{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:L4BLHWMWSDKYBAS5K6IYSI237Z","short_pith_number":"pith:L4BLHWMW","schema_version":"1.0","canonical_sha256":"5f02b3d99690d580825d579189235bfe71f9a8da3b189d933fd9313bcf52b41c","source":{"kind":"arxiv","id":"1507.06076","version":4},"attestation_state":"computed","paper":{"title":"Second order Boltzmann-Gibbs principle for polynomial functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marielle Simon, Milton Jara, Patricia Gon\\c{c}alves","submitted_at":"2015-07-22T06:59:40Z","abstract_excerpt":"In this paper we give a new proof of the second order Boltzmann-Gibbs principle. The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards 1) a trivial process in case of supper-diffusive systems, 2) an Ornstein-Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, in case of weakly asymmetric diffusive systems. Exam"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.06076","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-22T06:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"1f8f65dfbc7b7b8be62291bb2a0be53009be75b59f16530552b40677fb3ae3b9","abstract_canon_sha256":"888ff892111988eab24d5d7a39d8b4a884ac00d42c97a4c5020b04f8089bf6d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:33.595119Z","signature_b64":"iWOd0JOWbj9PYs5oGbvCapVDqQNHH32R4brRTGgUeTMeF/Y8jjs9OjE+BRExdhjyeQl93YK3cvLyZK1g9lXZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f02b3d99690d580825d579189235bfe71f9a8da3b189d933fd9313bcf52b41c","last_reissued_at":"2026-05-18T00:36:33.594578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:33.594578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order Boltzmann-Gibbs principle for polynomial functions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marielle Simon, Milton Jara, Patricia Gon\\c{c}alves","submitted_at":"2015-07-22T06:59:40Z","abstract_excerpt":"In this paper we give a new proof of the second order Boltzmann-Gibbs principle. The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards 1) a trivial process in case of supper-diffusive systems, 2) an Ornstein-Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, in case of weakly asymmetric diffusive systems. Exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06076","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.06076","created_at":"2026-05-18T00:36:33.594677+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06076v4","created_at":"2026-05-18T00:36:33.594677+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06076","created_at":"2026-05-18T00:36:33.594677+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4BLHWMWSDKY","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4BLHWMWSDKYBAS5","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4BLHWMW","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z","json":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z.json","graph_json":"https://pith.science/api/pith-number/L4BLHWMWSDKYBAS5K6IYSI237Z/graph.json","events_json":"https://pith.science/api/pith-number/L4BLHWMWSDKYBAS5K6IYSI237Z/events.json","paper":"https://pith.science/paper/L4BLHWMW"},"agent_actions":{"view_html":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z","download_json":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z.json","view_paper":"https://pith.science/paper/L4BLHWMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06076&json=true","fetch_graph":"https://pith.science/api/pith-number/L4BLHWMWSDKYBAS5K6IYSI237Z/graph.json","fetch_events":"https://pith.science/api/pith-number/L4BLHWMWSDKYBAS5K6IYSI237Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z/action/storage_attestation","attest_author":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z/action/author_attestation","sign_citation":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z/action/citation_signature","submit_replication":"https://pith.science/pith/L4BLHWMWSDKYBAS5K6IYSI237Z/action/replication_record"}},"created_at":"2026-05-18T00:36:33.594677+00:00","updated_at":"2026-05-18T00:36:33.594677+00:00"}