{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RH6LKEVYN6SMFXDYLU5JNAKZ7G","short_pith_number":"pith:RH6LKEVY","schema_version":"1.0","canonical_sha256":"89fcb512b86fa4c2dc785d3a968159f9af505ad5090e28a6343de8fd44c1fa37","source":{"kind":"arxiv","id":"1509.02665","version":3},"attestation_state":"computed","paper":{"title":"Applications of the duality between the Complex Monge-Amp\\`ere Equation and the Hele-Shaw flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"David Witt Nystrom, Julius Ross","submitted_at":"2015-09-09T07:55:58Z","abstract_excerpt":"We give two applications of the the duality between the complex Homogeneous Monge-Amp\\`ere Equation (HMAE) and the Hele-Shaw flow. First, we prove existence of smooth boundary data for which the weak solution to the Dirichlet problem for the HMAE over $\\mathbb P^1\\times \\overline{\\mathbb D}$ is not twice differentiable at a given collection of points, and also examples that are not twice differentiable along a set of codimension one in $\\mathbb{P}^1\\times \\partial \\mathbb{D}$. Second, we produce explicit families of smooth geodesic rays in the space of K\\\"ahler metrics on $\\mathbb P^1$ and on "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.02665","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-09T07:55:58Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"a57e75e82a46a436a5dbc0163f7ca5acf892660b9965ce1fd753dbb9d07ebb99","abstract_canon_sha256":"6e6f57875f2ece6d09cd9ba45ff6114bc743e86de1d9760f49243b953aaf907f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:32.683737Z","signature_b64":"vb6htx+mOMH/gGxMq2bZ4krN6BI8cyuwptlgLuZUzi700S1VjpM7lZ2NYYE5WR9yfm24UUjqbv32FV2zdgCeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89fcb512b86fa4c2dc785d3a968159f9af505ad5090e28a6343de8fd44c1fa37","last_reissued_at":"2026-05-18T00:28:32.683021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:32.683021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Applications of the duality between the Complex Monge-Amp\\`ere Equation and the Hele-Shaw flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"David Witt Nystrom, Julius Ross","submitted_at":"2015-09-09T07:55:58Z","abstract_excerpt":"We give two applications of the the duality between the complex Homogeneous Monge-Amp\\`ere Equation (HMAE) and the Hele-Shaw flow. First, we prove existence of smooth boundary data for which the weak solution to the Dirichlet problem for the HMAE over $\\mathbb P^1\\times \\overline{\\mathbb D}$ is not twice differentiable at a given collection of points, and also examples that are not twice differentiable along a set of codimension one in $\\mathbb{P}^1\\times \\partial \\mathbb{D}$. Second, we produce explicit families of smooth geodesic rays in the space of K\\\"ahler metrics on $\\mathbb P^1$ and on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02665","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.02665","created_at":"2026-05-18T00:28:32.683125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02665v3","created_at":"2026-05-18T00:28:32.683125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02665","created_at":"2026-05-18T00:28:32.683125+00:00"},{"alias_kind":"pith_short_12","alias_value":"RH6LKEVYN6SM","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RH6LKEVYN6SMFXDY","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RH6LKEVY","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G","json":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G.json","graph_json":"https://pith.science/api/pith-number/RH6LKEVYN6SMFXDYLU5JNAKZ7G/graph.json","events_json":"https://pith.science/api/pith-number/RH6LKEVYN6SMFXDYLU5JNAKZ7G/events.json","paper":"https://pith.science/paper/RH6LKEVY"},"agent_actions":{"view_html":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G","download_json":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G.json","view_paper":"https://pith.science/paper/RH6LKEVY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02665&json=true","fetch_graph":"https://pith.science/api/pith-number/RH6LKEVYN6SMFXDYLU5JNAKZ7G/graph.json","fetch_events":"https://pith.science/api/pith-number/RH6LKEVYN6SMFXDYLU5JNAKZ7G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G/action/storage_attestation","attest_author":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G/action/author_attestation","sign_citation":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G/action/citation_signature","submit_replication":"https://pith.science/pith/RH6LKEVYN6SMFXDYLU5JNAKZ7G/action/replication_record"}},"created_at":"2026-05-18T00:28:32.683125+00:00","updated_at":"2026-05-18T00:28:32.683125+00:00"}