{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3DJ3DT7M42IASEWGAKOK6XCH45","short_pith_number":"pith:3DJ3DT7M","schema_version":"1.0","canonical_sha256":"d8d3b1cfece6900912c6029caf5c47e74504ab3b9c89242bfc1d45633444480e","source":{"kind":"arxiv","id":"1402.1990","version":1},"attestation_state":"computed","paper":{"title":"Variational Modelling: Energies, gradient flows, and large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Mark A. Peletier","submitted_at":"2014-02-09T20:53:10Z","abstract_excerpt":"These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route.\n  A central example is diffusion, in combination with various other processes, and a large part of the notes are devoted to this phenomenon. In the Variational Modelling methodology, diffusion is commonly modelled by including entropic terms in the driving functional and Wassers"},"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":"1402.1990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-09T20:53:10Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"01dd4b28e8baeb506e927009b7581c672917aecc529b6f7a4eadf26423d4535f","abstract_canon_sha256":"cf312bd3432aaaa03f943e5400bdf581e46d2a4a83fd94a98807091e24ae245e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:32.776779Z","signature_b64":"1kfrSrVaGF0i62D6s0o82Bb17RLY06p+NzsChJcMnWjvZj/QrtjETBzHY5dyS87TO2eBxJLn9W4qBSVBFDqyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8d3b1cfece6900912c6029caf5c47e74504ab3b9c89242bfc1d45633444480e","last_reissued_at":"2026-05-18T02:59:32.776007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:32.776007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational Modelling: Energies, gradient flows, and large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Mark A. Peletier","submitted_at":"2014-02-09T20:53:10Z","abstract_excerpt":"These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route.\n  A central example is diffusion, in combination with various other processes, and a large part of the notes are devoted to this phenomenon. In the Variational Modelling methodology, diffusion is commonly modelled by including entropic terms in the driving functional and Wassers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1990","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":"1402.1990","created_at":"2026-05-18T02:59:32.776134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1990v1","created_at":"2026-05-18T02:59:32.776134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1990","created_at":"2026-05-18T02:59:32.776134+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DJ3DT7M42IA","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DJ3DT7M42IASEWG","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DJ3DT7M","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.11519","citing_title":"Generative Path-Finding Method for Wasserstein Gradient Flow","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20188","citing_title":"Structure-Aware Variational Learning of a Class of Generalized Diffusions","ref_index":39,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45","json":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45.json","graph_json":"https://pith.science/api/pith-number/3DJ3DT7M42IASEWGAKOK6XCH45/graph.json","events_json":"https://pith.science/api/pith-number/3DJ3DT7M42IASEWGAKOK6XCH45/events.json","paper":"https://pith.science/paper/3DJ3DT7M"},"agent_actions":{"view_html":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45","download_json":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45.json","view_paper":"https://pith.science/paper/3DJ3DT7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1990&json=true","fetch_graph":"https://pith.science/api/pith-number/3DJ3DT7M42IASEWGAKOK6XCH45/graph.json","fetch_events":"https://pith.science/api/pith-number/3DJ3DT7M42IASEWGAKOK6XCH45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45/action/storage_attestation","attest_author":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45/action/author_attestation","sign_citation":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45/action/citation_signature","submit_replication":"https://pith.science/pith/3DJ3DT7M42IASEWGAKOK6XCH45/action/replication_record"}},"created_at":"2026-05-18T02:59:32.776134+00:00","updated_at":"2026-05-18T02:59:32.776134+00:00"}