{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FX2ISBMPMVIDGYRGDQGLGE2ZCW","short_pith_number":"pith:FX2ISBMP","canonical_record":{"source":{"id":"1603.01527","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-04T16:36:50Z","cross_cats_sorted":[],"title_canon_sha256":"0a49d62c7893f6594dee6931d20d1d500cace6c0465fee3e639b90653e2e8395","abstract_canon_sha256":"ef0166708a82a400f54bc339bed053dbf58fa41224add9f783f8f302efb87bf6"},"schema_version":"1.0"},"canonical_sha256":"2df489058f65503362261c0cb313591582991632b1f4a93ddcb4cca7af71be8d","source":{"kind":"arxiv","id":"1603.01527","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01527","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01527v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01527","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"FX2ISBMPMVID","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FX2ISBMPMVIDGYRG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FX2ISBMP","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FX2ISBMPMVIDGYRGDQGLGE2ZCW","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01527","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-04T16:36:50Z","cross_cats_sorted":[],"title_canon_sha256":"0a49d62c7893f6594dee6931d20d1d500cace6c0465fee3e639b90653e2e8395","abstract_canon_sha256":"ef0166708a82a400f54bc339bed053dbf58fa41224add9f783f8f302efb87bf6"},"schema_version":"1.0"},"canonical_sha256":"2df489058f65503362261c0cb313591582991632b1f4a93ddcb4cca7af71be8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:14.341960Z","signature_b64":"LUOKaEdGLKBU4YqHbbMvX3N+i0nfBCqteXAMkaYiqYraRkgHy9lj5Lw9iwksONBC3srYfaeAXk7jgguXbnk0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df489058f65503362261c0cb313591582991632b1f4a93ddcb4cca7af71be8d","last_reissued_at":"2026-05-18T00:19:14.341236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:14.341236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01527","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4Z20jtrJamHCkFUPoUYkctQhTgSCrZHWdKRphnTv4Z1CJB7byKcT1h2kAbtgU8a8Z6xnokjUuw4hpCadoylBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:42:11.216798Z"},"content_sha256":"df3348d67efb8b8207d799fef26a0022943a2f455fb6cd7092c0e394ff811336","schema_version":"1.0","event_id":"sha256:df3348d67efb8b8207d799fef26a0022943a2f455fb6cd7092c0e394ff811336"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FX2ISBMPMVIDGYRGDQGLGE2ZCW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Locations of Periodic Stationary Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jie Shen, Ruodu Wang, Yi Shen","submitted_at":"2016-03-04T16:36:50Z","abstract_excerpt":"We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01527","kind":"arxiv","version":3},"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":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7MIg4xSf04LSPzUiL7CfxY/NTXiMzCgfyRvXe5KnjUSY3uOYxHapgG5R+f+VwEdiMYtK42dfO1cT/KElOeAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:42:11.217440Z"},"content_sha256":"14a18dcab37e1dc3128ae73610293379b4fa5163a84d1d7708b3b20b55d4ba05","schema_version":"1.0","event_id":"sha256:14a18dcab37e1dc3128ae73610293379b4fa5163a84d1d7708b3b20b55d4ba05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/bundle.json","state_url":"https://pith.science/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/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":"2026-05-31T14:42:11Z","links":{"resolver":"https://pith.science/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW","bundle":"https://pith.science/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/bundle.json","state":"https://pith.science/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FX2ISBMPMVIDGYRGDQGLGE2ZCW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FX2ISBMPMVIDGYRGDQGLGE2ZCW","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":"ef0166708a82a400f54bc339bed053dbf58fa41224add9f783f8f302efb87bf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-04T16:36:50Z","title_canon_sha256":"0a49d62c7893f6594dee6931d20d1d500cace6c0465fee3e639b90653e2e8395"},"schema_version":"1.0","source":{"id":"1603.01527","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01527","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01527v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01527","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"FX2ISBMPMVID","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FX2ISBMPMVIDGYRG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FX2ISBMP","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:14a18dcab37e1dc3128ae73610293379b4fa5163a84d1d7708b3b20b55d4ba05","target":"graph","created_at":"2026-05-18T00:19:14Z","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":"We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are ","authors_text":"Jie Shen, Ruodu Wang, Yi Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-04T16:36:50Z","title":"Random Locations of Periodic Stationary Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01527","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:df3348d67efb8b8207d799fef26a0022943a2f455fb6cd7092c0e394ff811336","target":"record","created_at":"2026-05-18T00:19:14Z","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":"ef0166708a82a400f54bc339bed053dbf58fa41224add9f783f8f302efb87bf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-04T16:36:50Z","title_canon_sha256":"0a49d62c7893f6594dee6931d20d1d500cace6c0465fee3e639b90653e2e8395"},"schema_version":"1.0","source":{"id":"1603.01527","kind":"arxiv","version":3}},"canonical_sha256":"2df489058f65503362261c0cb313591582991632b1f4a93ddcb4cca7af71be8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2df489058f65503362261c0cb313591582991632b1f4a93ddcb4cca7af71be8d","first_computed_at":"2026-05-18T00:19:14.341236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:14.341236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LUOKaEdGLKBU4YqHbbMvX3N+i0nfBCqteXAMkaYiqYraRkgHy9lj5Lw9iwksONBC3srYfaeAXk7jgguXbnk0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:14.341960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01527","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df3348d67efb8b8207d799fef26a0022943a2f455fb6cd7092c0e394ff811336","sha256:14a18dcab37e1dc3128ae73610293379b4fa5163a84d1d7708b3b20b55d4ba05"],"state_sha256":"c740a014bc3afe6f42d536d4b4b8517d02667419c340195ab870b186486cb52a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8VtuS6dwxWBn+e2D6jq8FB4xDpzI6EW1wXQil3VU/xo3deEuzkOcGGdw70GnDJWU3XxF67zoWL3/Ivj24BhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:42:11.220620Z","bundle_sha256":"0a38fe5ddd16f0507487c30f4a2cf5e843ee500c1d300cca15d403fc3c189707"}}