{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W5ENL5IZDM4LXIFXOWHZ4KUVK7","short_pith_number":"pith:W5ENL5IZ","canonical_record":{"source":{"id":"1308.0379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-02T00:00:06Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ef753cd06b105ed913682fef5e40d90d4b1d5cf47b21a6d8fe315bea65fd8544","abstract_canon_sha256":"499dd74d42acc01c496932149df2c2ddbd2d428fd0d0f8ae8e75d82c3bbbf279"},"schema_version":"1.0"},"canonical_sha256":"b748d5f5191b38bba0b7758f9e2a9557c32186975d31974b2eebabff1031693c","source":{"kind":"arxiv","id":"1308.0379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0379","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0379v2","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0379","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"W5ENL5IZDM4L","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W5ENL5IZDM4LXIFX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W5ENL5IZ","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W5ENL5IZDM4LXIFXOWHZ4KUVK7","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-02T00:00:06Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ef753cd06b105ed913682fef5e40d90d4b1d5cf47b21a6d8fe315bea65fd8544","abstract_canon_sha256":"499dd74d42acc01c496932149df2c2ddbd2d428fd0d0f8ae8e75d82c3bbbf279"},"schema_version":"1.0"},"canonical_sha256":"b748d5f5191b38bba0b7758f9e2a9557c32186975d31974b2eebabff1031693c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:57.551286Z","signature_b64":"UbS/W4Vh6iyw9Rz3wfMKQQ7a/FTWBcQ9g3em3oU7ucUuERJSZk+7aZQquDMrP7xpXeVQTLgHHhVnn37e68icBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b748d5f5191b38bba0b7758f9e2a9557c32186975d31974b2eebabff1031693c","last_reissued_at":"2026-05-18T01:35:57.550756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:57.550756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0379","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7mBKInlhtlhlSrKqGNEzFiPPuYIBTCVUwzokW7nA2ahUTik7mqxcI/8CBEviT4X5leVC1zso1zwQ/zMM6ZFPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:21:52.941795Z"},"content_sha256":"5bfbbed9bad8ce17c26d1e3d527feb02682b4462c57b4beb0cc7c488382d3607","schema_version":"1.0","event_id":"sha256:5bfbbed9bad8ce17c26d1e3d527feb02682b4462c57b4beb0cc7c488382d3607"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W5ENL5IZDM4LXIFXOWHZ4KUVK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Example of a Non-standard Extreme Value Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Michal Kupsa, Nicolai Haydn","submitted_at":"2013-08-02T00:00:06Z","abstract_excerpt":"It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\\'echet and Weibull distributions. In this short note we give an example which has a non-standard limiting distribution for its extreme values. Rotations of the circle by irrational numbers are used and it will be shown that the limiting distribution is a step function where the limit has to be taken along a suitable sequence given by the convergents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0379","kind":"arxiv","version":2},"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":"2026-05-18T01:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQgKJyIAtxrmZIB8vqDPxwSouWZPbQTjoMzAsv+ICFbqMzdIH1rwyX0D9u5YL1C8nTQFY7c9d30d9nGT+XHqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:21:52.942515Z"},"content_sha256":"681f6d1da63244199aedf02d9ad8b38b5d44c8d2683017b8ad61c1b00c7b7d14","schema_version":"1.0","event_id":"sha256:681f6d1da63244199aedf02d9ad8b38b5d44c8d2683017b8ad61c1b00c7b7d14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/bundle.json","state_url":"https://pith.science/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/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":"2026-05-25T21:21:52Z","links":{"resolver":"https://pith.science/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7","bundle":"https://pith.science/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/bundle.json","state":"https://pith.science/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5ENL5IZDM4LXIFXOWHZ4KUVK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W5ENL5IZDM4LXIFXOWHZ4KUVK7","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":"499dd74d42acc01c496932149df2c2ddbd2d428fd0d0f8ae8e75d82c3bbbf279","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-02T00:00:06Z","title_canon_sha256":"ef753cd06b105ed913682fef5e40d90d4b1d5cf47b21a6d8fe315bea65fd8544"},"schema_version":"1.0","source":{"id":"1308.0379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0379","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0379v2","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0379","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"W5ENL5IZDM4L","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W5ENL5IZDM4LXIFX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W5ENL5IZ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:681f6d1da63244199aedf02d9ad8b38b5d44c8d2683017b8ad61c1b00c7b7d14","target":"graph","created_at":"2026-05-18T01:35:57Z","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":"It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\\'echet and Weibull distributions. In this short note we give an example which has a non-standard limiting distribution for its extreme values. Rotations of the circle by irrational numbers are used and it will be shown that the limiting distribution is a step function where the limit has to be taken along a suitable sequence given by the convergents.","authors_text":"Michal Kupsa, Nicolai Haydn","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-02T00:00:06Z","title":"Example of a Non-standard Extreme Value Law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0379","kind":"arxiv","version":2},"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":"sha256:5bfbbed9bad8ce17c26d1e3d527feb02682b4462c57b4beb0cc7c488382d3607","target":"record","created_at":"2026-05-18T01:35:57Z","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":"499dd74d42acc01c496932149df2c2ddbd2d428fd0d0f8ae8e75d82c3bbbf279","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-02T00:00:06Z","title_canon_sha256":"ef753cd06b105ed913682fef5e40d90d4b1d5cf47b21a6d8fe315bea65fd8544"},"schema_version":"1.0","source":{"id":"1308.0379","kind":"arxiv","version":2}},"canonical_sha256":"b748d5f5191b38bba0b7758f9e2a9557c32186975d31974b2eebabff1031693c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b748d5f5191b38bba0b7758f9e2a9557c32186975d31974b2eebabff1031693c","first_computed_at":"2026-05-18T01:35:57.550756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.550756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UbS/W4Vh6iyw9Rz3wfMKQQ7a/FTWBcQ9g3em3oU7ucUuERJSZk+7aZQquDMrP7xpXeVQTLgHHhVnn37e68icBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.551286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bfbbed9bad8ce17c26d1e3d527feb02682b4462c57b4beb0cc7c488382d3607","sha256:681f6d1da63244199aedf02d9ad8b38b5d44c8d2683017b8ad61c1b00c7b7d14"],"state_sha256":"8415e39b3bbfe3866dc1e504c64076ab94220b9da342dca18115fe72e6eaa451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1Vu5JuT+XnVLjABWpIdTGjLN8kwE6kJOmTx00IG7U8cl4tbVOzeBKoBJBAsyzN5ii4ZLOS25TUL4kPZtkEkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:21:52.945966Z","bundle_sha256":"7c371de34333baa449c9380a3f6002becb9c3c86771aa5671f26c74cdf6ba29e"}}