{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XLSAIM4CIVW6MC37IJHUC2PCJX","short_pith_number":"pith:XLSAIM4C","canonical_record":{"source":{"id":"1302.3097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T14:05:39Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"71ce0b34f2f94bbd001be7e22011f2ba36fe9499100794f671a83c7425e4918b","abstract_canon_sha256":"18dcfe81cf88df7e1dbd870a6cd53f4a07338e889bd105f3004ae828f8b1c1fc"},"schema_version":"1.0"},"canonical_sha256":"bae4043382456de60b7f424f4169e24dfb4b1b862e904d167e5826ff6785cbd8","source":{"kind":"arxiv","id":"1302.3097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3097","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3097v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3097","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"XLSAIM4CIVW6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLSAIM4CIVW6MC37","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLSAIM4C","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XLSAIM4CIVW6MC37IJHUC2PCJX","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T14:05:39Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"71ce0b34f2f94bbd001be7e22011f2ba36fe9499100794f671a83c7425e4918b","abstract_canon_sha256":"18dcfe81cf88df7e1dbd870a6cd53f4a07338e889bd105f3004ae828f8b1c1fc"},"schema_version":"1.0"},"canonical_sha256":"bae4043382456de60b7f424f4169e24dfb4b1b862e904d167e5826ff6785cbd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:48.766360Z","signature_b64":"0EylUNblLQGnEDnnAuvp20z2Ylz0lhSXRcD0P2AcPtvxorCeQImocW/F6Ij6I0xbYwA5YgywVL+zCV2M7hkQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bae4043382456de60b7f424f4169e24dfb4b1b862e904d167e5826ff6785cbd8","last_reissued_at":"2026-05-18T03:33:48.765860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:48.765860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3097","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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oa5eLOa1D2RAz/N98xSMjlZYzgaGtLik3IaiMmywWJWkX/cOtXo7LqsaKWGk2ACjJ9sILiDGttUqsGoRujEEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:09:14.704631Z"},"content_sha256":"bf95d31715b388d6c8e06ad389f9a55866571a0424ed141dde9cabaf26a971c1","schema_version":"1.0","event_id":"sha256:bf95d31715b388d6c8e06ad389f9a55866571a0424ed141dde9cabaf26a971c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XLSAIM4CIVW6MC37IJHUC2PCJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the self-decomposability of the Fr\\'echet distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Pierre Bosch (LPP), Thomas Simon (LPP)","submitted_at":"2013-02-13T14:05:39Z","abstract_excerpt":"Let $\\{\\Gamma_t, \\, t\\ge 0\\}$ be the Gamma subordinator. Using a moment identification due to Bertoin-Yor (2002), we observe that for every $t > 0$ and $\\alpha\\in (0,1)$ the random variable $\\Gamma_t^{-\\alpha}$ is distributed as the exponential functional of some spectrally negative L\\'evy process. This entails that all size-biased samplings of Fr\\'echet distributions are self-decomposable and that the extreme value distribution $F_\\xi$ is infinitely divisible if and only if $\\xi\\not\\in (0,1),$ solving problems raised by Steutel (1973) and Bondesson (1992). We also review different analytical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3097","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":"2026-05-18T03:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"buNor0tAExwQdt9LttM8ZhzQ3JcmFeORsl4eK67x4QP6c94BidS+kCtxPk6V5HIBLxFFD7ZhChgnbu66MWuFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:09:14.705338Z"},"content_sha256":"03e96ee7a207fbe9c026edf6c52b941e2749206664c995cf187361308fc0d85e","schema_version":"1.0","event_id":"sha256:03e96ee7a207fbe9c026edf6c52b941e2749206664c995cf187361308fc0d85e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/bundle.json","state_url":"https://pith.science/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/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":"2026-06-09T05:09:14Z","links":{"resolver":"https://pith.science/pith/XLSAIM4CIVW6MC37IJHUC2PCJX","bundle":"https://pith.science/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/bundle.json","state":"https://pith.science/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLSAIM4CIVW6MC37IJHUC2PCJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XLSAIM4CIVW6MC37IJHUC2PCJX","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":"18dcfe81cf88df7e1dbd870a6cd53f4a07338e889bd105f3004ae828f8b1c1fc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T14:05:39Z","title_canon_sha256":"71ce0b34f2f94bbd001be7e22011f2ba36fe9499100794f671a83c7425e4918b"},"schema_version":"1.0","source":{"id":"1302.3097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3097","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3097v1","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3097","created_at":"2026-05-18T03:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"XLSAIM4CIVW6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLSAIM4CIVW6MC37","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLSAIM4C","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:03e96ee7a207fbe9c026edf6c52b941e2749206664c995cf187361308fc0d85e","target":"graph","created_at":"2026-05-18T03:33:48Z","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":"Let $\\{\\Gamma_t, \\, t\\ge 0\\}$ be the Gamma subordinator. Using a moment identification due to Bertoin-Yor (2002), we observe that for every $t > 0$ and $\\alpha\\in (0,1)$ the random variable $\\Gamma_t^{-\\alpha}$ is distributed as the exponential functional of some spectrally negative L\\'evy process. This entails that all size-biased samplings of Fr\\'echet distributions are self-decomposable and that the extreme value distribution $F_\\xi$ is infinitely divisible if and only if $\\xi\\not\\in (0,1),$ solving problems raised by Steutel (1973) and Bondesson (1992). We also review different analytical ","authors_text":"Pierre Bosch (LPP), Thomas Simon (LPP)","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T14:05:39Z","title":"On the self-decomposability of the Fr\\'echet distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3097","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:bf95d31715b388d6c8e06ad389f9a55866571a0424ed141dde9cabaf26a971c1","target":"record","created_at":"2026-05-18T03:33:48Z","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":"18dcfe81cf88df7e1dbd870a6cd53f4a07338e889bd105f3004ae828f8b1c1fc","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T14:05:39Z","title_canon_sha256":"71ce0b34f2f94bbd001be7e22011f2ba36fe9499100794f671a83c7425e4918b"},"schema_version":"1.0","source":{"id":"1302.3097","kind":"arxiv","version":1}},"canonical_sha256":"bae4043382456de60b7f424f4169e24dfb4b1b862e904d167e5826ff6785cbd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bae4043382456de60b7f424f4169e24dfb4b1b862e904d167e5826ff6785cbd8","first_computed_at":"2026-05-18T03:33:48.765860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:48.765860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0EylUNblLQGnEDnnAuvp20z2Ylz0lhSXRcD0P2AcPtvxorCeQImocW/F6Ij6I0xbYwA5YgywVL+zCV2M7hkQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:48.766360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf95d31715b388d6c8e06ad389f9a55866571a0424ed141dde9cabaf26a971c1","sha256:03e96ee7a207fbe9c026edf6c52b941e2749206664c995cf187361308fc0d85e"],"state_sha256":"7e8d051c220a5929ba9ebe56778bf9b4bab9a0ce2d0327c0237c75447b88bec0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34/5vHDZxg0gEH3oW17D84lhTzUIReXmQ1HsPA9pxWv1U3eTZucJjsVKbpME0FHHEJraUbtiP/FUL+qTdz2ABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:09:14.709307Z","bundle_sha256":"f10e721648d32ba85aa71819e4a9501e9cd2f25c72aab3701fa58eb4c0e46021"}}