{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4RXXNJGQE4QRAALNBNBHSRGKZU","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":"df031de4079b51a38abb5edd646eb11222441d00e2d51020b5b6a249a0a3a896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:33:19Z","title_canon_sha256":"101776a1d44923ba1f45a8dfc863faeb66ded876073abc5c0aa307b08d096bbe"},"schema_version":"1.0","source":{"id":"1509.05178","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05178","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05178v3","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05178","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"4RXXNJGQE4QR","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4RXXNJGQE4QRAALN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4RXXNJGQ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:9e4f834176d244f424ee341fa8a11b28667b89fbf1957bfc7a6b85cb54c6f24c","target":"graph","created_at":"2026-05-18T00:14:57Z","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":"We analyze controllability properties for the one-dimensional heat equation with singular inverse-square potential $$ u_t-u_{xx}-\\frac{\\mu}{x^2}u=0,\\;\\;\\; (x,t)\\in(0,1)\\times(0,T).$$ For any $\\mu<1/4$, we prove that the equation is null controllable through a boundary control $f\\in H^1(0,T)$ acting at the singularity point $x=0$. This result is obtained employing the moment method by Fattorini and Russell.","authors_text":"Umberto Biccari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:33:19Z","title":"Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05178","kind":"arxiv","version":3},"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":"sha256:9f6f89d4fce7400664de4f7709f5450d8ae261712e7f65be7e0576dbc0b2c0c2","target":"record","created_at":"2026-05-18T00:14:57Z","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":"df031de4079b51a38abb5edd646eb11222441d00e2d51020b5b6a249a0a3a896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T09:33:19Z","title_canon_sha256":"101776a1d44923ba1f45a8dfc863faeb66ded876073abc5c0aa307b08d096bbe"},"schema_version":"1.0","source":{"id":"1509.05178","kind":"arxiv","version":3}},"canonical_sha256":"e46f76a4d0272110016d0b427944cacd3f6ea382c60a481df1b5cf68aa23d25c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e46f76a4d0272110016d0b427944cacd3f6ea382c60a481df1b5cf68aa23d25c","first_computed_at":"2026-05-18T00:14:57.548429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:57.548429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMy/K4FJ+xsFcQUnizXzMKlipLYuP6r4J/vQNHw2/JoTIQNFwQS7JTJuA5MqJSzd2C9S2jNdbk+FujNB1RnSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:57.549175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05178","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f6f89d4fce7400664de4f7709f5450d8ae261712e7f65be7e0576dbc0b2c0c2","sha256:9e4f834176d244f424ee341fa8a11b28667b89fbf1957bfc7a6b85cb54c6f24c"],"state_sha256":"1563c7ecce4f1b4e47f29a9dfc5605f0b121abf55cd34644fb590d469c1b77fd"}