{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DS54T3PQ7GK4TNXRTBLIE735YC","short_pith_number":"pith:DS54T3PQ","canonical_record":{"source":{"id":"1610.04471","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-14T14:09:01Z","cross_cats_sorted":[],"title_canon_sha256":"cf36b62535bf8e3dc15bcb6a6f13f2923517adfa2c7ef3ad18e556d4b5f87b52","abstract_canon_sha256":"e46ea733253f55cd6315b31cc9ac649de058ac7ca224aa7cfae905085ea3d86b"},"schema_version":"1.0"},"canonical_sha256":"1cbbc9edf0f995c9b6f19856827f7dc08360bd2f05d0d7890ca2f74fca699764","source":{"kind":"arxiv","id":"1610.04471","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04471","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04471v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04471","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"DS54T3PQ7GK4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS54T3PQ7GK4TNXR","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS54T3PQ","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DS54T3PQ7GK4TNXRTBLIE735YC","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04471","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-14T14:09:01Z","cross_cats_sorted":[],"title_canon_sha256":"cf36b62535bf8e3dc15bcb6a6f13f2923517adfa2c7ef3ad18e556d4b5f87b52","abstract_canon_sha256":"e46ea733253f55cd6315b31cc9ac649de058ac7ca224aa7cfae905085ea3d86b"},"schema_version":"1.0"},"canonical_sha256":"1cbbc9edf0f995c9b6f19856827f7dc08360bd2f05d0d7890ca2f74fca699764","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:18.178845Z","signature_b64":"ZYpXlczPGNacfujbCOFOaXY7OGrQOASCIzBb6W82STtFceaxckslrDLuismU8+CgHnO2LKdV08D0tHvcpllHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cbbc9edf0f995c9b6f19856827f7dc08360bd2f05d0d7890ca2f74fca699764","last_reissued_at":"2026-05-18T00:41:18.178191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:18.178191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04471","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/3/6YjnLFSfnare3pCH/x8QyuNL24jl2zBXwMgNKyS1X10gkair/LoObYQUQCWHvctK6NqAVTmcAv3kAJo3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:14:29.282910Z"},"content_sha256":"d6175f38fc3f003bbe64a5fc53a8fcb0a93807f497493f97d25f387788aa391e","schema_version":"1.0","event_id":"sha256:d6175f38fc3f003bbe64a5fc53a8fcb0a93807f497493f97d25f387788aa391e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DS54T3PQ7GK4TNXRTBLIE735YC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zooming in on a L\\'evy process at its supremum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jevgenijs Ivanovs","submitted_at":"2016-10-14T14:09:01Z","abstract_excerpt":"Let $M$ and $\\tau$ be the supremum and its time of a L\\'evy process $X$ on some finite time interval. It is shown that zooming in on $X$ at its supremum, that is, considering $((X_{\\tau+t\\varepsilon}-M)/a_\\varepsilon)_{t\\in\\mathbb R}$ as $\\varepsilon\\downarrow 0$, results in $(\\xi_t)_{t\\in\\mathbb R}$ constructed from two independent processes having the laws of some self-similar L\\'evy process $\\widehat X$ conditioned to stay positive and negative. This holds when $X$ is in the domain of attraction of $\\widehat X$ under the zooming-in procedure as opposed to the classical zooming out of Lamper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04471","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eYoKOyifvtqTsNP4RKbqLf8pkO3QqNuzGWqSYjyHnpZ238QvLnf27+a7HsniVApNRb5I3Se7tFjD/gxesVlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:14:29.283254Z"},"content_sha256":"4b8b3cb6fedc60fb5af3cb75d258a8ef01c398d8299836d17b0650cdcdee5eea","schema_version":"1.0","event_id":"sha256:4b8b3cb6fedc60fb5af3cb75d258a8ef01c398d8299836d17b0650cdcdee5eea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS54T3PQ7GK4TNXRTBLIE735YC/bundle.json","state_url":"https://pith.science/pith/DS54T3PQ7GK4TNXRTBLIE735YC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS54T3PQ7GK4TNXRTBLIE735YC/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":"2026-05-30T21:14:29Z","links":{"resolver":"https://pith.science/pith/DS54T3PQ7GK4TNXRTBLIE735YC","bundle":"https://pith.science/pith/DS54T3PQ7GK4TNXRTBLIE735YC/bundle.json","state":"https://pith.science/pith/DS54T3PQ7GK4TNXRTBLIE735YC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS54T3PQ7GK4TNXRTBLIE735YC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DS54T3PQ7GK4TNXRTBLIE735YC","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":"e46ea733253f55cd6315b31cc9ac649de058ac7ca224aa7cfae905085ea3d86b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-14T14:09:01Z","title_canon_sha256":"cf36b62535bf8e3dc15bcb6a6f13f2923517adfa2c7ef3ad18e556d4b5f87b52"},"schema_version":"1.0","source":{"id":"1610.04471","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04471","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04471v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04471","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"DS54T3PQ7GK4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS54T3PQ7GK4TNXR","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS54T3PQ","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:4b8b3cb6fedc60fb5af3cb75d258a8ef01c398d8299836d17b0650cdcdee5eea","target":"graph","created_at":"2026-05-18T00:41:18Z","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 $M$ and $\\tau$ be the supremum and its time of a L\\'evy process $X$ on some finite time interval. It is shown that zooming in on $X$ at its supremum, that is, considering $((X_{\\tau+t\\varepsilon}-M)/a_\\varepsilon)_{t\\in\\mathbb R}$ as $\\varepsilon\\downarrow 0$, results in $(\\xi_t)_{t\\in\\mathbb R}$ constructed from two independent processes having the laws of some self-similar L\\'evy process $\\widehat X$ conditioned to stay positive and negative. This holds when $X$ is in the domain of attraction of $\\widehat X$ under the zooming-in procedure as opposed to the classical zooming out of Lamper","authors_text":"Jevgenijs Ivanovs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-14T14:09:01Z","title":"Zooming in on a L\\'evy process at its supremum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04471","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:d6175f38fc3f003bbe64a5fc53a8fcb0a93807f497493f97d25f387788aa391e","target":"record","created_at":"2026-05-18T00:41:18Z","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":"e46ea733253f55cd6315b31cc9ac649de058ac7ca224aa7cfae905085ea3d86b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-14T14:09:01Z","title_canon_sha256":"cf36b62535bf8e3dc15bcb6a6f13f2923517adfa2c7ef3ad18e556d4b5f87b52"},"schema_version":"1.0","source":{"id":"1610.04471","kind":"arxiv","version":3}},"canonical_sha256":"1cbbc9edf0f995c9b6f19856827f7dc08360bd2f05d0d7890ca2f74fca699764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cbbc9edf0f995c9b6f19856827f7dc08360bd2f05d0d7890ca2f74fca699764","first_computed_at":"2026-05-18T00:41:18.178191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:18.178191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZYpXlczPGNacfujbCOFOaXY7OGrQOASCIzBb6W82STtFceaxckslrDLuismU8+CgHnO2LKdV08D0tHvcpllHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:18.178845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04471","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6175f38fc3f003bbe64a5fc53a8fcb0a93807f497493f97d25f387788aa391e","sha256:4b8b3cb6fedc60fb5af3cb75d258a8ef01c398d8299836d17b0650cdcdee5eea"],"state_sha256":"374d7008b320ce53be872d037bcc2e4d576d2045c092eff2ceac4b0f846fa557"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GahYLqetWuR0JJv2RPg5eqoDO00ZCfv6TWw3nnrjFHdssmfzQXqQEx4oG2kc6RPu3fiHip8dqCO73viwJgUzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:14:29.285566Z","bundle_sha256":"7ee932db4abe3cdb538bb630244d955a07126c8ea4b8b5315cd54fb010985351"}}