{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DDMRYHTZLLMMESN7U3FNFK35GP","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":"07119f962aaaddd1e78a2d251f7bedd56734ac2f3c20df2e161a43058a106d6e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-15T14:06:02Z","title_canon_sha256":"f96cb0ddf41a192dff58077cd367abf60e86a397df53e22fde1c2fcf2871e9d7"},"schema_version":"1.0","source":{"id":"1405.3856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3856","created_at":"2026-05-18T02:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3856v1","created_at":"2026-05-18T02:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3856","created_at":"2026-05-18T02:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"DDMRYHTZLLMM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DDMRYHTZLLMMESN7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DDMRYHTZ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:67d5da7b35ad4cd68bc3d58f3873d37ea494c30b07a92178955cd5d769036fdd","target":"graph","created_at":"2026-05-18T02:51:49Z","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 radial nonlinear wave equation $-\\partial_t^2 u + \\Delta u = u^3$, $u :\\mathbb{R}_t \\times \\mathbb{R}_x^3 \\to \\mathbb{R}$, $u(t,x) = u(t,|x|)$. In this paper, we construct a Gibbs measure for this system and prove its invariance under the flow of the NLW. In particular, we are in the infinite volume setting. For the finite volume analogue, specifically on the unit ball with zero boundary values, an invariant Gibbs measure was constructed by Burq, Tvetkov, and de Suzzoni as a Borel measure on super-critical Sobolev spaces. In this paper, we advocate that the finite volume Gibbs mea","authors_text":"Samantha Xu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-15T14:06:02Z","title":"Invariant Gibbs Measure for 3D NLW in Infinite Volume"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3856","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:e18653dc6606cc4db24ffdd20f15382c6a6ca9a2010c2737c8a3675d3f98cf9d","target":"record","created_at":"2026-05-18T02:51:49Z","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":"07119f962aaaddd1e78a2d251f7bedd56734ac2f3c20df2e161a43058a106d6e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-15T14:06:02Z","title_canon_sha256":"f96cb0ddf41a192dff58077cd367abf60e86a397df53e22fde1c2fcf2871e9d7"},"schema_version":"1.0","source":{"id":"1405.3856","kind":"arxiv","version":1}},"canonical_sha256":"18d91c1e795ad8c249bfa6cad2ab7d33d00ac7d16e0c92dc9de3ee59199cd4cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18d91c1e795ad8c249bfa6cad2ab7d33d00ac7d16e0c92dc9de3ee59199cd4cc","first_computed_at":"2026-05-18T02:51:49.155525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:49.155525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D4b8c7cfctTZ/2tipJRzkox9Fx7FYNDXmTJ/l001tlw9o0xkcIylzRqvXTHJAlDdEWwk0md9soWETe00LlNeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:49.155927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e18653dc6606cc4db24ffdd20f15382c6a6ca9a2010c2737c8a3675d3f98cf9d","sha256:67d5da7b35ad4cd68bc3d58f3873d37ea494c30b07a92178955cd5d769036fdd"],"state_sha256":"13530448fbb5f155cae6a14e843a47141726ab44a942d7145a92636ca3e10c24"}