{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LYYIRQ52HQCFWCM2EEAM3IRG6W","short_pith_number":"pith:LYYIRQ52","schema_version":"1.0","canonical_sha256":"5e3088c3ba3c045b099a2100cda226f5add9b690d539ee07cc7cf78ff3b0e87d","source":{"kind":"arxiv","id":"1303.1401","version":2},"attestation_state":"computed","paper":{"title":"Elliptic Yang-Mills Flow Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jan Swoboda, Remi Janner","submitted_at":"2013-03-06T17:45:14Z","abstract_excerpt":"We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\\mathcal J$. While the critical points of $\\mathcal J$ correspond to Yang-Mills connections on $P$, its $L^2$-gradient gives rise to a novel system of elliptic equations. This contrasts previous approaches to a study of the Yang-Mills functional via a parabolic gradient flow. We carry out the complete analytical details of our program in the case of a compact two-dimensional base manifold $Y$. We furthermore discuss i"},"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":"1303.1401","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-06T17:45:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"7073934bd928f5cbf78358f4f0f7cc7ee52be5abc0a366a4ebcdd9c1dcfe246f","abstract_canon_sha256":"bb50682c7ba6d71ff9a92626c66ec08b515d5ac6925dc25e57458abc1275da3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:28.215310Z","signature_b64":"TWSAO1xrFSbX3QboPgsKEgZaGw6soPEgEBZVA1yDuBcKozfEmoPFN4t66SfsM6Mmfpb40M8XBYEgglawnFobAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e3088c3ba3c045b099a2100cda226f5add9b690d539ee07cc7cf78ff3b0e87d","last_reissued_at":"2026-05-18T03:05:28.214642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:28.214642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic Yang-Mills Flow Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jan Swoboda, Remi Janner","submitted_at":"2013-03-06T17:45:14Z","abstract_excerpt":"We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\\mathcal J$. While the critical points of $\\mathcal J$ correspond to Yang-Mills connections on $P$, its $L^2$-gradient gives rise to a novel system of elliptic equations. This contrasts previous approaches to a study of the Yang-Mills functional via a parabolic gradient flow. We carry out the complete analytical details of our program in the case of a compact two-dimensional base manifold $Y$. We furthermore discuss i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1401","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":""},"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":"1303.1401","created_at":"2026-05-18T03:05:28.214738+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1401v2","created_at":"2026-05-18T03:05:28.214738+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1401","created_at":"2026-05-18T03:05:28.214738+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYYIRQ52HQCF","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYYIRQ52HQCFWCM2","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYYIRQ52","created_at":"2026-05-18T12:27:51.066281+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/LYYIRQ52HQCFWCM2EEAM3IRG6W","json":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W.json","graph_json":"https://pith.science/api/pith-number/LYYIRQ52HQCFWCM2EEAM3IRG6W/graph.json","events_json":"https://pith.science/api/pith-number/LYYIRQ52HQCFWCM2EEAM3IRG6W/events.json","paper":"https://pith.science/paper/LYYIRQ52"},"agent_actions":{"view_html":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W","download_json":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W.json","view_paper":"https://pith.science/paper/LYYIRQ52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1401&json=true","fetch_graph":"https://pith.science/api/pith-number/LYYIRQ52HQCFWCM2EEAM3IRG6W/graph.json","fetch_events":"https://pith.science/api/pith-number/LYYIRQ52HQCFWCM2EEAM3IRG6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W/action/storage_attestation","attest_author":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W/action/author_attestation","sign_citation":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W/action/citation_signature","submit_replication":"https://pith.science/pith/LYYIRQ52HQCFWCM2EEAM3IRG6W/action/replication_record"}},"created_at":"2026-05-18T03:05:28.214738+00:00","updated_at":"2026-05-18T03:05:28.214738+00:00"}