{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W5A4D7KR7EPXQW5LCXJAZCOECP","short_pith_number":"pith:W5A4D7KR","canonical_record":{"source":{"id":"1506.07391","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2015-06-10T06:33:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5d5592156e19184a18e41710a32a0b034b26e871f3a829b864ef013bb508dc34","abstract_canon_sha256":"6c5c4e5834c88206fb9aa1e959a363ba2dcfffb8524c08ae3524514bc9562e4a"},"schema_version":"1.0"},"canonical_sha256":"b741c1fd51f91f785bab15d20c89c413e49189b0403d716d0d126400bd5dc61c","source":{"kind":"arxiv","id":"1506.07391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07391","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07391v1","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07391","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"W5A4D7KR7EPX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W5A4D7KR7EPXQW5L","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W5A4D7KR","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W5A4D7KR7EPXQW5LCXJAZCOECP","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07391","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2015-06-10T06:33:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5d5592156e19184a18e41710a32a0b034b26e871f3a829b864ef013bb508dc34","abstract_canon_sha256":"6c5c4e5834c88206fb9aa1e959a363ba2dcfffb8524c08ae3524514bc9562e4a"},"schema_version":"1.0"},"canonical_sha256":"b741c1fd51f91f785bab15d20c89c413e49189b0403d716d0d126400bd5dc61c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.186716Z","signature_b64":"dIT+REJJG22dY1sfwyp9syj1g38xJX9JM6SpvyduQto6CFNcdtbkP1JU4PkVMdJ+2odDkvlKSUeVx/dwPABvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b741c1fd51f91f785bab15d20c89c413e49189b0403d716d0d126400bd5dc61c","last_reissued_at":"2026-05-18T01:39:54.186243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.186243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07391","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":"2026-05-18T01:39:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lD5izjHHQWizd5YLfqrNkPmlRw+38MmE4AagFDZNzGxsRzya6vMF4VIByT4BqyAqhVl0XUYBkPfeqHpDgOcsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:09:14.877528Z"},"content_sha256":"3acadbf0d35cd7189a2c891fb7a5c0dc36acbe6535b2905398d8b5103a09dbce","schema_version":"1.0","event_id":"sha256:3acadbf0d35cd7189a2c891fb7a5c0dc36acbe6535b2905398d8b5103a09dbce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W5A4D7KR7EPXQW5LCXJAZCOECP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hermite-hadamard type inequalities for generalized $s$-convex functions on real linear fractal set $\\mathbb{R}^{\\alpha}(0<\\alpha<1)$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Huixia Mo, Xin Sui","submitted_at":"2015-06-10T06:33:13Z","abstract_excerpt":"In the paper, we establish the Hermite-Hadamard type inequalities for the generalized s-convex functions in the second sense on real linear fractal set $\\mathbb{R}^{\\alpha}(0<\\alpha<1).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07391","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":"2026-05-18T01:39:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7Wi9fsw6uOopw1NDN33qeJh2Ve7uGRiDgAYmZjJNnlNLKvM4FRMMooe8/G0WSY0JagX3XfzOCdbOq6ryu/PDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:09:14.878271Z"},"content_sha256":"ffc5a854f6a98ad6e1d07c96dc12ac9d426de4eebd5cf56d5986044d4307bb1d","schema_version":"1.0","event_id":"sha256:ffc5a854f6a98ad6e1d07c96dc12ac9d426de4eebd5cf56d5986044d4307bb1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/bundle.json","state_url":"https://pith.science/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/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":"2026-06-11T20:09:14Z","links":{"resolver":"https://pith.science/pith/W5A4D7KR7EPXQW5LCXJAZCOECP","bundle":"https://pith.science/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/bundle.json","state":"https://pith.science/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5A4D7KR7EPXQW5LCXJAZCOECP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W5A4D7KR7EPXQW5LCXJAZCOECP","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":"6c5c4e5834c88206fb9aa1e959a363ba2dcfffb8524c08ae3524514bc9562e4a","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2015-06-10T06:33:13Z","title_canon_sha256":"5d5592156e19184a18e41710a32a0b034b26e871f3a829b864ef013bb508dc34"},"schema_version":"1.0","source":{"id":"1506.07391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07391","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07391v1","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07391","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"W5A4D7KR7EPX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W5A4D7KR7EPXQW5L","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W5A4D7KR","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:ffc5a854f6a98ad6e1d07c96dc12ac9d426de4eebd5cf56d5986044d4307bb1d","target":"graph","created_at":"2026-05-18T01:39:54Z","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 the paper, we establish the Hermite-Hadamard type inequalities for the generalized s-convex functions in the second sense on real linear fractal set $\\mathbb{R}^{\\alpha}(0<\\alpha<1).$","authors_text":"Huixia Mo, Xin Sui","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2015-06-10T06:33:13Z","title":"Hermite-hadamard type inequalities for generalized $s$-convex functions on real linear fractal set $\\mathbb{R}^{\\alpha}(0<\\alpha<1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07391","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":"sha256:3acadbf0d35cd7189a2c891fb7a5c0dc36acbe6535b2905398d8b5103a09dbce","target":"record","created_at":"2026-05-18T01:39:54Z","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":"6c5c4e5834c88206fb9aa1e959a363ba2dcfffb8524c08ae3524514bc9562e4a","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2015-06-10T06:33:13Z","title_canon_sha256":"5d5592156e19184a18e41710a32a0b034b26e871f3a829b864ef013bb508dc34"},"schema_version":"1.0","source":{"id":"1506.07391","kind":"arxiv","version":1}},"canonical_sha256":"b741c1fd51f91f785bab15d20c89c413e49189b0403d716d0d126400bd5dc61c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b741c1fd51f91f785bab15d20c89c413e49189b0403d716d0d126400bd5dc61c","first_computed_at":"2026-05-18T01:39:54.186243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:54.186243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dIT+REJJG22dY1sfwyp9syj1g38xJX9JM6SpvyduQto6CFNcdtbkP1JU4PkVMdJ+2odDkvlKSUeVx/dwPABvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:54.186716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3acadbf0d35cd7189a2c891fb7a5c0dc36acbe6535b2905398d8b5103a09dbce","sha256:ffc5a854f6a98ad6e1d07c96dc12ac9d426de4eebd5cf56d5986044d4307bb1d"],"state_sha256":"1405be7cff86f5b1619b406a52315868725225263deb7378c61202fb1975b08a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rbxNTSnc3Rk08AVhSUuvUqe8v0bQfbOE9mpAh26H6kvin+cf+yIPo1tamdDcCsFomUqPCnLOMHF5YpHBBuFjBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:09:14.883216Z","bundle_sha256":"f9e83e7a207b441dc05f826366b96e9703cb9d56ce1ced08450aff9d190c4f8f"}}