{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4MM4FMINRXOE6E2TZHJACKXV33","short_pith_number":"pith:4MM4FMIN","canonical_record":{"source":{"id":"1503.05310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-18T09:00:08Z","cross_cats_sorted":[],"title_canon_sha256":"7773c6fb5257b353ecca8fe15874edca2e422cd11557620d43446476d36c2b40","abstract_canon_sha256":"c2ecfe30a1ead79ffffb0598058c7fbaebfb7965955761dc03300e907717b329"},"schema_version":"1.0"},"canonical_sha256":"e319c2b10d8ddc4f1353c9d2012af5deda755f0fc3a0e99c9ef4e072bdf9bd2c","source":{"kind":"arxiv","id":"1503.05310","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05310","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05310v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05310","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"4MM4FMINRXOE","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MM4FMINRXOE6E2T","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MM4FMIN","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4MM4FMINRXOE6E2TZHJACKXV33","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-18T09:00:08Z","cross_cats_sorted":[],"title_canon_sha256":"7773c6fb5257b353ecca8fe15874edca2e422cd11557620d43446476d36c2b40","abstract_canon_sha256":"c2ecfe30a1ead79ffffb0598058c7fbaebfb7965955761dc03300e907717b329"},"schema_version":"1.0"},"canonical_sha256":"e319c2b10d8ddc4f1353c9d2012af5deda755f0fc3a0e99c9ef4e072bdf9bd2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:50.793783Z","signature_b64":"NFlY7KaAiW74pWO2ei3K64FHtz5PdZh4906v/Z1CAOGz6yu5EAXPf9QZDRxfc3hDIk6igbMZA1jN7OFUeBAZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e319c2b10d8ddc4f1353c9d2012af5deda755f0fc3a0e99c9ef4e072bdf9bd2c","last_reissued_at":"2026-05-18T02:21:50.792979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:50.792979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05310","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":"2026-05-18T02:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qbp7u7jk+QYaFmgPnsSnT8f9A8Jz+nU7QSesv4QPWmTqzT7IRYTE9b6yQLhj4QUAYvFO+JgqwsAQ4DK7IN9PDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:42:01.440160Z"},"content_sha256":"26de366769a59bf4eeff7fd8f6a51b30fecba145e2cd4ac94e5116186d62b6e3","schema_version":"1.0","event_id":"sha256:26de366769a59bf4eeff7fd8f6a51b30fecba145e2cd4ac94e5116186d62b6e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4MM4FMINRXOE6E2TZHJACKXV33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Fabio Zanolin, Guglielmo Feltrin","submitted_at":"2015-03-18T09:00:08Z","abstract_excerpt":"We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation \\begin{equation*} u'' + c u' + \\lambda a(t) g(u) = 0, \\end{equation*} where $g \\colon \\mathopen{[}0,+\\infty\\mathclose{[}\\to \\mathopen{[}0,+\\infty\\mathclose{[}$ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when $\\int_{0}^{T} a(t) \\!dt < 0$ and $\\lambda > 0$ is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05310","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":"2026-05-18T02:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/p9b49C5YPVWolTFic6D4JVKDHkDicokTwPnlRIFjr+gjReGezUqbBivNjb2VzW+broH0bJHfqfGgQUbioABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:42:01.440828Z"},"content_sha256":"978ce088697c22d909102565fab315345ba843fa61e5ec3d60fd3c1af6fb75e0","schema_version":"1.0","event_id":"sha256:978ce088697c22d909102565fab315345ba843fa61e5ec3d60fd3c1af6fb75e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MM4FMINRXOE6E2TZHJACKXV33/bundle.json","state_url":"https://pith.science/pith/4MM4FMINRXOE6E2TZHJACKXV33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MM4FMINRXOE6E2TZHJACKXV33/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":"2026-06-02T12:42:01Z","links":{"resolver":"https://pith.science/pith/4MM4FMINRXOE6E2TZHJACKXV33","bundle":"https://pith.science/pith/4MM4FMINRXOE6E2TZHJACKXV33/bundle.json","state":"https://pith.science/pith/4MM4FMINRXOE6E2TZHJACKXV33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MM4FMINRXOE6E2TZHJACKXV33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4MM4FMINRXOE6E2TZHJACKXV33","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":"c2ecfe30a1ead79ffffb0598058c7fbaebfb7965955761dc03300e907717b329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-18T09:00:08Z","title_canon_sha256":"7773c6fb5257b353ecca8fe15874edca2e422cd11557620d43446476d36c2b40"},"schema_version":"1.0","source":{"id":"1503.05310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05310","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05310v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05310","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"4MM4FMINRXOE","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MM4FMINRXOE6E2T","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MM4FMIN","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:978ce088697c22d909102565fab315345ba843fa61e5ec3d60fd3c1af6fb75e0","target":"graph","created_at":"2026-05-18T02:21:50Z","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 and the Neumann boundary value problems associated with the second order nonlinear differential equation \\begin{equation*} u'' + c u' + \\lambda a(t) g(u) = 0, \\end{equation*} where $g \\colon \\mathopen{[}0,+\\infty\\mathclose{[}\\to \\mathopen{[}0,+\\infty\\mathclose{[}$ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when $\\int_{0}^{T} a(t) \\!dt < 0$ and $\\lambda > 0$ is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.","authors_text":"Alberto Boscaggin, Fabio Zanolin, Guglielmo Feltrin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-18T09:00:08Z","title":"Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05310","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":"sha256:26de366769a59bf4eeff7fd8f6a51b30fecba145e2cd4ac94e5116186d62b6e3","target":"record","created_at":"2026-05-18T02:21:50Z","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":"c2ecfe30a1ead79ffffb0598058c7fbaebfb7965955761dc03300e907717b329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-18T09:00:08Z","title_canon_sha256":"7773c6fb5257b353ecca8fe15874edca2e422cd11557620d43446476d36c2b40"},"schema_version":"1.0","source":{"id":"1503.05310","kind":"arxiv","version":1}},"canonical_sha256":"e319c2b10d8ddc4f1353c9d2012af5deda755f0fc3a0e99c9ef4e072bdf9bd2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e319c2b10d8ddc4f1353c9d2012af5deda755f0fc3a0e99c9ef4e072bdf9bd2c","first_computed_at":"2026-05-18T02:21:50.792979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.792979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NFlY7KaAiW74pWO2ei3K64FHtz5PdZh4906v/Z1CAOGz6yu5EAXPf9QZDRxfc3hDIk6igbMZA1jN7OFUeBAZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.793783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26de366769a59bf4eeff7fd8f6a51b30fecba145e2cd4ac94e5116186d62b6e3","sha256:978ce088697c22d909102565fab315345ba843fa61e5ec3d60fd3c1af6fb75e0"],"state_sha256":"b32b7c818a0de38640cee921a7325abe4b7466091fcc8917e24ff4c9572614c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OwYKLAoralHWIw/WTGjtkUEqMpVgJdT9XRTmghwS6Jg20v83MIMMqSwDvwrCItiw/l88IcdYBvvvcfvnVLPfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:42:01.444170Z","bundle_sha256":"b34bbf22c8dcb37794d0e006af0b45169f87d577dd01a675625e1a6a6e107230"}}