{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7DYABYOULGOQYBT2PTVQZBZYCB","short_pith_number":"pith:7DYABYOU","canonical_record":{"source":{"id":"1107.5136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-26T08:54:55Z","cross_cats_sorted":[],"title_canon_sha256":"0452beec42d11473a6c8a573faacee4cb41577c116fc4f1002ea801e588bdba7","abstract_canon_sha256":"61f2a0140338002969ad69bd5e292b7f6e07a7934e1d509647c1cbab6c8d85c6"},"schema_version":"1.0"},"canonical_sha256":"f8f000e1d4599d0c067a7ceb0c873810610e55069e15cef8eb1c104471ec04ca","source":{"kind":"arxiv","id":"1107.5136","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5136","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5136v3","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5136","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"7DYABYOULGOQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7DYABYOULGOQYBT2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7DYABYOU","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7DYABYOULGOQYBT2PTVQZBZYCB","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-26T08:54:55Z","cross_cats_sorted":[],"title_canon_sha256":"0452beec42d11473a6c8a573faacee4cb41577c116fc4f1002ea801e588bdba7","abstract_canon_sha256":"61f2a0140338002969ad69bd5e292b7f6e07a7934e1d509647c1cbab6c8d85c6"},"schema_version":"1.0"},"canonical_sha256":"f8f000e1d4599d0c067a7ceb0c873810610e55069e15cef8eb1c104471ec04ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:02.576357Z","signature_b64":"t/Ov+SoYcg3pqMYbrD8OrFswcxf/dNiD/vLC2LhO14E/iL2X1zL11oK1dI/TKOXmkXbe7JdQ6QLFuDKON5saCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8f000e1d4599d0c067a7ceb0c873810610e55069e15cef8eb1c104471ec04ca","last_reissued_at":"2026-05-18T03:41:02.575827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:02.575827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5136","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":"2026-05-18T03:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zoc8hwSWs3VkGvnoXGWD0zj/+X8LoRKNLfR5TEu+G4vWBFP14U8LwL0SQkcpRQCU5ZnqDNPm1g7M5df+YputCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:51:27.135469Z"},"content_sha256":"601e9210c445e0526e8a956447541a195a2d7a15f2698500853e5b3024aab0d0","schema_version":"1.0","event_id":"sha256:601e9210c445e0526e8a956447541a195a2d7a15f2698500853e5b3024aab0d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7DYABYOULGOQYBT2PTVQZBZYCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Max-Stable Processes and the Functional D-Norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Martin Hofmann, Michael Falk, Stefan Aulbach","submitted_at":"2011-07-26T08:54:55Z","abstract_excerpt":"We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence.\n  The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case.\n  Applying this fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5136","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":"2026-05-18T03:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"abKjbndNr0n9pq645hVI08sH3oUJH1CaO3g4k+jhhPgrxcFv09eWNOt0ykSrbeyaTStCv3IO1priWC9Twhp/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:51:27.135818Z"},"content_sha256":"4ac50d7e2122a2b3f472536898b323f3317b156f899404ee81ad54f79d0fdd49","schema_version":"1.0","event_id":"sha256:4ac50d7e2122a2b3f472536898b323f3317b156f899404ee81ad54f79d0fdd49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DYABYOULGOQYBT2PTVQZBZYCB/bundle.json","state_url":"https://pith.science/pith/7DYABYOULGOQYBT2PTVQZBZYCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DYABYOULGOQYBT2PTVQZBZYCB/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":"2026-06-20T03:51:27Z","links":{"resolver":"https://pith.science/pith/7DYABYOULGOQYBT2PTVQZBZYCB","bundle":"https://pith.science/pith/7DYABYOULGOQYBT2PTVQZBZYCB/bundle.json","state":"https://pith.science/pith/7DYABYOULGOQYBT2PTVQZBZYCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DYABYOULGOQYBT2PTVQZBZYCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7DYABYOULGOQYBT2PTVQZBZYCB","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":"61f2a0140338002969ad69bd5e292b7f6e07a7934e1d509647c1cbab6c8d85c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-26T08:54:55Z","title_canon_sha256":"0452beec42d11473a6c8a573faacee4cb41577c116fc4f1002ea801e588bdba7"},"schema_version":"1.0","source":{"id":"1107.5136","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5136","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5136v3","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5136","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"7DYABYOULGOQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7DYABYOULGOQYBT2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7DYABYOU","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4ac50d7e2122a2b3f472536898b323f3317b156f899404ee81ad54f79d0fdd49","target":"graph","created_at":"2026-05-18T03:41:02Z","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 introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence.\n  The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case.\n  Applying this fra","authors_text":"Martin Hofmann, Michael Falk, Stefan Aulbach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-26T08:54:55Z","title":"On Max-Stable Processes and the Functional D-Norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5136","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":"sha256:601e9210c445e0526e8a956447541a195a2d7a15f2698500853e5b3024aab0d0","target":"record","created_at":"2026-05-18T03:41:02Z","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":"61f2a0140338002969ad69bd5e292b7f6e07a7934e1d509647c1cbab6c8d85c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-26T08:54:55Z","title_canon_sha256":"0452beec42d11473a6c8a573faacee4cb41577c116fc4f1002ea801e588bdba7"},"schema_version":"1.0","source":{"id":"1107.5136","kind":"arxiv","version":3}},"canonical_sha256":"f8f000e1d4599d0c067a7ceb0c873810610e55069e15cef8eb1c104471ec04ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8f000e1d4599d0c067a7ceb0c873810610e55069e15cef8eb1c104471ec04ca","first_computed_at":"2026-05-18T03:41:02.575827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:02.575827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/Ov+SoYcg3pqMYbrD8OrFswcxf/dNiD/vLC2LhO14E/iL2X1zL11oK1dI/TKOXmkXbe7JdQ6QLFuDKON5saCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:02.576357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5136","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:601e9210c445e0526e8a956447541a195a2d7a15f2698500853e5b3024aab0d0","sha256:4ac50d7e2122a2b3f472536898b323f3317b156f899404ee81ad54f79d0fdd49"],"state_sha256":"942ba57784b6027b75b1d6016ec63f68f5ee061e0b5a8e3dfdd5dea5e6bbf5fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9lNfrr1gKjzvSCFuTomxwBmnH44+DO3VOXVKkmCsuiacFng4vnjCyDNwqHv5WEGN2FCtcznt+4WHqMJmT8pNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:51:27.137857Z","bundle_sha256":"a37a941501b57d1c5bf4d5f88a1232ed654eec49e9f23b9f3b53590f43806be8"}}