{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7RR7UIYWIXDBKQEOWJKW4MKS55","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":"4cd6f79aab584b6d8365e87c47e77ebcbde862fbfcc390a343458149cf081205","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:21:21Z","title_canon_sha256":"2ce65f284d3e23a6b256213c4f4ee29be6fa22c4944609e521073ae879d2c4e6"},"schema_version":"1.0","source":{"id":"1212.1573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1573","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1573v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1573","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"7RR7UIYWIXDB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7RR7UIYWIXDBKQEO","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7RR7UIYW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:8419630e4e57f4d4d28b2088dc3fdc074c9e788cbf61617c9cf267c15e09f600","target":"graph","created_at":"2026-05-18T03:38:56Z","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 are interested in understanding the dynamics of dissipative partial differential equations on unbounded spatial domains. We consider systems for which the energy density $e \\ge 0$ satisfies an evolution law of the form $\\partial_t e = div_x f - d$, where $-f$ is the energy flux and $d \\ge 0$ the energy dissipation rate. We also suppose that $|f|^2 \\le b(e)d$ for some nonnegative function $b$. Under these assumptions we establish simple and universal bounds on the time-integrated energy flux, which in turn allow us to estimate the amount of energy that is dissipated in a given domain over a ","authors_text":"Sinisa Slijepcevic, Thierry Gallay","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:21:21Z","title":"Distribution of Energy and Convergence to Equilibria in Extended Dissipative Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1573","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":"sha256:48f4d5a46f0ed17880d0a3708438ed50dcf0ac170c09063b701d905833f1e493","target":"record","created_at":"2026-05-18T03:38:56Z","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":"4cd6f79aab584b6d8365e87c47e77ebcbde862fbfcc390a343458149cf081205","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-07T10:21:21Z","title_canon_sha256":"2ce65f284d3e23a6b256213c4f4ee29be6fa22c4944609e521073ae879d2c4e6"},"schema_version":"1.0","source":{"id":"1212.1573","kind":"arxiv","version":1}},"canonical_sha256":"fc63fa231645c615408eb2556e3152ef422b28d6765a27c09bec3442791333b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc63fa231645c615408eb2556e3152ef422b28d6765a27c09bec3442791333b0","first_computed_at":"2026-05-18T03:38:56.893415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:56.893415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e3C3Pjzi4O3gCC+g2hUKGCUQeHHZEevKc+Mi6KUIQNUuYFubzi83KQYTBfxKveZW4jVrWR5o4aK05z5jF3BoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:56.893868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48f4d5a46f0ed17880d0a3708438ed50dcf0ac170c09063b701d905833f1e493","sha256:8419630e4e57f4d4d28b2088dc3fdc074c9e788cbf61617c9cf267c15e09f600"],"state_sha256":"35da794f2ce659166acabb7cec3fc1ec2e15e0664655675f4723e5a5a31cd403"}