{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F3QURA2NKBCOTGAX3LP4N4KQQH","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":"96540bae19830abc387fe1b63eb0968614d9e129c5e709210bbab5a0ce9521d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-26T02:34:02Z","title_canon_sha256":"05feaecb30293f915186d196b64c9bd6b776d0df1c43b955ed45a8d3f512df16"},"schema_version":"1.0","source":{"id":"1201.5432","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5432","created_at":"2026-05-18T03:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5432v3","created_at":"2026-05-18T03:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5432","created_at":"2026-05-18T03:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"F3QURA2NKBCO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F3QURA2NKBCOTGAX","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F3QURA2N","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:a72e57fc882bf560c8653d946e2980ce2354a3a52729d9013e6a1a2ca6371695","target":"graph","created_at":"2026-05-18T03:57:36Z","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 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","authors_text":"John A. Pelesko, Nicholas D. Brubaker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-26T02:34:02Z","title":"Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5432","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":"sha256:8cdff3b8f62a28a12571a91635803897ebc08eab89229aa7d5da9927b935d4dd","target":"record","created_at":"2026-05-18T03:57:36Z","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":"96540bae19830abc387fe1b63eb0968614d9e129c5e709210bbab5a0ce9521d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-01-26T02:34:02Z","title_canon_sha256":"05feaecb30293f915186d196b64c9bd6b776d0df1c43b955ed45a8d3f512df16"},"schema_version":"1.0","source":{"id":"1201.5432","kind":"arxiv","version":3}},"canonical_sha256":"2ee148834d5044e99817dadfc6f15081d26cb38fbea9e90dfbcb86ebe41557a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ee148834d5044e99817dadfc6f15081d26cb38fbea9e90dfbcb86ebe41557a7","first_computed_at":"2026-05-18T03:57:36.852602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:36.852602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8JHgTTWbl2qf+Wx03dDDCcl4INLXWVCWfjWJH/qw+zwX5xtx5H8+dGSyQyFymUX+0n5k+dYRrbaTTcZOV0KzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:36.853125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5432","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cdff3b8f62a28a12571a91635803897ebc08eab89229aa7d5da9927b935d4dd","sha256:a72e57fc882bf560c8653d946e2980ce2354a3a52729d9013e6a1a2ca6371695"],"state_sha256":"8a2e61aa7a81210b63302a28225e9761f5318afac83866731145828e2a22f6f1"}