{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VRUCPEYQ4GACWUWLY3EQ6YFFXM","short_pith_number":"pith:VRUCPEYQ","canonical_record":{"source":{"id":"1309.6798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-26T11:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"bf0708cb5501fae91ab9982319b739822dc7febf49f78fd8efae33ce0f1a54ef","abstract_canon_sha256":"e83c88723e912a93f220d3529a4621f717214ce5d82c405e6e8eafb2e9bd2e9c"},"schema_version":"1.0"},"canonical_sha256":"ac68279310e1802b52cbc6c90f60a5bb224d050cfdb7ac24b1ce16c54344e8fc","source":{"kind":"arxiv","id":"1309.6798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6798","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6798v1","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6798","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"VRUCPEYQ4GAC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VRUCPEYQ4GACWUWL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VRUCPEYQ","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VRUCPEYQ4GACWUWLY3EQ6YFFXM","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-26T11:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"bf0708cb5501fae91ab9982319b739822dc7febf49f78fd8efae33ce0f1a54ef","abstract_canon_sha256":"e83c88723e912a93f220d3529a4621f717214ce5d82c405e6e8eafb2e9bd2e9c"},"schema_version":"1.0"},"canonical_sha256":"ac68279310e1802b52cbc6c90f60a5bb224d050cfdb7ac24b1ce16c54344e8fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:10.469808Z","signature_b64":"62r3U0TrC+9eN4yehXQ9KxiM9ZN5OIBVqxd9ikihl4SjtytSsXuG64xClPtg0jTFa8ovxeLBd89CIxNXGinSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac68279310e1802b52cbc6c90f60a5bb224d050cfdb7ac24b1ce16c54344e8fc","last_reissued_at":"2026-05-18T03:12:10.468919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:10.468919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6798","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":"2026-05-18T03:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1un3vSWRMOY3JKdu3J2GQySUgLqMfEXQMFWxNap1M6P9kXfzzDYTkGfrpBvvT5kxpE7Z9Kb3q5s1eu8+7sVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:46:13.513639Z"},"content_sha256":"72d593d42615450df9338d6b494f2591dd21034633d119adbbc0fafccb244a31","schema_version":"1.0","event_id":"sha256:72d593d42615450df9338d6b494f2591dd21034633d119adbbc0fafccb244a31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VRUCPEYQ4GACWUWLY3EQ6YFFXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inequalities for a number of different types of convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Merve Avci Ardic","submitted_at":"2013-09-26T11:10:11Z","abstract_excerpt":"Some inequalities for different types of convexity are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6798","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":"2026-05-18T03:12:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58mtViUnUFcLdJlAMnXu8YBGUbrDkujxTNNS1POfZMavMw26mZZVJxVzNMHZV2M/ETC1wh/s54CAgKfGphorCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:46:13.513970Z"},"content_sha256":"213123b55f4c79a61c0e243f2a2f8a01c09939f9a75ad17f27c7da1df51bc179","schema_version":"1.0","event_id":"sha256:213123b55f4c79a61c0e243f2a2f8a01c09939f9a75ad17f27c7da1df51bc179"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/bundle.json","state_url":"https://pith.science/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/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":"2026-06-22T12:46:13Z","links":{"resolver":"https://pith.science/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM","bundle":"https://pith.science/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/bundle.json","state":"https://pith.science/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRUCPEYQ4GACWUWLY3EQ6YFFXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VRUCPEYQ4GACWUWLY3EQ6YFFXM","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":"e83c88723e912a93f220d3529a4621f717214ce5d82c405e6e8eafb2e9bd2e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-26T11:10:11Z","title_canon_sha256":"bf0708cb5501fae91ab9982319b739822dc7febf49f78fd8efae33ce0f1a54ef"},"schema_version":"1.0","source":{"id":"1309.6798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6798","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6798v1","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6798","created_at":"2026-05-18T03:12:10Z"},{"alias_kind":"pith_short_12","alias_value":"VRUCPEYQ4GAC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VRUCPEYQ4GACWUWL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VRUCPEYQ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:213123b55f4c79a61c0e243f2a2f8a01c09939f9a75ad17f27c7da1df51bc179","target":"graph","created_at":"2026-05-18T03:12:10Z","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":"Some inequalities for different types of convexity are established.","authors_text":"Merve Avci Ardic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-26T11:10:11Z","title":"Inequalities for a number of different types of convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6798","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":"sha256:72d593d42615450df9338d6b494f2591dd21034633d119adbbc0fafccb244a31","target":"record","created_at":"2026-05-18T03:12:10Z","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":"e83c88723e912a93f220d3529a4621f717214ce5d82c405e6e8eafb2e9bd2e9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-26T11:10:11Z","title_canon_sha256":"bf0708cb5501fae91ab9982319b739822dc7febf49f78fd8efae33ce0f1a54ef"},"schema_version":"1.0","source":{"id":"1309.6798","kind":"arxiv","version":1}},"canonical_sha256":"ac68279310e1802b52cbc6c90f60a5bb224d050cfdb7ac24b1ce16c54344e8fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac68279310e1802b52cbc6c90f60a5bb224d050cfdb7ac24b1ce16c54344e8fc","first_computed_at":"2026-05-18T03:12:10.468919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:10.468919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62r3U0TrC+9eN4yehXQ9KxiM9ZN5OIBVqxd9ikihl4SjtytSsXuG64xClPtg0jTFa8ovxeLBd89CIxNXGinSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:10.469808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d593d42615450df9338d6b494f2591dd21034633d119adbbc0fafccb244a31","sha256:213123b55f4c79a61c0e243f2a2f8a01c09939f9a75ad17f27c7da1df51bc179"],"state_sha256":"8fa80894e74b9ad4f72c46a3290c31ec6a66639d7558ac661ef5002b8d35accb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ECEnJ1LNyMY3nw8reXHyAkDHiThQYqhJ/OzRkv9zQA4jV6DK5Xbapp1hNRYIJH5ZxC1/Qyr8nns3yDHaG0SAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:46:13.515828Z","bundle_sha256":"97508f7d2d16a912566c67028d4b1de318641a0d01bc18e375f26fd82735c7cd"}}