{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TAYSMCPCDRX4AE5EFK7ZYWLJW3","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":"f0da2a5ccdc85dd141e96fc0d10502cae0bdd0c200e96317996f338c56120977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-04T15:31:15Z","title_canon_sha256":"402fc5938e800f7355319f036c3f06d89be8ec0ae854b1ce93699e4e6cb13d78"},"schema_version":"1.0","source":{"id":"1909.01884","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.01884","created_at":"2026-07-05T01:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1909.01884v3","created_at":"2026-07-05T01:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.01884","created_at":"2026-07-05T01:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"TAYSMCPCDRX4","created_at":"2026-07-05T01:34:32Z"},{"alias_kind":"pith_short_16","alias_value":"TAYSMCPCDRX4AE5E","created_at":"2026-07-05T01:34:32Z"},{"alias_kind":"pith_short_8","alias_value":"TAYSMCPC","created_at":"2026-07-05T01:34:32Z"}],"graph_snapshots":[{"event_id":"sha256:b29d3bee97cce1093981470193b1ff9f1313a9e0f2fde40c3588c88646c86548","target":"graph","created_at":"2026-07-05T01:34:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.01884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the following question: if $f$ is a nonzero measurable function on $[0,\\infty)$ and $m$ and $n$ distinct nonnegative integers, does the ratio $\\widehat{f^n}/\\widehat{f^m}$ of the Laplace transforms of the powers $f^n$ and $f^m$ of $f$ uniquely determine $f$? The answer is yes if one of $m, n$ is zero, by the inverse Laplace transform. Under some assumptions on the smoothness of $f$ we show that the answer in the general case is also affirmative. The question arose from a problem in economics, specifically in auction theory where $f$ is the cumulative distribution function of a certain","authors_text":"Linglong Yuan, Takis Konstantopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-04T15:31:15Z","title":"Does the ratio of Laplace transforms of powers of a function identify the function?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01884","kind":"arxiv","version":3},"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":"sha256:1ce56c2b65bf6eb242b2d30d9d85e60bb65cc8151eebe68dc71857d264f349f7","target":"record","created_at":"2026-07-05T01:34:32Z","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":"f0da2a5ccdc85dd141e96fc0d10502cae0bdd0c200e96317996f338c56120977","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-09-04T15:31:15Z","title_canon_sha256":"402fc5938e800f7355319f036c3f06d89be8ec0ae854b1ce93699e4e6cb13d78"},"schema_version":"1.0","source":{"id":"1909.01884","kind":"arxiv","version":3}},"canonical_sha256":"98312609e21c6fc013a42abf9c5969b6eb0d1837df17b1bc1953e62097b6dffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98312609e21c6fc013a42abf9c5969b6eb0d1837df17b1bc1953e62097b6dffd","first_computed_at":"2026-07-05T01:34:32.942075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:34:32.942075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ss5QmqJTatZv6wB4AVGFPUD7c53gFQ5i3cNVFR0nm8JttM7Uco5iNNCi0VBqf9aTUcMPEeU4J0Yg3pDxO4WfAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:34:32.942442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.01884","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ce56c2b65bf6eb242b2d30d9d85e60bb65cc8151eebe68dc71857d264f349f7","sha256:b29d3bee97cce1093981470193b1ff9f1313a9e0f2fde40c3588c88646c86548"],"state_sha256":"aa33c8094566f0c4489ae11a3db4ac1c6c829909fce3c916393f824d3d90adc1"}