{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2LJ4JS5UHH5EG7ENWF3IKIHXFS","short_pith_number":"pith:2LJ4JS5U","canonical_record":{"source":{"id":"1605.02500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"6688bf692602d2964c261982a005fc26b512c0a5ca27b1c9c45215f9f5c08994","abstract_canon_sha256":"d0ae3b3487985684232b0ee0350141d2c607564e6155c77bcef6d9670c1fce7d"},"schema_version":"1.0"},"canonical_sha256":"d2d3c4cbb439fa437c8db1768520f72ca843ed7e00d3eb1dd61200f520a9696f","source":{"kind":"arxiv","id":"1605.02500","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02500","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02500v1","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02500","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"pith_short_12","alias_value":"2LJ4JS5UHH5E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LJ4JS5UHH5EG7EN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LJ4JS5U","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2LJ4JS5UHH5EG7ENWF3IKIHXFS","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"6688bf692602d2964c261982a005fc26b512c0a5ca27b1c9c45215f9f5c08994","abstract_canon_sha256":"d0ae3b3487985684232b0ee0350141d2c607564e6155c77bcef6d9670c1fce7d"},"schema_version":"1.0"},"canonical_sha256":"d2d3c4cbb439fa437c8db1768520f72ca843ed7e00d3eb1dd61200f520a9696f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:16.372172Z","signature_b64":"CFejbvgx2si1SD8u3VU9xbgEnoPVpE1CQE1iQNtnLBTr2+FcvJBPZRwUjvjG0B917uAWrIlQ72AHacoX8iOfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2d3c4cbb439fa437c8db1768520f72ca843ed7e00d3eb1dd61200f520a9696f","last_reissued_at":"2026-05-18T01:15:16.371494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:16.371494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02500","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":"2026-05-18T01:15:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qy7qSBvRpdMgfMraKJ+Y4gsj9MNtvuFvvc5RnfxFUijJdPjkS0rH11nYpCmZMwwIlkgBeRDPRubEjQ5LjZE9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:48:12.113033Z"},"content_sha256":"765ff9e7339a67a2db48e3484dddef5cb2b34f341caa3262e1dd1a94b3b1e6a0","schema_version":"1.0","event_id":"sha256:765ff9e7339a67a2db48e3484dddef5cb2b34f341caa3262e1dd1a94b3b1e6a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2LJ4JS5UHH5EG7ENWF3IKIHXFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive subharmonic solutions to nonlinear ODEs with indefinite weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Guglielmo Feltrin","submitted_at":"2016-05-09T10:00:01Z","abstract_excerpt":"We prove that the superlinear indefinite equation \\begin{equation*} u\" + a(t)u^{p} = 0, \\end{equation*} where $p > 1$ and $a(t)$ is a $T$-periodic sign-changing function satisfying the (sharp) mean value condition $\\int_{0}^{T} a(t)~\\!dt < 0$, has positive subharmonic solutions of order $k$ for any large integer $k$, thus providing a further contribution to a problem raised by G. J. Butler in its pioneering paper (JDE, 1976). The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar\\'e-Birkhof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02500","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":"2026-05-18T01:15:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScNprKAFwvNog+Z1xiGPWcC9DKN787kOnKjFepSFulJ8TAFgpGwzHPpwwZZ7RnWultcdJMfDvP74xbyOxRyfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:48:12.113494Z"},"content_sha256":"a74291c217926d505b3a08a2c48d695cb31372e736433d9d16cf4046a998ffc1","schema_version":"1.0","event_id":"sha256:a74291c217926d505b3a08a2c48d695cb31372e736433d9d16cf4046a998ffc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/bundle.json","state_url":"https://pith.science/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/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":"2026-06-02T06:48:12Z","links":{"resolver":"https://pith.science/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS","bundle":"https://pith.science/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/bundle.json","state":"https://pith.science/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LJ4JS5UHH5EG7ENWF3IKIHXFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2LJ4JS5UHH5EG7ENWF3IKIHXFS","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":"d0ae3b3487985684232b0ee0350141d2c607564e6155c77bcef6d9670c1fce7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:00:01Z","title_canon_sha256":"6688bf692602d2964c261982a005fc26b512c0a5ca27b1c9c45215f9f5c08994"},"schema_version":"1.0","source":{"id":"1605.02500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02500","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02500v1","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02500","created_at":"2026-05-18T01:15:16Z"},{"alias_kind":"pith_short_12","alias_value":"2LJ4JS5UHH5E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LJ4JS5UHH5EG7EN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LJ4JS5U","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:a74291c217926d505b3a08a2c48d695cb31372e736433d9d16cf4046a998ffc1","target":"graph","created_at":"2026-05-18T01:15:16Z","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 prove that the superlinear indefinite equation \\begin{equation*} u\" + a(t)u^{p} = 0, \\end{equation*} where $p > 1$ and $a(t)$ is a $T$-periodic sign-changing function satisfying the (sharp) mean value condition $\\int_{0}^{T} a(t)~\\!dt < 0$, has positive subharmonic solutions of order $k$ for any large integer $k$, thus providing a further contribution to a problem raised by G. J. Butler in its pioneering paper (JDE, 1976). The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar\\'e-Birkhof","authors_text":"Alberto Boscaggin, Guglielmo Feltrin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:00:01Z","title":"Positive subharmonic solutions to nonlinear ODEs with indefinite weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02500","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":"sha256:765ff9e7339a67a2db48e3484dddef5cb2b34f341caa3262e1dd1a94b3b1e6a0","target":"record","created_at":"2026-05-18T01:15:16Z","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":"d0ae3b3487985684232b0ee0350141d2c607564e6155c77bcef6d9670c1fce7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-09T10:00:01Z","title_canon_sha256":"6688bf692602d2964c261982a005fc26b512c0a5ca27b1c9c45215f9f5c08994"},"schema_version":"1.0","source":{"id":"1605.02500","kind":"arxiv","version":1}},"canonical_sha256":"d2d3c4cbb439fa437c8db1768520f72ca843ed7e00d3eb1dd61200f520a9696f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2d3c4cbb439fa437c8db1768520f72ca843ed7e00d3eb1dd61200f520a9696f","first_computed_at":"2026-05-18T01:15:16.371494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:16.371494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CFejbvgx2si1SD8u3VU9xbgEnoPVpE1CQE1iQNtnLBTr2+FcvJBPZRwUjvjG0B917uAWrIlQ72AHacoX8iOfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:16.372172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:765ff9e7339a67a2db48e3484dddef5cb2b34f341caa3262e1dd1a94b3b1e6a0","sha256:a74291c217926d505b3a08a2c48d695cb31372e736433d9d16cf4046a998ffc1"],"state_sha256":"4369431b3133f6f6285edc4d09179fd01b6cbc2f7011e6490a1670f48f5d395c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0gjyLKUW6aAJUke803jf2wLUwZgJO1isf8UmdvbgzWFzh2RJr+7Eb3FUhbhpZh0UkiLidmi9ugn+lfNFsmHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:48:12.115986Z","bundle_sha256":"437e38879a5b751b558721c414e1a8a291abd938b355fc2da08dc8de70bb879f"}}