{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:V3QNKOG2OT2JQUGMU2247TXXPE","short_pith_number":"pith:V3QNKOG2","canonical_record":{"source":{"id":"1503.05838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-19T16:47:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1452bac39b0dc654b4f607bca4295d94356b26f0d832d3de65d2f335833e4926","abstract_canon_sha256":"927dc79823f594b8a1e2af795f80ff8fb6000865133173122acda32b85e7ead1"},"schema_version":"1.0"},"canonical_sha256":"aee0d538da74f49850cca6b5cfcef7792bc47f6d8cf39e2932c119ba0cd6870c","source":{"kind":"arxiv","id":"1503.05838","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05838","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05838v3","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05838","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"V3QNKOG2OT2J","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V3QNKOG2OT2JQUGM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V3QNKOG2","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:V3QNKOG2OT2JQUGMU2247TXXPE","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-19T16:47:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1452bac39b0dc654b4f607bca4295d94356b26f0d832d3de65d2f335833e4926","abstract_canon_sha256":"927dc79823f594b8a1e2af795f80ff8fb6000865133173122acda32b85e7ead1"},"schema_version":"1.0"},"canonical_sha256":"aee0d538da74f49850cca6b5cfcef7792bc47f6d8cf39e2932c119ba0cd6870c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:10.159518Z","signature_b64":"huEDoQumG5poTQSeCSmGzW4hgBeTkR0ID9ADNAJgdJQoSgJiVS4DKPmwZK+SKKSiuW9INxf49i93Rpue5ClfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aee0d538da74f49850cca6b5cfcef7792bc47f6d8cf39e2932c119ba0cd6870c","last_reissued_at":"2026-05-18T00:36:10.158841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:10.158841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05838","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":"2026-05-18T00:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBb+mtS+GeIWEkiwBZMKxloV0opxksNGISJ6/OQNHIxrG2ZduoQCWlFOMMNPHqq+B5wV0scD8Ytu/Psqrkt5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:02:46.049529Z"},"content_sha256":"f6d7faabc5c7b61c8608f73bf08ab2488faca9ef71352e526744df0608d61aee","schema_version":"1.0","event_id":"sha256:f6d7faabc5c7b61c8608f73bf08ab2488faca9ef71352e526744df0608d61aee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:V3QNKOG2OT2JQUGMU2247TXXPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density fluctuations for exclusion processes with long jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Milton Jara, Patr\\'icia Gon\\c{c}alves","submitted_at":"2015-03-19T16:47:34Z","abstract_excerpt":"We show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form $c^\\pm |y-x|^{-(1+\\alpha)}$ where $c\\pm$ depends on the sign of $y-x$, are given by a fractional Ornstein-Uhlenbeck process for $\\alpha \\in (0,\\frac{3}{2})$. When $\\alpha =\\frac{3}{2}$ we show that the density fluctuations are tight, in a suitable topology, and that any limit point is an energy solution of the fractional Burgers equation, previously introduced in \\cite{GubJar} in the finite volume setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05838","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":"2026-05-18T00:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wr6St/koYGaeb0YIliF1QrRQw9zpGKgeqnXt5vmD0Ua0Qivpn03enTgsYnBMRiNbSsomkuySNhZFIz9SvtqkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:02:46.049873Z"},"content_sha256":"62e2deb2b6f6ae4f43f4709545b5f549a41da0312759d1419d82655a04ce5bd3","schema_version":"1.0","event_id":"sha256:62e2deb2b6f6ae4f43f4709545b5f549a41da0312759d1419d82655a04ce5bd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3QNKOG2OT2JQUGMU2247TXXPE/bundle.json","state_url":"https://pith.science/pith/V3QNKOG2OT2JQUGMU2247TXXPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3QNKOG2OT2JQUGMU2247TXXPE/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":"2026-06-06T13:02:46Z","links":{"resolver":"https://pith.science/pith/V3QNKOG2OT2JQUGMU2247TXXPE","bundle":"https://pith.science/pith/V3QNKOG2OT2JQUGMU2247TXXPE/bundle.json","state":"https://pith.science/pith/V3QNKOG2OT2JQUGMU2247TXXPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3QNKOG2OT2JQUGMU2247TXXPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V3QNKOG2OT2JQUGMU2247TXXPE","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":"927dc79823f594b8a1e2af795f80ff8fb6000865133173122acda32b85e7ead1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-19T16:47:34Z","title_canon_sha256":"1452bac39b0dc654b4f607bca4295d94356b26f0d832d3de65d2f335833e4926"},"schema_version":"1.0","source":{"id":"1503.05838","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05838","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05838v3","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05838","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"V3QNKOG2OT2J","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V3QNKOG2OT2JQUGM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V3QNKOG2","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:62e2deb2b6f6ae4f43f4709545b5f549a41da0312759d1419d82655a04ce5bd3","target":"graph","created_at":"2026-05-18T00:36:10Z","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 show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form $c^\\pm |y-x|^{-(1+\\alpha)}$ where $c\\pm$ depends on the sign of $y-x$, are given by a fractional Ornstein-Uhlenbeck process for $\\alpha \\in (0,\\frac{3}{2})$. When $\\alpha =\\frac{3}{2}$ we show that the density fluctuations are tight, in a suitable topology, and that any limit point is an energy solution of the fractional Burgers equation, previously introduced in \\cite{GubJar} in the finite volume setting.","authors_text":"Milton Jara, Patr\\'icia Gon\\c{c}alves","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-19T16:47:34Z","title":"Density fluctuations for exclusion processes with long jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05838","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:f6d7faabc5c7b61c8608f73bf08ab2488faca9ef71352e526744df0608d61aee","target":"record","created_at":"2026-05-18T00:36:10Z","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":"927dc79823f594b8a1e2af795f80ff8fb6000865133173122acda32b85e7ead1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-19T16:47:34Z","title_canon_sha256":"1452bac39b0dc654b4f607bca4295d94356b26f0d832d3de65d2f335833e4926"},"schema_version":"1.0","source":{"id":"1503.05838","kind":"arxiv","version":3}},"canonical_sha256":"aee0d538da74f49850cca6b5cfcef7792bc47f6d8cf39e2932c119ba0cd6870c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aee0d538da74f49850cca6b5cfcef7792bc47f6d8cf39e2932c119ba0cd6870c","first_computed_at":"2026-05-18T00:36:10.158841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:10.158841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"huEDoQumG5poTQSeCSmGzW4hgBeTkR0ID9ADNAJgdJQoSgJiVS4DKPmwZK+SKKSiuW9INxf49i93Rpue5ClfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:10.159518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05838","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6d7faabc5c7b61c8608f73bf08ab2488faca9ef71352e526744df0608d61aee","sha256:62e2deb2b6f6ae4f43f4709545b5f549a41da0312759d1419d82655a04ce5bd3"],"state_sha256":"8b280bb52acb9005158abe121d7cca432a88f539bf81891ab91e50bfad26dc0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etMkxzSRuXCxIDD0O8LOThUL54kr9jA/A5qCleXw2idgPuYCN6YG2lew6XwYFGclFvwo9cPXuyr/ZSZdGQQ/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:02:46.051731Z","bundle_sha256":"ee73319925d6b2fe3893bd3a0cdda206c2e6529fcabf29aebca2f29391d8dcfb"}}