{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IFXZMWC3HLY5RZ6XJ2RCBDGDIS","short_pith_number":"pith:IFXZMWC3","schema_version":"1.0","canonical_sha256":"416f96585b3af1d8e7d74ea2208cc3448de2129397a279f8d4d063ae689c5352","source":{"kind":"arxiv","id":"1311.0923","version":1},"attestation_state":"computed","paper":{"title":"Fine properties of branch point singularities: Two-valued harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Brian Krummel, Neshan Wickramasekera","submitted_at":"2013-11-04T23:17:06Z","abstract_excerpt":"In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on $n$ dimensional domains and used it, in an essential way, to bound the Hausdorff dimension of the singular sets of area minimizing rectifiable currents of dimension $n$ and codimension $\\geq 2$. Recent work of the second author shows that two-valued $C^{1, \\mu}$ harmonic functions on $n$ dimensional domains, which are typically-non-minimizing stationary points of Dirichlet energy, play an essential role in the study of multiplicity 2 branch points of stable codimension 1 rectifiable currents of d"},"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":"1311.0923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T23:17:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9f78dc8e27c2e5d698335c935bab36614b10e0ed8b16380be537199d45e2dd3a","abstract_canon_sha256":"827fdcac597e1a9d5ebe9459328bc3cd1f6a756b420722efe9905f3b0a6804f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:56.066082Z","signature_b64":"KHU7MEQ8XC1JKkkHtmcxm1BcJB43nAPsz9T07cqT0ZmIfaHZYjfysQiDNSeyHwU7VVrOOT4QU0HusLilBz1eCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"416f96585b3af1d8e7d74ea2208cc3448de2129397a279f8d4d063ae689c5352","last_reissued_at":"2026-05-18T03:07:56.065311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:56.065311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fine properties of branch point singularities: Two-valued harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Brian Krummel, Neshan Wickramasekera","submitted_at":"2013-11-04T23:17:06Z","abstract_excerpt":"In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on $n$ dimensional domains and used it, in an essential way, to bound the Hausdorff dimension of the singular sets of area minimizing rectifiable currents of dimension $n$ and codimension $\\geq 2$. Recent work of the second author shows that two-valued $C^{1, \\mu}$ harmonic functions on $n$ dimensional domains, which are typically-non-minimizing stationary points of Dirichlet energy, play an essential role in the study of multiplicity 2 branch points of stable codimension 1 rectifiable currents of d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0923","kind":"arxiv","version":1},"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":"1311.0923","created_at":"2026-05-18T03:07:56.065451+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0923v1","created_at":"2026-05-18T03:07:56.065451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0923","created_at":"2026-05-18T03:07:56.065451+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFXZMWC3HLY5","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFXZMWC3HLY5RZ6X","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFXZMWC3","created_at":"2026-05-18T12:27:46.883200+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/IFXZMWC3HLY5RZ6XJ2RCBDGDIS","json":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS.json","graph_json":"https://pith.science/api/pith-number/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/graph.json","events_json":"https://pith.science/api/pith-number/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/events.json","paper":"https://pith.science/paper/IFXZMWC3"},"agent_actions":{"view_html":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS","download_json":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS.json","view_paper":"https://pith.science/paper/IFXZMWC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0923&json=true","fetch_graph":"https://pith.science/api/pith-number/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/graph.json","fetch_events":"https://pith.science/api/pith-number/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/action/storage_attestation","attest_author":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/action/author_attestation","sign_citation":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/action/citation_signature","submit_replication":"https://pith.science/pith/IFXZMWC3HLY5RZ6XJ2RCBDGDIS/action/replication_record"}},"created_at":"2026-05-18T03:07:56.065451+00:00","updated_at":"2026-05-18T03:07:56.065451+00:00"}