{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PSW6SXK5WGFRAO6AKE4TG6E3SZ","short_pith_number":"pith:PSW6SXK5","canonical_record":{"source":{"id":"1804.00439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-02T10:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"dd38f420a6ba32996024b9cedfdcf57a6873bb3e02a9cb504f19101315173f1a","abstract_canon_sha256":"a0ea56cb8e3865881b870b6b0226f00223c5a4aaf62305f41ab19871210a4dd5"},"schema_version":"1.0"},"canonical_sha256":"7cade95d5db18b103bc0513933789b964fa9a0f649fe6c8814558f2feb403c5b","source":{"kind":"arxiv","id":"1804.00439","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00439","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00439v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00439","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"PSW6SXK5WGFR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PSW6SXK5WGFRAO6A","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PSW6SXK5","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PSW6SXK5WGFRAO6AKE4TG6E3SZ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-02T10:00:02Z","cross_cats_sorted":[],"title_canon_sha256":"dd38f420a6ba32996024b9cedfdcf57a6873bb3e02a9cb504f19101315173f1a","abstract_canon_sha256":"a0ea56cb8e3865881b870b6b0226f00223c5a4aaf62305f41ab19871210a4dd5"},"schema_version":"1.0"},"canonical_sha256":"7cade95d5db18b103bc0513933789b964fa9a0f649fe6c8814558f2feb403c5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:17.821274Z","signature_b64":"sNStPMIu/nlDv7zrPmUJjIH8sQhMvtad5h4BAfELSPpqXUdDhsweiEIjUkqLVdzualuKQjSa0EjmJpGapLL0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cade95d5db18b103bc0513933789b964fa9a0f649fe6c8814558f2feb403c5b","last_reissued_at":"2026-05-18T00:07:17.820536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:17.820536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00439","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":"2026-05-18T00:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhZv79XucMffypHvv5O9U+yxidHbKb3bcfK8RgiiTi+CWQJXyMCMf8roNH77+gx+0c7GETBbtLtYF3140c3XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:08:08.852894Z"},"content_sha256":"8e99ee39b142813dbbc82a160f96f4d99ff3c8a8c3dd285a0a6f6cec1f566134","schema_version":"1.0","event_id":"sha256:8e99ee39b142813dbbc82a160f96f4d99ff3c8a8c3dd285a0a6f6cec1f566134"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PSW6SXK5WGFRAO6AKE4TG6E3SZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic solutions to parameter-dependent equations with a $\\phi$-Laplacian type operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elisa Sovrano, Fabio Zanolin, Guglielmo Feltrin","submitted_at":"2018-04-02T10:00:02Z","abstract_excerpt":"We study the periodic boundary value problem associated with the $\\phi$-Laplacian equation of the form $(\\phi(u'))'+f(u)u'+g(t,u)=s$, where $s$ is a real parameter, $f$ and $g$ are continuous functions, and $g$ is $T$-periodic in the variable $t$. The interest is in Ambrosetti-Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter $s$. We investigate this problem for a broad family of nonlinearities, under non-uniform type conditions on $g(t,u)$ as $u\\to \\pm\\infty$. We generalize, in a unified framework, various classical and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00439","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":"2026-05-18T00:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aa1lRu7pteff9RtPXsr2y/10yAd32aewhKCGLoEFkXYQ0KYp3SjpTzah1pLhYqh4prbBhCBPxlpcyysg6dUvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:08:08.853239Z"},"content_sha256":"1db30b492720a7523c522997e87d0fdfabdbc7ad29c4bdc5927bd765fd7328bf","schema_version":"1.0","event_id":"sha256:1db30b492720a7523c522997e87d0fdfabdbc7ad29c4bdc5927bd765fd7328bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/bundle.json","state_url":"https://pith.science/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/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":"2026-06-02T21:08:08Z","links":{"resolver":"https://pith.science/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ","bundle":"https://pith.science/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/bundle.json","state":"https://pith.science/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSW6SXK5WGFRAO6AKE4TG6E3SZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PSW6SXK5WGFRAO6AKE4TG6E3SZ","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":"a0ea56cb8e3865881b870b6b0226f00223c5a4aaf62305f41ab19871210a4dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-02T10:00:02Z","title_canon_sha256":"dd38f420a6ba32996024b9cedfdcf57a6873bb3e02a9cb504f19101315173f1a"},"schema_version":"1.0","source":{"id":"1804.00439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00439","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00439v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00439","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"PSW6SXK5WGFR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PSW6SXK5WGFRAO6A","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PSW6SXK5","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:1db30b492720a7523c522997e87d0fdfabdbc7ad29c4bdc5927bd765fd7328bf","target":"graph","created_at":"2026-05-18T00:07:17Z","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 study the periodic boundary value problem associated with the $\\phi$-Laplacian equation of the form $(\\phi(u'))'+f(u)u'+g(t,u)=s$, where $s$ is a real parameter, $f$ and $g$ are continuous functions, and $g$ is $T$-periodic in the variable $t$. The interest is in Ambrosetti-Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter $s$. We investigate this problem for a broad family of nonlinearities, under non-uniform type conditions on $g(t,u)$ as $u\\to \\pm\\infty$. We generalize, in a unified framework, various classical and ","authors_text":"Elisa Sovrano, Fabio Zanolin, Guglielmo Feltrin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-02T10:00:02Z","title":"Periodic solutions to parameter-dependent equations with a $\\phi$-Laplacian type operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00439","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":"sha256:8e99ee39b142813dbbc82a160f96f4d99ff3c8a8c3dd285a0a6f6cec1f566134","target":"record","created_at":"2026-05-18T00:07:17Z","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":"a0ea56cb8e3865881b870b6b0226f00223c5a4aaf62305f41ab19871210a4dd5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-02T10:00:02Z","title_canon_sha256":"dd38f420a6ba32996024b9cedfdcf57a6873bb3e02a9cb504f19101315173f1a"},"schema_version":"1.0","source":{"id":"1804.00439","kind":"arxiv","version":2}},"canonical_sha256":"7cade95d5db18b103bc0513933789b964fa9a0f649fe6c8814558f2feb403c5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cade95d5db18b103bc0513933789b964fa9a0f649fe6c8814558f2feb403c5b","first_computed_at":"2026-05-18T00:07:17.820536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.820536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sNStPMIu/nlDv7zrPmUJjIH8sQhMvtad5h4BAfELSPpqXUdDhsweiEIjUkqLVdzualuKQjSa0EjmJpGapLL0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.821274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e99ee39b142813dbbc82a160f96f4d99ff3c8a8c3dd285a0a6f6cec1f566134","sha256:1db30b492720a7523c522997e87d0fdfabdbc7ad29c4bdc5927bd765fd7328bf"],"state_sha256":"0271eb6e25b0bd3c0d2ee19897c15eb73b1c063a0cf82ce65ccd7aa0f2351adf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qU591H1dYDUixtv8U1c2xO0qn9+CB4s+ntlFypwskrUCMxLbVK8pD0QyOzAEfrYxo3I2ODp/yNAssIi+vklcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:08:08.855292Z","bundle_sha256":"ce7e280af944deb2b2dd19983901cf330b11d3a49e09e3d288c0fb4040d79984"}}