{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NGB7KQQQARPZ6ATIJKDEIIPDN7","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":"9321d904c7e260e9dec5a4c6a97801e24f2a1391efacc12fccb05a07e101e6e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-13T14:27:30Z","title_canon_sha256":"9082d4b182b62210a08621efc91ef1ef4d47c7f7d73b294a6e4f1c46b2ed5600"},"schema_version":"1.0","source":{"id":"1803.04830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04830","created_at":"2026-05-18T00:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04830v1","created_at":"2026-05-18T00:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04830","created_at":"2026-05-18T00:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"NGB7KQQQARPZ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NGB7KQQQARPZ6ATI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NGB7KQQQ","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:ab159b4f35939e6387d7c713ab8b53fee59f572c80de875d2b66c9e2581d3c29","target":"graph","created_at":"2026-05-18T00:21:17Z","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 short note, we prove that on the three-sphere with any bumpy metric there exist at least four solutions of the Allen-Cahn equation with spherical interface and index at most two. The proof combines several recent results from the literature.","authors_text":"Mohammad N. Ivaki, Robert Haslhofer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-13T14:27:30Z","title":"Low complexity solutions of the Allen-Cahn equation on three-spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04830","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":"sha256:68c180426351298747b9278ab73ee9e0e7f403de9534f119fcdbf0353ae89642","target":"record","created_at":"2026-05-18T00:21:17Z","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":"9321d904c7e260e9dec5a4c6a97801e24f2a1391efacc12fccb05a07e101e6e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-13T14:27:30Z","title_canon_sha256":"9082d4b182b62210a08621efc91ef1ef4d47c7f7d73b294a6e4f1c46b2ed5600"},"schema_version":"1.0","source":{"id":"1803.04830","kind":"arxiv","version":1}},"canonical_sha256":"6983f54210045f9f02684a864421e36ff48e2b036f5ddda665ef5393e16b7259","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6983f54210045f9f02684a864421e36ff48e2b036f5ddda665ef5393e16b7259","first_computed_at":"2026-05-18T00:21:17.646683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:17.646683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVufaYJaIUNUH0nhv8exNQhg+GtNGS4iESveQmzKjViRk/tXTwffrFIk23Yvg8shoPTpL6oAwlmSwY4/YQRvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:17.648873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68c180426351298747b9278ab73ee9e0e7f403de9534f119fcdbf0353ae89642","sha256:ab159b4f35939e6387d7c713ab8b53fee59f572c80de875d2b66c9e2581d3c29"],"state_sha256":"fd2cc7fc8e8d6028f2be5e57b9856d6b5d74faf734ae5e0c26cc5c2ec218704b"}