{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q5A4ZG57TJRWSRN7XC4R4DDN6Z","short_pith_number":"pith:Q5A4ZG57","canonical_record":{"source":{"id":"1210.4229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-16T01:48:30Z","cross_cats_sorted":[],"title_canon_sha256":"4ac336bf5b0670aeed56d46e881b869e4c616c9338c94d3e7b4869a46c04a7e6","abstract_canon_sha256":"3315f4ca4a6f940711540b17a6f2fab0aa3a93715d299e059ab1e71c55ef9ec8"},"schema_version":"1.0"},"canonical_sha256":"8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2","source":{"kind":"arxiv","id":"1210.4229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4229","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4229v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4229","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q5A4ZG57TJRW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q5A4ZG57TJRWSRN7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q5A4ZG57","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q5A4ZG57TJRWSRN7XC4R4DDN6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1210.4229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-16T01:48:30Z","cross_cats_sorted":[],"title_canon_sha256":"4ac336bf5b0670aeed56d46e881b869e4c616c9338c94d3e7b4869a46c04a7e6","abstract_canon_sha256":"3315f4ca4a6f940711540b17a6f2fab0aa3a93715d299e059ab1e71c55ef9ec8"},"schema_version":"1.0"},"canonical_sha256":"8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:06.599286Z","signature_b64":"tB5si9S/1aSnDZzS1E7A4eF1D6NIp/mMMEnpF1whkSIbKAvuMuRYVD35XSAspDWV6LPIvo3xyn8nmtlc7tarCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2","last_reissued_at":"2026-05-18T03:43:06.598606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:06.598606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.4229","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzUtlI3EAM/SbFSqwniSz8PvZsp/oMCGB8YoJ92qRkgYKvIPy9hdxiLaVBiMyHq+JxRvYB7U79TfGilEowE+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:35:38.202899Z"},"content_sha256":"33b66b2c2d6b55968dd86d152015a4d49f6ac1ea95ca74584e2a791ad5d9ce6d","schema_version":"1.0","event_id":"sha256:33b66b2c2d6b55968dd86d152015a4d49f6ac1ea95ca74584e2a791ad5d9ce6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q5A4ZG57TJRWSRN7XC4R4DDN6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alternating sign multibump solutions of nonlinear elliptic equations in expanding tubular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Monica Clapp, Nils Ackermann","submitted_at":"2012-10-16T01:48:30Z","abstract_excerpt":"Let $\\Gamma$ denote a smooth simple curve in $\\mathbb{R}^{N}$, $N\\geq2$, possibly with boundary. Let $\\Omega_{R}$ be the open normal tubular neighborhood of radius 1 of the expanded curve $R\\Gamma:=\\{Rx\\mid x\\in \\Gamma\\smallsetminus\\partial\\Gamma\\}$. Consider the superlinear problem $-\\Delta u+\\lambda u=f(u)$ on the domains $\\Omega_{R}$, as $R\\rightarrow \\infty$, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along $R\\Gamma$ with alternating signs. The function $f$ is superlinear at 0 and at $\\infty$, but it is not assumed to be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4229","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3j5ty7dkmE9i3DPfUzeOaIogdyt4FlZxAa1uPrkLrv8k9JN92D1nWdYEgt/BFVjWf2DSNwk7p8sdsowNsS2LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:35:38.203245Z"},"content_sha256":"89125a2733b36a8ffc440bf4a39c19895a97f27edadebf1087cf716f1d4614fd","schema_version":"1.0","event_id":"sha256:89125a2733b36a8ffc440bf4a39c19895a97f27edadebf1087cf716f1d4614fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/bundle.json","state_url":"https://pith.science/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/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":"2026-06-02T08:35:38Z","links":{"resolver":"https://pith.science/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z","bundle":"https://pith.science/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/bundle.json","state":"https://pith.science/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5A4ZG57TJRWSRN7XC4R4DDN6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q5A4ZG57TJRWSRN7XC4R4DDN6Z","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":"3315f4ca4a6f940711540b17a6f2fab0aa3a93715d299e059ab1e71c55ef9ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-16T01:48:30Z","title_canon_sha256":"4ac336bf5b0670aeed56d46e881b869e4c616c9338c94d3e7b4869a46c04a7e6"},"schema_version":"1.0","source":{"id":"1210.4229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4229","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4229v1","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4229","created_at":"2026-05-18T03:43:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q5A4ZG57TJRW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q5A4ZG57TJRWSRN7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q5A4ZG57","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:89125a2733b36a8ffc440bf4a39c19895a97f27edadebf1087cf716f1d4614fd","target":"graph","created_at":"2026-05-18T03:43:06Z","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":"Let $\\Gamma$ denote a smooth simple curve in $\\mathbb{R}^{N}$, $N\\geq2$, possibly with boundary. Let $\\Omega_{R}$ be the open normal tubular neighborhood of radius 1 of the expanded curve $R\\Gamma:=\\{Rx\\mid x\\in \\Gamma\\smallsetminus\\partial\\Gamma\\}$. Consider the superlinear problem $-\\Delta u+\\lambda u=f(u)$ on the domains $\\Omega_{R}$, as $R\\rightarrow \\infty$, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along $R\\Gamma$ with alternating signs. The function $f$ is superlinear at 0 and at $\\infty$, but it is not assumed to be","authors_text":"Filomena Pacella, Monica Clapp, Nils Ackermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-16T01:48:30Z","title":"Alternating sign multibump solutions of nonlinear elliptic equations in expanding tubular domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4229","kind":"arxiv","version":1},"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":"sha256:33b66b2c2d6b55968dd86d152015a4d49f6ac1ea95ca74584e2a791ad5d9ce6d","target":"record","created_at":"2026-05-18T03:43:06Z","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":"3315f4ca4a6f940711540b17a6f2fab0aa3a93715d299e059ab1e71c55ef9ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-16T01:48:30Z","title_canon_sha256":"4ac336bf5b0670aeed56d46e881b869e4c616c9338c94d3e7b4869a46c04a7e6"},"schema_version":"1.0","source":{"id":"1210.4229","kind":"arxiv","version":1}},"canonical_sha256":"8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8741cc9bbf9a636945bfb8b91e0c6df64c80751f5881649b727dc8d10f898db2","first_computed_at":"2026-05-18T03:43:06.598606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:06.598606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tB5si9S/1aSnDZzS1E7A4eF1D6NIp/mMMEnpF1whkSIbKAvuMuRYVD35XSAspDWV6LPIvo3xyn8nmtlc7tarCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:06.599286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33b66b2c2d6b55968dd86d152015a4d49f6ac1ea95ca74584e2a791ad5d9ce6d","sha256:89125a2733b36a8ffc440bf4a39c19895a97f27edadebf1087cf716f1d4614fd"],"state_sha256":"e76f4c04fd3f4a6098d648b7c779d7442d6e6e0f03cda5812fec6a204d69aba9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxJ+98pt/N7pfnTogir8u+722MEHAlA3KUSLbGFpoFHRzNpRRt3EAdK82ayAVIHEB6At27Dsp+XOwbuU/19lBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:35:38.205686Z","bundle_sha256":"916ab613b5447dbfe146b31d734a2dff465982569079d36fa0eb5f75ea02a4a1"}}