{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:F3QURA2NKBCOTGAX3LP4N4KQQH","short_pith_number":"pith:F3QURA2N","schema_version":"1.0","canonical_sha256":"2ee148834d5044e99817dadfc6f15081d26cb38fbea9e90dfbcb86ebe41557a7","source":{"kind":"arxiv","id":"1201.5432","version":3},"attestation_state":"computed","paper":{"title":"Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John A. Pelesko, Nicholas D. Brubaker","submitted_at":"2012-01-26T02:34:02Z","abstract_excerpt":"In this paper we analyze the classical solution set ({\\lambda},u), for {\\lambda}>0, of a one-dimensional prescribed mean curvature equation on the interval [-L,L]. It is shown that the solution set depends on the two parameters, {\\lambda} and L, and undergoes two bifurcations. The first is a standard saddle node bifurcation, which happens for all L at {\\lambda} = {\\lambda}*(L). The second is a splitting bifurcation; specifically, there exists a value L* such that as L transitions from greater than or equal L* to less than L* the upper branch of the bifurcation diagram splits into two parts. In"},"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":"1201.5432","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-26T02:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"05feaecb30293f915186d196b64c9bd6b776d0df1c43b955ed45a8d3f512df16","abstract_canon_sha256":"96540bae19830abc387fe1b63eb0968614d9e129c5e709210bbab5a0ce9521d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:36.853125Z","signature_b64":"8JHgTTWbl2qf+Wx03dDDCcl4INLXWVCWfjWJH/qw+zwX5xtx5H8+dGSyQyFymUX+0n5k+dYRrbaTTcZOV0KzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ee148834d5044e99817dadfc6f15081d26cb38fbea9e90dfbcb86ebe41557a7","last_reissued_at":"2026-05-18T03:57:36.852602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:36.852602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"John A. Pelesko, Nicholas D. Brubaker","submitted_at":"2012-01-26T02:34:02Z","abstract_excerpt":"In this paper we analyze the classical solution set ({\\lambda},u), for {\\lambda}>0, of a one-dimensional prescribed mean curvature equation on the interval [-L,L]. It is shown that the solution set depends on the two parameters, {\\lambda} and L, and undergoes two bifurcations. The first is a standard saddle node bifurcation, which happens for all L at {\\lambda} = {\\lambda}*(L). The second is a splitting bifurcation; specifically, there exists a value L* such that as L transitions from greater than or equal L* to less than L* the upper branch of the bifurcation diagram splits into two parts. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5432","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":"1201.5432","created_at":"2026-05-18T03:57:36.852681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5432v3","created_at":"2026-05-18T03:57:36.852681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5432","created_at":"2026-05-18T03:57:36.852681+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3QURA2NKBCO","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3QURA2NKBCOTGAX","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3QURA2N","created_at":"2026-05-18T12:27:04.183437+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/F3QURA2NKBCOTGAX3LP4N4KQQH","json":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH.json","graph_json":"https://pith.science/api/pith-number/F3QURA2NKBCOTGAX3LP4N4KQQH/graph.json","events_json":"https://pith.science/api/pith-number/F3QURA2NKBCOTGAX3LP4N4KQQH/events.json","paper":"https://pith.science/paper/F3QURA2N"},"agent_actions":{"view_html":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH","download_json":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH.json","view_paper":"https://pith.science/paper/F3QURA2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5432&json=true","fetch_graph":"https://pith.science/api/pith-number/F3QURA2NKBCOTGAX3LP4N4KQQH/graph.json","fetch_events":"https://pith.science/api/pith-number/F3QURA2NKBCOTGAX3LP4N4KQQH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH/action/storage_attestation","attest_author":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH/action/author_attestation","sign_citation":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH/action/citation_signature","submit_replication":"https://pith.science/pith/F3QURA2NKBCOTGAX3LP4N4KQQH/action/replication_record"}},"created_at":"2026-05-18T03:57:36.852681+00:00","updated_at":"2026-05-18T03:57:36.852681+00:00"}