{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J6L3P76EPYMYBWGRW7ZRBQGS3L","short_pith_number":"pith:J6L3P76E","canonical_record":{"source":{"id":"1505.00617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-04T13:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"ecdab8499d0712a7ce5cf5d7539892edbe66405533549ac3a1a02f9bf5043d76","abstract_canon_sha256":"a4b7b181d5fa5e0bad4122897daf98ca8b89b13ac74a81d4863d2d9df333caad"},"schema_version":"1.0"},"canonical_sha256":"4f97b7ffc47e1980d8d1b7f310c0d2dadb12dcdba349e7f2d780cb58c349b875","source":{"kind":"arxiv","id":"1505.00617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00617","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00617v1","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00617","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"J6L3P76EPYMY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J6L3P76EPYMYBWGR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J6L3P76E","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J6L3P76EPYMYBWGRW7ZRBQGS3L","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-04T13:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"ecdab8499d0712a7ce5cf5d7539892edbe66405533549ac3a1a02f9bf5043d76","abstract_canon_sha256":"a4b7b181d5fa5e0bad4122897daf98ca8b89b13ac74a81d4863d2d9df333caad"},"schema_version":"1.0"},"canonical_sha256":"4f97b7ffc47e1980d8d1b7f310c0d2dadb12dcdba349e7f2d780cb58c349b875","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:23.422090Z","signature_b64":"PyLMm0N5gpi0uEaQTukrVf2yuQarZYStPAF0EgnYXTPwAV6c0ZfeAMWaRYWnBDPyYNAe35iA2RwqGH96+yqcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f97b7ffc47e1980d8d1b7f310c0d2dadb12dcdba349e7f2d780cb58c349b875","last_reissued_at":"2026-05-18T00:41:23.421480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:23.421480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00617","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":"2026-05-18T00:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHvhytdIefArG2+qF+I+JO/BGQoFmcjsVGiAJc95Nq0D1FmaVB9e21VRaN9bkrJVlpNsCWYR9jI/QC5Ea8yaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:54:50.721846Z"},"content_sha256":"42e86d7d2c6c066c54e9de3e2a26e1fd8195825c9e2f818e78cafdc7f9d9ad58","schema_version":"1.0","event_id":"sha256:42e86d7d2c6c066c54e9de3e2a26e1fd8195825c9e2f818e78cafdc7f9d9ad58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J6L3P76EPYMYBWGRW7ZRBQGS3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of higher-order convexity properties with respect to Chebyshev systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"\\'Eva Sz\\'ekelyn\\'e Rad\\'acsi, Zsolt P\\'ales","submitted_at":"2015-05-04T13:03:50Z","abstract_excerpt":"In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a related lower Dinghas type derivative are also defined. The main results of the paper offer various characterizations of the convexity notions in terms of the nonnegativity of a generalized divided difference and the corresponding lower Dinghas type derivative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00617","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":"2026-05-18T00:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NFFrpsBbfzb9CLPiiGwhhUsGgOHhADCc+serM7SixkJcqLMTASpSX19+Eai0fw9RyXqKkANCWjUvW2zkcgXOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:54:50.722476Z"},"content_sha256":"9d7ef6fb779398498c26f6a785e17694624a544b6a3f0193f238df6e8870f299","schema_version":"1.0","event_id":"sha256:9d7ef6fb779398498c26f6a785e17694624a544b6a3f0193f238df6e8870f299"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/bundle.json","state_url":"https://pith.science/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/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":"2026-06-06T03:54:50Z","links":{"resolver":"https://pith.science/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L","bundle":"https://pith.science/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/bundle.json","state":"https://pith.science/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6L3P76EPYMYBWGRW7ZRBQGS3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J6L3P76EPYMYBWGRW7ZRBQGS3L","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":"a4b7b181d5fa5e0bad4122897daf98ca8b89b13ac74a81d4863d2d9df333caad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-04T13:03:50Z","title_canon_sha256":"ecdab8499d0712a7ce5cf5d7539892edbe66405533549ac3a1a02f9bf5043d76"},"schema_version":"1.0","source":{"id":"1505.00617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00617","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00617v1","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00617","created_at":"2026-05-18T00:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"J6L3P76EPYMY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"J6L3P76EPYMYBWGR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"J6L3P76E","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:9d7ef6fb779398498c26f6a785e17694624a544b6a3f0193f238df6e8870f299","target":"graph","created_at":"2026-05-18T00:41:23Z","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 various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a related lower Dinghas type derivative are also defined. The main results of the paper offer various characterizations of the convexity notions in terms of the nonnegativity of a generalized divided difference and the corresponding lower Dinghas type derivative.","authors_text":"\\'Eva Sz\\'ekelyn\\'e Rad\\'acsi, Zsolt P\\'ales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-04T13:03:50Z","title":"Characterizations of higher-order convexity properties with respect to Chebyshev systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00617","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":"sha256:42e86d7d2c6c066c54e9de3e2a26e1fd8195825c9e2f818e78cafdc7f9d9ad58","target":"record","created_at":"2026-05-18T00:41:23Z","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":"a4b7b181d5fa5e0bad4122897daf98ca8b89b13ac74a81d4863d2d9df333caad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-04T13:03:50Z","title_canon_sha256":"ecdab8499d0712a7ce5cf5d7539892edbe66405533549ac3a1a02f9bf5043d76"},"schema_version":"1.0","source":{"id":"1505.00617","kind":"arxiv","version":1}},"canonical_sha256":"4f97b7ffc47e1980d8d1b7f310c0d2dadb12dcdba349e7f2d780cb58c349b875","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f97b7ffc47e1980d8d1b7f310c0d2dadb12dcdba349e7f2d780cb58c349b875","first_computed_at":"2026-05-18T00:41:23.421480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:23.421480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PyLMm0N5gpi0uEaQTukrVf2yuQarZYStPAF0EgnYXTPwAV6c0ZfeAMWaRYWnBDPyYNAe35iA2RwqGH96+yqcBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:23.422090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42e86d7d2c6c066c54e9de3e2a26e1fd8195825c9e2f818e78cafdc7f9d9ad58","sha256:9d7ef6fb779398498c26f6a785e17694624a544b6a3f0193f238df6e8870f299"],"state_sha256":"6aef34311b5cfe411ac54a0c8e3f2db3b21302d4804710367df87e76c9e21fff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7VHUma+zcQmmqwD7ui+kSpkr3VnslZDzcyU3dvUcSNGXnQvLaGQmRJY6RNfsCI8riaY4p7V59LSAyDrhZS1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:54:50.726504Z","bundle_sha256":"61ee921dd6d6e779edf1664c76ad3381076545ea58a5addf847b6ea6cd9c5990"}}