ad61412"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ORI6DEIVILRS5RFNAMDREDQV4T/bundle.json","state_url":"https://pith.science/pith/ORI6DEIVILRS5RFNAMDREDQV4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ORI6DEIVILRS5RFNAMDREDQV4T/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":"2026-06-07T05:37:21Z","links":{"resolver":"https://pith.science/pith/ORI6DEIVILRS5RFNAMDREDQV4T","bundle":"https://pith.science/pith/ORI6DEIVILRS5RFNAMDREDQV4T/bundle.json","state":"https://pith.science/pith/ORI6DEIVILRS5RFNAMDREDQV4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ORI6DEIVILRS5RFNAMDREDQV4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ORI6DEIVILRS5RFNAMDREDQV4T","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":"16243baed8b2ada1b30147f492cc1c037ccd6ec7785269da212a776256ec62e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-10T06:28:06Z","title_canon_sha256":"579e21ce30e3072911ee352c77c1e2ac8ab11076a2078cf62d33bb4f37f5b4f0"},"schema_version":"1.0","source":{"id":"1401.2236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2236","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2236v1","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2236","created_at":"2026-05-18T03:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ORI6DEIVILRS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"ORI6DEIVILRS5RFN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"ORI6DEIV","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e55e491c997cac0b7c53918dc34e27c2fa749b5677809c34113da33d4ad61412","target":"graph","created_at":"2026-05-18T03:02:45Z","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 note, we present new properties for a sequence arising in some refinements of Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001) 651-659] and Alzer and Berg [some classes of completely monotonic functions Ann. Acad. Sci. Fennicae 27(2002) 445-460].","authors_text":"Cristinel Mortici, Yue Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-10T06:28:06Z","title":"On the coefficients of an expansion of $(1+1/x)^x$ related to Carleman's inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2236","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:e69b0bbe74fc7f0fb6c937bac83d9020d919601b5f232d7aba8cc2fe17a69dce","target":"record","created_at":"2026-05-18T03:02:45Z","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":"16243baed8b2ada1b30147f492cc1c037ccd6ec7785269da212a776256ec62e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-10T06:28:06Z","title_canon_sha256":"579e21ce30e3072911ee352c77c1e2ac8ab11076a2078cf62d33bb4f37f5b4f0"},"schema_version":"1.0","source":{"id":"1401.2236","kind":"arxiv","version":1}},"canonical_sha256":"7451e1911542e32ec4ad0307120e15e4e5e22b201c7c388bc9b9fb06687f5501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7451e1911542e32ec4ad0307120e15e4e5e22b201c7c388bc9b9fb06687f5501","first_computed_at":"2026-05-18T03:02:45.955727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:45.955727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NhEJ6y3WHQ9qnP19kmMx7xkzyxy1A87b4iKT6miyWC5SSeXgVVjjBPj3C7RN8p1+AciP+KD0QZhBEqmfmRjSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:45.956193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e69b0bbe74fc7f0fb6c937bac83d9020d919601b5f232d7aba8cc2fe17a69dce","sha256:e55e491c997cac0b7c53918dc34e27c2fa749b5677809c34113da33d4ad61412"],"state_sha256":"fcccb46a0d737f387eaf34de9798eb23512ef1746c70db2b7b11446888e53649"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+X27TiS7QK38xaKP223R0keB8qo0mYiRP5KoTk+/yxankVhPmz/s9mAR5NC/OdkUjFagwYsx9NRZSnj/iAHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:37:21.669632Z","bundle_sha256":"d5482766c8eb63f70178685d870b4a78fe09298175830814379bf8192be7ced5"}}