{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NPYN6K27KXZMJCPBKR5L4G7MIE","short_pith_number":"pith:NPYN6K27","canonical_record":{"source":{"id":"1001.0377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T14:58:46Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"be0b7234fa6abeecfd5b35377210adc25a139105c0cd844ac301a27dd0e0d824","abstract_canon_sha256":"caa6694dc2e60bbbc5f5d71b53e3ab3bca435b6bf069cb3e650decdd934468a6"},"schema_version":"1.0"},"canonical_sha256":"6bf0df2b5f55f2c489e1547abe1bec4134a8f64f57fb76212621b50f0eef4b39","source":{"kind":"arxiv","id":"1001.0377","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0377","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0377v2","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0377","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"NPYN6K27KXZM","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NPYN6K27KXZMJCPB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NPYN6K27","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NPYN6K27KXZMJCPBKR5L4G7MIE","target":"record","payload":{"canonical_record":{"source":{"id":"1001.0377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T14:58:46Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"be0b7234fa6abeecfd5b35377210adc25a139105c0cd844ac301a27dd0e0d824","abstract_canon_sha256":"caa6694dc2e60bbbc5f5d71b53e3ab3bca435b6bf069cb3e650decdd934468a6"},"schema_version":"1.0"},"canonical_sha256":"6bf0df2b5f55f2c489e1547abe1bec4134a8f64f57fb76212621b50f0eef4b39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.990054Z","signature_b64":"ko4jwbvL+Ko6XVN9miDS/p65NHfbh4jW4UcBfpxluT8iKqeztGBJV9W+NAXZOPDrlu7xuT/2KSGTC023TORRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf0df2b5f55f2c489e1547abe1bec4134a8f64f57fb76212621b50f0eef4b39","last_reissued_at":"2026-05-17T23:51:44.989465Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.989465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.0377","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbH0NLD/3OHRpno2fI49VdKL+DI/lmE7n3Kg/er2OuUdBJvji0zBPfh75Fz5xl57sXPtX+n3s22KXEMFOdLwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:29:05.038448Z"},"content_sha256":"495d05b5e8f58d33c45012de2a60dfb80fc85e3b0667cc220094a47891489619","schema_version":"1.0","event_id":"sha256:495d05b5e8f58d33c45012de2a60dfb80fc85e3b0667cc220094a47891489619"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NPYN6K27KXZMJCPBKR5L4G7MIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Shingo Takeuchi","submitted_at":"2010-01-03T14:58:46Z","abstract_excerpt":"The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description of the spectra and a closed form representation of the corresponding eigenfunctions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of another eigenvalue problem with $p/2$-Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0377","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAmz3SKojLgmbGJDo9jNfpkMPPIc9kX00K5/MlAcdRaFJ6O/Y+jxBgHML9gQQDt+XClMxvdJxbJg0FRlI6BIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:29:05.038993Z"},"content_sha256":"5884910a2b6955a6c57dd18491f8b22cc856b7132fd38a891ec29fd760d08e9d","schema_version":"1.0","event_id":"sha256:5884910a2b6955a6c57dd18491f8b22cc856b7132fd38a891ec29fd760d08e9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/bundle.json","state_url":"https://pith.science/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T01:29:05Z","links":{"resolver":"https://pith.science/pith/NPYN6K27KXZMJCPBKR5L4G7MIE","bundle":"https://pith.science/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/bundle.json","state":"https://pith.science/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPYN6K27KXZMJCPBKR5L4G7MIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NPYN6K27KXZMJCPBKR5L4G7MIE","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":"caa6694dc2e60bbbc5f5d71b53e3ab3bca435b6bf069cb3e650decdd934468a6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T14:58:46Z","title_canon_sha256":"be0b7234fa6abeecfd5b35377210adc25a139105c0cd844ac301a27dd0e0d824"},"schema_version":"1.0","source":{"id":"1001.0377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0377","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0377v2","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0377","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"NPYN6K27KXZM","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NPYN6K27KXZMJCPB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NPYN6K27","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5884910a2b6955a6c57dd18491f8b22cc856b7132fd38a891ec29fd760d08e9d","target":"graph","created_at":"2026-05-17T23:51:44Z","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":"The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description of the spectra and a closed form representation of the corresponding eigenfunctions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of another eigenvalue problem with $p/2$-Laplacian.","authors_text":"Shingo Takeuchi","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T14:58:46Z","title":"Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0377","kind":"arxiv","version":2},"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":"sha256:495d05b5e8f58d33c45012de2a60dfb80fc85e3b0667cc220094a47891489619","target":"record","created_at":"2026-05-17T23:51:44Z","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":"caa6694dc2e60bbbc5f5d71b53e3ab3bca435b6bf069cb3e650decdd934468a6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T14:58:46Z","title_canon_sha256":"be0b7234fa6abeecfd5b35377210adc25a139105c0cd844ac301a27dd0e0d824"},"schema_version":"1.0","source":{"id":"1001.0377","kind":"arxiv","version":2}},"canonical_sha256":"6bf0df2b5f55f2c489e1547abe1bec4134a8f64f57fb76212621b50f0eef4b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bf0df2b5f55f2c489e1547abe1bec4134a8f64f57fb76212621b50f0eef4b39","first_computed_at":"2026-05-17T23:51:44.989465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:44.989465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ko4jwbvL+Ko6XVN9miDS/p65NHfbh4jW4UcBfpxluT8iKqeztGBJV9W+NAXZOPDrlu7xuT/2KSGTC023TORRDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:44.990054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:495d05b5e8f58d33c45012de2a60dfb80fc85e3b0667cc220094a47891489619","sha256:5884910a2b6955a6c57dd18491f8b22cc856b7132fd38a891ec29fd760d08e9d"],"state_sha256":"fb272ab9c513fe888a11f0d4b5204d5ab5c949f8c399bf487c4a6e808879dadb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nxnMXyjGpjsBL9qc6SrJqCr5S7YlxsnzoA2oF/u3s/3nKwLCNQID38oU4bzloMStbQLP6LDpwF/+hO0YEYUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:29:05.042721Z","bundle_sha256":"e83399c40e1985a16e01a55ddf38021af91e1e58178f49dfb17dcd99193d1511"}}