{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4UIO6RYDPBXVTUA36DG7EVJYPC","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":"e9b6a1b99dbaecd19932b26b76454c2a06e1e3c47977fd3e36a4f1c14c190ac6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T18:03:36Z","title_canon_sha256":"8edcad9dee7a3260247d7a56d7ad09aaef8f5f547d65b95d91580ec8ebfddfb3"},"schema_version":"1.0","source":{"id":"1009.2463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2463","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2463v1","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2463","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"4UIO6RYDPBXV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4UIO6RYDPBXVTUA3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4UIO6RYD","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:f9e7c19f2c32ff7d490cad738d404f6ab8856e02dc82fe578585affe76e2f471","target":"graph","created_at":"2026-05-18T04:19:23Z","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":"Brown (1980, 1981) proved that the renewal function is concave if the inter-renewal distribution is DFR (decreasing failure rate), and conjectured the converse. This note settles Brown's conjecture with a class of counter-examples. We also give a short proof of Shanthikumar's (1988) result that the DFR property is closed under geometric compounding.","authors_text":"Yaming Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T18:03:36Z","title":"Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2463","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:a73a02d2ce8f779d87bfa503d806cb5aa709ca76fda5902d6d2b5562c931fb6f","target":"record","created_at":"2026-05-18T04:19:23Z","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":"e9b6a1b99dbaecd19932b26b76454c2a06e1e3c47977fd3e36a4f1c14c190ac6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T18:03:36Z","title_canon_sha256":"8edcad9dee7a3260247d7a56d7ad09aaef8f5f547d65b95d91580ec8ebfddfb3"},"schema_version":"1.0","source":{"id":"1009.2463","kind":"arxiv","version":1}},"canonical_sha256":"e510ef4703786f59d01bf0cdf2553878a10eff2716b0bbbd65cc83ab061d3396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e510ef4703786f59d01bf0cdf2553878a10eff2716b0bbbd65cc83ab061d3396","first_computed_at":"2026-05-18T04:19:23.216121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:23.216121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7XQuTj+i9TPVZ/cgqVbQ4dzB+9WJbuX3jZNwf/MyVLix3OycYl2xaTWnV9VXCdfN8Rm6LIuoLRHna0GCXF0KDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:23.216612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a73a02d2ce8f779d87bfa503d806cb5aa709ca76fda5902d6d2b5562c931fb6f","sha256:f9e7c19f2c32ff7d490cad738d404f6ab8856e02dc82fe578585affe76e2f471"],"state_sha256":"794f317f36901f560b22d17cca77480793c9b3e16ff08fce699e5c36b0d2b107"}