{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OYKWT6PQSJALWAIXNIKZH2ANEC","short_pith_number":"pith:OYKWT6PQ","canonical_record":{"source":{"id":"1407.1334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-04T21:56:54Z","cross_cats_sorted":[],"title_canon_sha256":"90532f0dc2c88763979b9970e67acb89d0a102db017e03782bc997b33960483e","abstract_canon_sha256":"edcc014eb5cda74d9c15d0968b2e23f05030f92a8403e0dc61c02a7e94021091"},"schema_version":"1.0"},"canonical_sha256":"761569f9f09240bb01176a1593e80d20bb09e5f5ea5ca755783978fadafb67cf","source":{"kind":"arxiv","id":"1407.1334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1334","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1334v1","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1334","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"pith_short_12","alias_value":"OYKWT6PQSJAL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYKWT6PQSJALWAIX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYKWT6PQ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OYKWT6PQSJALWAIXNIKZH2ANEC","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-04T21:56:54Z","cross_cats_sorted":[],"title_canon_sha256":"90532f0dc2c88763979b9970e67acb89d0a102db017e03782bc997b33960483e","abstract_canon_sha256":"edcc014eb5cda74d9c15d0968b2e23f05030f92a8403e0dc61c02a7e94021091"},"schema_version":"1.0"},"canonical_sha256":"761569f9f09240bb01176a1593e80d20bb09e5f5ea5ca755783978fadafb67cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:16.798350Z","signature_b64":"iuI7lrgRgE6O36vRIlt79rTpFjM1+qlOiNwhtIownt3Kj9czQqLm5Zk0ApB6rh5bG52RvRdnHMqHjR3vbIj7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"761569f9f09240bb01176a1593e80d20bb09e5f5ea5ca755783978fadafb67cf","last_reissued_at":"2026-05-18T02:48:16.797814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:16.797814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1334","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":"2026-05-18T02:48:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brf1EPKYMuvQG+4hks4kPZ15sTyD8p0MVwYHq6RbEyTat2EH3fjajbEwemTRDhsOCD2SYCzk3RW6cqAWUp5RBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:50:05.996716Z"},"content_sha256":"c6316042e69aa64f7c5f0b22b71bd3f48106f4b4b9735d7b0f57288f8db0e6d3","schema_version":"1.0","event_id":"sha256:c6316042e69aa64f7c5f0b22b71bd3f48106f4b4b9735d7b0f57288f8db0e6d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OYKWT6PQSJALWAIXNIKZH2ANEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive solutions with a complex behavior for superlinear indefinite ODEs on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Gianmaria Verzini, Vivina Barutello","submitted_at":"2014-07-04T21:56:54Z","abstract_excerpt":"We show the existence of infinitely many positive solutions, defined on the real line, for the nonlinear scalar ODE \\[ \\ddot u + (a^+(t) - \\mu a^-(t)) u^3 = 0, \\] where $a$ is a periodic, sign-changing function, and the parameter $\\mu>0$ is large. Such solutions are characterized by the fact of being either small or large in each interval of positivity of $a$. In this way, we find periodic solutions, having minimal period arbitrarily large, and bounded non-periodic solutions, exhibiting a complex behavior. The proof is variational, exploiting suitable natural constraints of Nehari type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1334","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":"2026-05-18T02:48:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSlaMUSeZhXQyfdqMqXyCn92CAO6RRAlBNwdH8PdMqnAD5M3gOCiBiLh0wnR+iSGh7NOKvWyXU03jn+o1fWtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:50:05.997070Z"},"content_sha256":"79a7b453d66fbe99250d4ce5c268f6b2740acbbba1357a9e41b01f2eeacf28a4","schema_version":"1.0","event_id":"sha256:79a7b453d66fbe99250d4ce5c268f6b2740acbbba1357a9e41b01f2eeacf28a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/bundle.json","state_url":"https://pith.science/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/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":"2026-06-02T07:50:05Z","links":{"resolver":"https://pith.science/pith/OYKWT6PQSJALWAIXNIKZH2ANEC","bundle":"https://pith.science/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/bundle.json","state":"https://pith.science/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYKWT6PQSJALWAIXNIKZH2ANEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OYKWT6PQSJALWAIXNIKZH2ANEC","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":"edcc014eb5cda74d9c15d0968b2e23f05030f92a8403e0dc61c02a7e94021091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-04T21:56:54Z","title_canon_sha256":"90532f0dc2c88763979b9970e67acb89d0a102db017e03782bc997b33960483e"},"schema_version":"1.0","source":{"id":"1407.1334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1334","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1334v1","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1334","created_at":"2026-05-18T02:48:16Z"},{"alias_kind":"pith_short_12","alias_value":"OYKWT6PQSJAL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYKWT6PQSJALWAIX","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYKWT6PQ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:79a7b453d66fbe99250d4ce5c268f6b2740acbbba1357a9e41b01f2eeacf28a4","target":"graph","created_at":"2026-05-18T02:48:16Z","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":"We show the existence of infinitely many positive solutions, defined on the real line, for the nonlinear scalar ODE \\[ \\ddot u + (a^+(t) - \\mu a^-(t)) u^3 = 0, \\] where $a$ is a periodic, sign-changing function, and the parameter $\\mu>0$ is large. Such solutions are characterized by the fact of being either small or large in each interval of positivity of $a$. In this way, we find periodic solutions, having minimal period arbitrarily large, and bounded non-periodic solutions, exhibiting a complex behavior. The proof is variational, exploiting suitable natural constraints of Nehari type.","authors_text":"Alberto Boscaggin, Gianmaria Verzini, Vivina Barutello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-04T21:56:54Z","title":"Positive solutions with a complex behavior for superlinear indefinite ODEs on the real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1334","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:c6316042e69aa64f7c5f0b22b71bd3f48106f4b4b9735d7b0f57288f8db0e6d3","target":"record","created_at":"2026-05-18T02:48:16Z","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":"edcc014eb5cda74d9c15d0968b2e23f05030f92a8403e0dc61c02a7e94021091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-04T21:56:54Z","title_canon_sha256":"90532f0dc2c88763979b9970e67acb89d0a102db017e03782bc997b33960483e"},"schema_version":"1.0","source":{"id":"1407.1334","kind":"arxiv","version":1}},"canonical_sha256":"761569f9f09240bb01176a1593e80d20bb09e5f5ea5ca755783978fadafb67cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"761569f9f09240bb01176a1593e80d20bb09e5f5ea5ca755783978fadafb67cf","first_computed_at":"2026-05-18T02:48:16.797814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:16.797814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iuI7lrgRgE6O36vRIlt79rTpFjM1+qlOiNwhtIownt3Kj9czQqLm5Zk0ApB6rh5bG52RvRdnHMqHjR3vbIj7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:16.798350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6316042e69aa64f7c5f0b22b71bd3f48106f4b4b9735d7b0f57288f8db0e6d3","sha256:79a7b453d66fbe99250d4ce5c268f6b2740acbbba1357a9e41b01f2eeacf28a4"],"state_sha256":"56187d30a86bbfde89c07319e53b7360f705a406e8a823e289452b7c93821ae4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TtDGFKKRq8h5xrkPDOZqvO/jSHBvdJ+4KDGJUv/cfNkloVgkU/Cbdtd1K0htpzzWb5UMgr3OrcEa5IkhIscaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:50:05.999019Z","bundle_sha256":"b9c8e150f2d7d97394072852196777b9b4200a9a0f55b230427ef0065bc4e8f1"}}