{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FXTAOOLZJN5KAL54S3WWRJIMDR","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":"88c8612cd09395eef5d647a428d7a11fa8819a2608eb71c9e728a3afaa7e5685","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-30T20:49:45Z","title_canon_sha256":"59740c16a1deedf9981662c447a6f240f9e65e1ea4a0d27d8d3b91426929a3c4"},"schema_version":"1.0","source":{"id":"1205.6828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6828","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6828v1","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6828","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"FXTAOOLZJN5K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FXTAOOLZJN5KAL54","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FXTAOOLZ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:7aba9e200044388d3a7141558f4ce12b78f49b1d8e6f5114191d4bab86454441","target":"graph","created_at":"2026-05-18T03:54:36Z","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"},"paper":{"abstract_excerpt":"In this paper, we construct a dumbbell domain for which the associated principle $\\infty$-eigenvalue is not simple. This gives a negative answer to the outstanding problem posed by Juutinen-Lindquivst-Manfredi (\"The $\\infty$-eigenvalue problem\", Arch. Ration. Mech. Anal. 148, 1999, no.2, 89-105). It remains a challenge to determine whether simplicity holds for convex domains.","authors_text":"Charles K. Smart, Ryan Hynd, Yifeng Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-30T20:49:45Z","title":"Nonuniqueness of infinity ground states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6828","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:b0e00e88ff8d739346566f1a135a99abb2621602c160e5845df905f53d50a4a8","target":"record","created_at":"2026-05-18T03:54:36Z","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":"88c8612cd09395eef5d647a428d7a11fa8819a2608eb71c9e728a3afaa7e5685","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-30T20:49:45Z","title_canon_sha256":"59740c16a1deedf9981662c447a6f240f9e65e1ea4a0d27d8d3b91426929a3c4"},"schema_version":"1.0","source":{"id":"1205.6828","kind":"arxiv","version":1}},"canonical_sha256":"2de60739794b7aa02fbc96ed68a50c1c7d2ddb725415650472c9c446e05b7c15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2de60739794b7aa02fbc96ed68a50c1c7d2ddb725415650472c9c446e05b7c15","first_computed_at":"2026-05-18T03:54:36.809359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:36.809359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73e8HDcWkjeRBvN4OAMnqOB9O7tVLWtStZmGAdC8lvR8zL4YC2lYz9O2rYftaoP+6Ydqb0D1APMyKQHzk6kOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:36.809959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0e00e88ff8d739346566f1a135a99abb2621602c160e5845df905f53d50a4a8","sha256:7aba9e200044388d3a7141558f4ce12b78f49b1d8e6f5114191d4bab86454441"],"state_sha256":"e66342cf49d4be85ac99a3625db4558bacc79e502f81ca3ddd69c07f58702940"}