{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EDLVDRSH7PTPIEBCTTVMP4GRW5","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":"699ddd1dca4bff3ac091ee1cefc84d6b270b749cd9abe71450b07d232c05d2f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-30T02:17:51Z","title_canon_sha256":"35cf261c41e258c497e8dfc111433d691460b4ddad516060ce777540508671eb"},"schema_version":"1.0","source":{"id":"2408.16973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.16973","created_at":"2026-07-05T09:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"2408.16973v2","created_at":"2026-07-05T09:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.16973","created_at":"2026-07-05T09:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"EDLVDRSH7PTP","created_at":"2026-07-05T09:05:38Z"},{"alias_kind":"pith_short_16","alias_value":"EDLVDRSH7PTPIEBC","created_at":"2026-07-05T09:05:38Z"},{"alias_kind":"pith_short_8","alias_value":"EDLVDRSH","created_at":"2026-07-05T09:05:38Z"}],"graph_snapshots":[{"event_id":"sha256:f8262cae379310820965fca17e3fc6baa7d3c9516c3b74359aa24af215adb635","target":"graph","created_at":"2026-07-05T09:05:38Z","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/2408.16973/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider equivariant solutions for the Schr\\\"odinger Map equation in $2+1$ dimensions, with values into $\\mathbb{S}^2$. Within each equivariance class $m \\in \\mathbb{Z}$ this admits a lowest energy nontrivial steady state $Q^m$, which extends to a two dimensional family of steady states by scaling and rotation. If $|m| \\geq 3$ then these ground states are known to be stable in the energy space $\\dot H^1$, whereas instability and even finite time blow-up along the ground state family may occur if $|m| = 1$. In this article we consider the most delicate case $|m| = 2$. Our main result asserts","authors_text":"Daniel Tataru, Ioan Bejenaru, Mohandas Pillai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-30T02:17:51Z","title":"Near soliton evolution for $2$-equivariant Schr\\\"odinger Maps in two space dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16973","kind":"arxiv","version":2},"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:c90aeb4c99b6f38e323d9d3798e198c62f07aab5afcae14d5718d463fc76b961","target":"record","created_at":"2026-07-05T09:05:38Z","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":"699ddd1dca4bff3ac091ee1cefc84d6b270b749cd9abe71450b07d232c05d2f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-30T02:17:51Z","title_canon_sha256":"35cf261c41e258c497e8dfc111433d691460b4ddad516060ce777540508671eb"},"schema_version":"1.0","source":{"id":"2408.16973","kind":"arxiv","version":2}},"canonical_sha256":"20d751c647fbe6f410229ceac7f0d1b7613739556e1ed51313bf68f0c6bb3ef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20d751c647fbe6f410229ceac7f0d1b7613739556e1ed51313bf68f0c6bb3ef8","first_computed_at":"2026-07-05T09:05:38.732041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:38.732041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iRIGbR5KbRKojNyTVJeODkfK1cnt6Xl67hh2PqkQeRV9K5Cm42ujwaULaLXURpoCuRj0AN3yhlDSzGWLPwtxAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:38.732533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.16973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90aeb4c99b6f38e323d9d3798e198c62f07aab5afcae14d5718d463fc76b961","sha256:f8262cae379310820965fca17e3fc6baa7d3c9516c3b74359aa24af215adb635"],"state_sha256":"40eeeecf31b2d8e2610718ce4c6935e86c7f77f45082a41522cfdfb1ca4034cd"}