{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ZKSA4VWDMJMDPY74443ERC6RKL","short_pith_number":"pith:ZKSA4VWD","schema_version":"1.0","canonical_sha256":"caa40e56c3625837e3fce736488bd152f3f329d430a3cdcdf1587ca22e8a6f18","source":{"kind":"arxiv","id":"2306.04856","version":2},"attestation_state":"computed","paper":{"title":"Ground states for aggregation-diffusion models on Cartan-Hadamard manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Hansol Park, Razvan C. Fetecau","submitted_at":"2023-06-08T01:09:45Z","abstract_excerpt":"We consider a free energy functional on Cartan-Hadamard manifolds, and investigate the existence of its global minimizers. The energy functional consists of two components: an entropy (or internal energy) and an interaction energy modelled by an attractive potential. The two components have competing effects, as they favour spreading by linear diffusion and blow-up by nonlocal attractive interactions, respectively. We find necessary and sufficient conditions for existence of ground states for manifolds with sectional curvatures bounded above and below, respectively. In particular, for general "},"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":"2306.04856","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-08T01:09:45Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"cc03dafec391d293b2a00ed468bb16ed7e893652992f32e5697ad7fe5d739b97","abstract_canon_sha256":"85d18fec9e1708754d456b4acb54bc768cfe0e6bcaddb63ea875b14fb8864445"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:29:02.489123Z","signature_b64":"dr1RLrOQ4+/900BElYlWuPxrmMk7QtI9n5frhweIrDlxkgdSSGuDk3T6WI8Cj9UKurjBlByMiceLzCw3oOiPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caa40e56c3625837e3fce736488bd152f3f329d430a3cdcdf1587ca22e8a6f18","last_reissued_at":"2026-07-05T06:29:02.488651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:29:02.488651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states for aggregation-diffusion models on Cartan-Hadamard manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Hansol Park, Razvan C. Fetecau","submitted_at":"2023-06-08T01:09:45Z","abstract_excerpt":"We consider a free energy functional on Cartan-Hadamard manifolds, and investigate the existence of its global minimizers. The energy functional consists of two components: an entropy (or internal energy) and an interaction energy modelled by an attractive potential. The two components have competing effects, as they favour spreading by linear diffusion and blow-up by nonlocal attractive interactions, respectively. We find necessary and sufficient conditions for existence of ground states for manifolds with sectional curvatures bounded above and below, respectively. In particular, for general "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.04856","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.04856/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2306.04856","created_at":"2026-07-05T06:29:02.488706+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.04856v2","created_at":"2026-07-05T06:29:02.488706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.04856","created_at":"2026-07-05T06:29:02.488706+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKSA4VWDMJMD","created_at":"2026-07-05T06:29:02.488706+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKSA4VWDMJMDPY74","created_at":"2026-07-05T06:29:02.488706+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKSA4VWD","created_at":"2026-07-05T06:29:02.488706+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.14813","citing_title":"Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL","json":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL.json","graph_json":"https://pith.science/api/pith-number/ZKSA4VWDMJMDPY74443ERC6RKL/graph.json","events_json":"https://pith.science/api/pith-number/ZKSA4VWDMJMDPY74443ERC6RKL/events.json","paper":"https://pith.science/paper/ZKSA4VWD"},"agent_actions":{"view_html":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL","download_json":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL.json","view_paper":"https://pith.science/paper/ZKSA4VWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.04856&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKSA4VWDMJMDPY74443ERC6RKL/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKSA4VWDMJMDPY74443ERC6RKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL/action/storage_attestation","attest_author":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL/action/author_attestation","sign_citation":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL/action/citation_signature","submit_replication":"https://pith.science/pith/ZKSA4VWDMJMDPY74443ERC6RKL/action/replication_record"}},"created_at":"2026-07-05T06:29:02.488706+00:00","updated_at":"2026-07-05T06:29:02.488706+00:00"}