{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I5Z2IAHCMSWGDUNVCPM4PI636J","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":"c5145bc50cc89404fee6c3ce2ab75133bd47dab7662920b972ebe05351bbf24a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T13:57:42Z","title_canon_sha256":"bf83fc701d664a3160c01de2b9e7129d77d35c96c3e83ded90d084b0f71cccd7"},"schema_version":"1.0","source":{"id":"2503.02632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02632","created_at":"2026-07-05T10:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02632v1","created_at":"2026-07-05T10:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02632","created_at":"2026-07-05T10:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"I5Z2IAHCMSWG","created_at":"2026-07-05T10:24:10Z"},{"alias_kind":"pith_short_16","alias_value":"I5Z2IAHCMSWGDUNV","created_at":"2026-07-05T10:24:10Z"},{"alias_kind":"pith_short_8","alias_value":"I5Z2IAHC","created_at":"2026-07-05T10:24:10Z"}],"graph_snapshots":[{"event_id":"sha256:dc3ba9b0a01baee337a49a14ea174d1f91f2cac6bbc86ed7527f472f01e69dd8","target":"graph","created_at":"2026-07-05T10:24:10Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.02632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The wave maps equation in three spatial dimensions with a spherical target admits an explicit blow-up solution. Numerical studies suggest this solution captures the generic blow-up behaviour in the backward light cone of the singularity. In this work, we establish the mode stability of this blow-up solution in the backward light cone of the blow-up point without any assumptions on the symmetries of the perturbation. We classify all smooth mode solutions for growth rates $\\lambda$ with $\\mathrm{Re} \\, \\lambda \\geq 0$ and demonstrate that the blow-up solution is stable up to the mode solutions a","authors_text":"Herbert Koch, Max Weissenbacher, Roland Donninger","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T13:57:42Z","title":"Mode stability of blow-up for wave maps in the absence of symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02632","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7ab5ee3fac2c3bc01824743032f4a93d5ebcbdae6deb78d0fcfe4487f8f7dc3a","target":"record","created_at":"2026-07-05T10:24:10Z","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":"c5145bc50cc89404fee6c3ce2ab75133bd47dab7662920b972ebe05351bbf24a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T13:57:42Z","title_canon_sha256":"bf83fc701d664a3160c01de2b9e7129d77d35c96c3e83ded90d084b0f71cccd7"},"schema_version":"1.0","source":{"id":"2503.02632","kind":"arxiv","version":1}},"canonical_sha256":"4773a400e264ac61d1b513d9c7a3dbf2514e4d5c392e387e6f0e00c1f31ae323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4773a400e264ac61d1b513d9c7a3dbf2514e4d5c392e387e6f0e00c1f31ae323","first_computed_at":"2026-07-05T10:24:10.206133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:10.206133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOaxW9V2RESOmXybRSGxiTSWLbgJfuBhHt4jL9P/ULKCza9jnJ4hr8Wja7atBLLzqpaCMKDfaIqhkNXPNjc5CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:10.207039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.02632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ab5ee3fac2c3bc01824743032f4a93d5ebcbdae6deb78d0fcfe4487f8f7dc3a","sha256:dc3ba9b0a01baee337a49a14ea174d1f91f2cac6bbc86ed7527f472f01e69dd8"],"state_sha256":"85d1673323971117bbab9dbba05497c75a1a6647f90bbaf868b66e27ca6c2340"}