{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WUBTNL6UJDPZFUEWXSWLXR77GE","short_pith_number":"pith:WUBTNL6U","schema_version":"1.0","canonical_sha256":"b50336afd448df92d096bcacbbc7ff31140437ce5d551cfe38abc125e0a17a59","source":{"kind":"arxiv","id":"1311.6525","version":1},"attestation_state":"computed","paper":{"title":"The spectrum of a family of fourth-order equations near the global attractor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Seis, Robert J. McCann","submitted_at":"2013-11-26T00:37:49Z","abstract_excerpt":"The thin-film and quantum drift diffusion equations belong to a fourth-order family of evolution equations proposed in ref. 16 to be analogous to the (second-order) porous medium family. They are $2$-Wasserstein gradient ($W_2$) flows of the generalized Fisher information $I(u)$ just as the porous medium family was shown to be the $W_2$ gradient flow of the generalized entropy $E(u)$ by Otto. The identity $I(u) = |\\nabla_{W_2} E(u)|^2/2$ (formally) becomes $\\Hess_{W_2} I(u_*) =\\Hess_{W_2}^2 E(u_*)$ when linearizing the equation around its self-similar solution $u_*$. We couple this relation wi"},"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":"1311.6525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T00:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"60e9a9afd1451b2bffefb51276099504067128ba91012736bb821c9bfd327e20","abstract_canon_sha256":"9c6e7f3a6b0c0976d801e5d468cea332824ad55f767c5d2dfbd9e10c73871245"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:12.459304Z","signature_b64":"AJExJE4245y7MJhSrkquqBCl1DO2HNd8Aq1kvKSh+2SFA85oHQkMrqJgpG5lWnzCvUBYKecYxCGv+TILFXyhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b50336afd448df92d096bcacbbc7ff31140437ce5d551cfe38abc125e0a17a59","last_reissued_at":"2026-05-18T03:06:12.458773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:12.458773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectrum of a family of fourth-order equations near the global attractor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Seis, Robert J. McCann","submitted_at":"2013-11-26T00:37:49Z","abstract_excerpt":"The thin-film and quantum drift diffusion equations belong to a fourth-order family of evolution equations proposed in ref. 16 to be analogous to the (second-order) porous medium family. They are $2$-Wasserstein gradient ($W_2$) flows of the generalized Fisher information $I(u)$ just as the porous medium family was shown to be the $W_2$ gradient flow of the generalized entropy $E(u)$ by Otto. The identity $I(u) = |\\nabla_{W_2} E(u)|^2/2$ (formally) becomes $\\Hess_{W_2} I(u_*) =\\Hess_{W_2}^2 E(u_*)$ when linearizing the equation around its self-similar solution $u_*$. We couple this relation wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6525","kind":"arxiv","version":1},"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":"1311.6525","created_at":"2026-05-18T03:06:12.458855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.6525v1","created_at":"2026-05-18T03:06:12.458855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6525","created_at":"2026-05-18T03:06:12.458855+00:00"},{"alias_kind":"pith_short_12","alias_value":"WUBTNL6UJDPZ","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WUBTNL6UJDPZFUEW","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WUBTNL6U","created_at":"2026-05-18T12:28:04.890932+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/WUBTNL6UJDPZFUEWXSWLXR77GE","json":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE.json","graph_json":"https://pith.science/api/pith-number/WUBTNL6UJDPZFUEWXSWLXR77GE/graph.json","events_json":"https://pith.science/api/pith-number/WUBTNL6UJDPZFUEWXSWLXR77GE/events.json","paper":"https://pith.science/paper/WUBTNL6U"},"agent_actions":{"view_html":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE","download_json":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE.json","view_paper":"https://pith.science/paper/WUBTNL6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.6525&json=true","fetch_graph":"https://pith.science/api/pith-number/WUBTNL6UJDPZFUEWXSWLXR77GE/graph.json","fetch_events":"https://pith.science/api/pith-number/WUBTNL6UJDPZFUEWXSWLXR77GE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE/action/storage_attestation","attest_author":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE/action/author_attestation","sign_citation":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE/action/citation_signature","submit_replication":"https://pith.science/pith/WUBTNL6UJDPZFUEWXSWLXR77GE/action/replication_record"}},"created_at":"2026-05-18T03:06:12.458855+00:00","updated_at":"2026-05-18T03:06:12.458855+00:00"}