{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HYOFGQRANYRFHLWLVONWCRXR7N","short_pith_number":"pith:HYOFGQRA","schema_version":"1.0","canonical_sha256":"3e1c5342206e2253aecbab9b6146f1fb62fee94efb0ef6a1d97c68eb92aa5edf","source":{"kind":"arxiv","id":"2607.14204","version":1},"attestation_state":"computed","paper":{"title":"A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Hanwen Liu","submitted_at":"2026-07-15T17:57:04Z","abstract_excerpt":"For a closed oriented Riemannian $4$-manifold $(M,g)$, we consider $\\operatorname{SO}(3)$ connections on the bundle $\\Lambda^+$ of self-dual $2$-forms. On the open locus where the self-dual curvature is an orientation-preserving frame, pointwise polar decomposition removes the gauge freedom and replaces the connection by a field $h$ of positive definite symmetric matrices. We show that $h$ determines a unique compatible connection $A(h)$ and that the Yang--Mills equation is equivalent to the exactly determined second order system $$ \\Phi_g(h):=F_{A(h)}^+h^{-1}-g=0. $$ We establish a variationa"},"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":"2607.14204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-15T17:57:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3e8d2e015fc12a508d5a301bda240e1c1d897cc8e913399ac62670815e54fa69","abstract_canon_sha256":"d4f486384bf9452e54b051ff3692c37f05c483c14db415adbc481a789b630d64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T00:20:57.916421Z","signature_b64":"V0VQeEvM1mVH77SdQOle5z4z8/hlEgjr4sgWfnlA0Gx5mB/T0dKrvzNqhW6Mjm9lJ1FxdL/p29xrKEzqMRWkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e1c5342206e2253aecbab9b6146f1fb62fee94efb0ef6a1d97c68eb92aa5edf","last_reissued_at":"2026-07-17T00:20:57.915579Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T00:20:57.915579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Hanwen Liu","submitted_at":"2026-07-15T17:57:04Z","abstract_excerpt":"For a closed oriented Riemannian $4$-manifold $(M,g)$, we consider $\\operatorname{SO}(3)$ connections on the bundle $\\Lambda^+$ of self-dual $2$-forms. On the open locus where the self-dual curvature is an orientation-preserving frame, pointwise polar decomposition removes the gauge freedom and replaces the connection by a field $h$ of positive definite symmetric matrices. We show that $h$ determines a unique compatible connection $A(h)$ and that the Yang--Mills equation is equivalent to the exactly determined second order system $$ \\Phi_g(h):=F_{A(h)}^+h^{-1}-g=0. $$ We establish a variationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14204","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14204/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":"2607.14204","created_at":"2026-07-17T00:20:57.916011+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.14204v1","created_at":"2026-07-17T00:20:57.916011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14204","created_at":"2026-07-17T00:20:57.916011+00:00"},{"alias_kind":"pith_short_12","alias_value":"HYOFGQRANYRF","created_at":"2026-07-17T00:20:57.916011+00:00"},{"alias_kind":"pith_short_16","alias_value":"HYOFGQRANYRFHLWL","created_at":"2026-07-17T00:20:57.916011+00:00"},{"alias_kind":"pith_short_8","alias_value":"HYOFGQRA","created_at":"2026-07-17T00:20:57.916011+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/HYOFGQRANYRFHLWLVONWCRXR7N","json":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N.json","graph_json":"https://pith.science/api/pith-number/HYOFGQRANYRFHLWLVONWCRXR7N/graph.json","events_json":"https://pith.science/api/pith-number/HYOFGQRANYRFHLWLVONWCRXR7N/events.json","paper":"https://pith.science/paper/HYOFGQRA"},"agent_actions":{"view_html":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N","download_json":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N.json","view_paper":"https://pith.science/paper/HYOFGQRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.14204&json=true","fetch_graph":"https://pith.science/api/pith-number/HYOFGQRANYRFHLWLVONWCRXR7N/graph.json","fetch_events":"https://pith.science/api/pith-number/HYOFGQRANYRFHLWLVONWCRXR7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N/action/storage_attestation","attest_author":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N/action/author_attestation","sign_citation":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N/action/citation_signature","submit_replication":"https://pith.science/pith/HYOFGQRANYRFHLWLVONWCRXR7N/action/replication_record"}},"created_at":"2026-07-17T00:20:57.916011+00:00","updated_at":"2026-07-17T00:20:57.916011+00:00"}