{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TUALTWL7SFNPXBLZUFDYESCOWG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f6b6146cfd2b59181147c7df10aeca366c25de654300bfec2601e3da83e0eac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-17T16:41:41Z","title_canon_sha256":"20052dbb137cb37f7fb79bd4374d9edeffcdadad3207215c269e0b08c885ff46"},"schema_version":"1.0","source":{"id":"2605.17536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17536","created_at":"2026-05-20T00:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17536v1","created_at":"2026-05-20T00:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17536","created_at":"2026-05-20T00:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"TUALTWL7SFNP","created_at":"2026-05-20T00:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"TUALTWL7SFNPXBLZ","created_at":"2026-05-20T00:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"TUALTWL7","created_at":"2026-05-20T00:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:5d18a730777f378bf3f11f146c619d59bd27b61dde698cc557715ff6e593d0ed","target":"graph","created_at":"2026-05-20T00:04:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The existence of global weak solutions of wave maps from R^n into S^{L-1} satisfying Box u perpendicular to T_u S^{L-1} is established as a singular limit of maps minimizing elliptic regularized variational functionals containing an exponential weight in the time direction with small parameter ε."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The paper assumes that the minimizers of the ε-regularized functionals exist for each ε > 0 and that a suitable compactness or convergence argument as ε → 0 produces a limit satisfying the wave map equation and the initial data in the weak sense (abstract, paragraph on the singular limit construction)."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Global weak solutions for wave maps from R^n to S^{L-1} are recovered as singular limits of minimizers of exponentially weighted elliptic regularized functionals with initial data as boundary conditions."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Global weak solutions for wave maps into spheres exist as singular limits of minimizers to time-weighted elliptic functionals."}],"snapshot_sha256":"a1a07e7aeca00d723605ffeb605c264030ee45d96d87ee0a9921fd097fe7564d"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"8d49d8b1bde8de40c2d5700262968204fdc75c749ce5b46dd532ee629df04759"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.598181Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:21:44.817991Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.616078Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.553131Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17536/integrity.json","findings":[],"snapshot_sha256":"c0f9cd22a4a53a7997978c729d5600a173f77de198db4b42a3274c1b1a61c903","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"n this paper, we revisit the existence of global weak solutions of wave maps from $\\R^n$ into the sphere $\\mathbb{S}^{L-1}$, $\\Box u\\perp T_u \\mathbb{S}^{L-1}$, by establishing it as a singular limit of maps from $\\R^n\\times \\R_+$ to $\\mathbb S^{L-1}$ that minimize elliptic regularized variational functionals that contain an exponential weight in the time direction with a small parameter $\\varepsilon$, where the initial data of the Cauchy problem serve as the boundary condition. The idea went back to De Giorgi \\cite{Giorgi1996}, which has been implemented by Serra and Tilli \\cite{Serra-Tilli20","authors_text":"Changyou Wang, Zhiyuan Geng","cross_cats":[],"headline":"Global weak solutions for wave maps into spheres exist as singular limits of minimizers to time-weighted elliptic functionals.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-17T16:41:41Z","title":"On Variational Approximations For Wave Maps"},"references":{"count":10,"internal_anchors":0,"resolved_work":10,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"De Giorgi,Conjectures concerning some evolution problems","work_id":"b4e65bef-e1df-4003-8440-6036ba65cead","year":1996},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Freire,Global weak solutions of the wave map system to compact homogeneous spaces.Manuscripta Math","work_id":"d2f65f44-3801-4a34-8e2a-853c4f407447","year":1996},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"A. Freire, S. Müller,M. Struwe,Weak convergence of wave maps from(1 + 2)-dimensional Minkowski space to Riemannian manifolds.Invent. Math. 130 (1997), no. 3, 589-617","work_id":"5cf4a656-588d-43a9-9f1a-2ae30feeee6d","year":1997},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"A. Freire, S. Müller,M. Struwe,Weak compactness of wave maps and harmonic maps. Ann. Inst. H. Poincaré C Anal. Non Lin´daire 15 (1998), no. 6, 725-754","work_id":"708e5ef6-782d-411f-a926-2839d14bd3e9","year":1998},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"S. Múller, M. Struwe,Global existence of wave maps in I+2 dimensions for finite energy data. Top. Merhods Nonlinear Anaiy.sis, Vol. 7, 1996, pp. 245-259","work_id":"c67fa255-321e-47fc-b440-7e6b950355e1","year":1996}],"snapshot_sha256":"ad2e1f200290930cc0a765fbf9f2b78a8966c66e826150168c8339f306e00691"},"source":{"id":"2605.17536","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:09:15.006385Z","id":"c3bc7276-5082-46cf-b0a4-3a5b14753ef7","model_set":{"reader":"grok-4.3"},"one_line_summary":"Global weak solutions for wave maps from R^n to S^{L-1} are recovered as singular limits of minimizers of exponentially weighted elliptic regularized functionals with initial data as boundary conditions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Global weak solutions for wave maps into spheres exist as singular limits of minimizers to time-weighted elliptic functionals.","strongest_claim":"The existence of global weak solutions of wave maps from R^n into S^{L-1} satisfying Box u perpendicular to T_u S^{L-1} is established as a singular limit of maps minimizing elliptic regularized variational functionals containing an exponential weight in the time direction with small parameter ε.","weakest_assumption":"The paper assumes that the minimizers of the ε-regularized functionals exist for each ε > 0 and that a suitable compactness or convergence argument as ε → 0 produces a limit satisfying the wave map equation and the initial data in the weak sense (abstract, paragraph on the singular limit construction)."}},"verdict_id":"c3bc7276-5082-46cf-b0a4-3a5b14753ef7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cd379aeab0e98a5ad4d534e811819a002c50e4c2f2fb530a96e7d64c73e98c46","target":"record","created_at":"2026-05-20T00:04:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f6b6146cfd2b59181147c7df10aeca366c25de654300bfec2601e3da83e0eac","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-17T16:41:41Z","title_canon_sha256":"20052dbb137cb37f7fb79bd4374d9edeffcdadad3207215c269e0b08c885ff46"},"schema_version":"1.0","source":{"id":"2605.17536","kind":"arxiv","version":1}},"canonical_sha256":"9d00b9d97f915afb8579a14782484eb1af76c7904ae04ce1fb9df64799736b44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d00b9d97f915afb8579a14782484eb1af76c7904ae04ce1fb9df64799736b44","first_computed_at":"2026-05-20T00:04:44.530492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:44.530492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DfT1Rz3mfarPYCjNNqDf2yQrh/Mb0+HLH9SC1XAI4UmkYa2uOm6B36l0D97oD0OB9PUJfsp01GrJ9QvNMQ4GAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:44.531260Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd379aeab0e98a5ad4d534e811819a002c50e4c2f2fb530a96e7d64c73e98c46","sha256:5d18a730777f378bf3f11f146c619d59bd27b61dde698cc557715ff6e593d0ed"],"state_sha256":"81362e96aa6d435c381efa8e7aa4433e20bde909013eb0e679aa9698aa957d0e"}