{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RUGJZGSPPNYNQYA75GPCS5UKFO","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":"f83a401f2982f033902a6d55c98b839eff81b6b5d4706fe53790f059137d0037","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-13T16:32:24Z","title_canon_sha256":"3966b45ff561a1d4dc91b17f9a1388b62dbe3113250643872499fed90224e9b3"},"schema_version":"1.0","source":{"id":"1004.2225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2225","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2225v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2225","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"RUGJZGSPPNYN","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RUGJZGSPPNYNQYA7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RUGJZGSP","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:ab324047590602277a0025e3d2cbe09e6f7a1490289c1562f7b6f16fa5d39659","target":"graph","created_at":"2026-05-18T01:24:13Z","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":"Consider the viscous Burgers equation $u_t + f(u)_x = \\epsilon\\, u_{xx}$ on the interval $[0,1]$ with the inhomogeneous Dirichlet boundary conditions $u(t,0) = \\rho_0$, $u(t,1) = \\rho_1$.  The flux $f$ is the function $f(u)= u(1-u)$, $\\epsilon>0$ is the viscosity, and the boundary data satisfy $0<\\rho_0<\\rho_1<1$.  We examine the quasi-potential corresponding to an action functional, arising from non-equilibrium statistical mechanical models, associated to the above equation.  We provide a static variational formula for the quasi-potential and characterize the optimal paths for the dynamical p","authors_text":"Alberto De Sole, Claudio Landim, Davide Gabrielli, Giovanni Jona-Lasinio, Lorenzo Bertini","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-13T16:32:24Z","title":"Action functional and quasi-potential for the Burgers equation in a bounded interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2225","kind":"arxiv","version":1},"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":"sha256:1f4cf013c5351a83fac824c88125252b2c015fe816960591ee057fe8eb1709f2","target":"record","created_at":"2026-05-18T01:24:13Z","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":"f83a401f2982f033902a6d55c98b839eff81b6b5d4706fe53790f059137d0037","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-13T16:32:24Z","title_canon_sha256":"3966b45ff561a1d4dc91b17f9a1388b62dbe3113250643872499fed90224e9b3"},"schema_version":"1.0","source":{"id":"1004.2225","kind":"arxiv","version":1}},"canonical_sha256":"8d0c9c9a4f7b70d8601fe99e29768a2ba72a6edf14f6cce7035f0d7c2018ba5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d0c9c9a4f7b70d8601fe99e29768a2ba72a6edf14f6cce7035f0d7c2018ba5b","first_computed_at":"2026-05-18T01:24:13.112185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:13.112185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C9XzTb98lbHTiO3zc4xADe96/6lE/jLjxTn+Uqv0I3iwIFYFMCcHxs1sUWXdPbORx51OwPVdC5mCThNYdFQcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:13.112640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f4cf013c5351a83fac824c88125252b2c015fe816960591ee057fe8eb1709f2","sha256:ab324047590602277a0025e3d2cbe09e6f7a1490289c1562f7b6f16fa5d39659"],"state_sha256":"c857762b37f569dd30e0b3065b3f1337cd5c6f673e357b820437613517f7c340"}