{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2AJONVPVGQB7XI7LM2WR2VLOTH","short_pith_number":"pith:2AJONVPV","canonical_record":{"source":{"id":"1007.3302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-19T22:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"76e4481e30222e1e7cc510e8f40bc8a994febaef3c00a6cb19438736549f9eaa","abstract_canon_sha256":"afcd189082f5ce668506b0b4880e234e9f57268a4fa7bf2f7163bba481726dcf"},"schema_version":"1.0"},"canonical_sha256":"d012e6d5f53403fba3eb66ad1d556e99dddc6be3a1c9bca368aac44d85552c7e","source":{"kind":"arxiv","id":"1007.3302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3302","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3302v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3302","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"2AJONVPVGQB7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2AJONVPVGQB7XI7L","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2AJONVPV","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2AJONVPVGQB7XI7LM2WR2VLOTH","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-19T22:43:32Z","cross_cats_sorted":[],"title_canon_sha256":"76e4481e30222e1e7cc510e8f40bc8a994febaef3c00a6cb19438736549f9eaa","abstract_canon_sha256":"afcd189082f5ce668506b0b4880e234e9f57268a4fa7bf2f7163bba481726dcf"},"schema_version":"1.0"},"canonical_sha256":"d012e6d5f53403fba3eb66ad1d556e99dddc6be3a1c9bca368aac44d85552c7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:54.389142Z","signature_b64":"uO64mLhv+qs9bezJ1vDMB1EneWzf4C9BQ5G8qhZIzBHqLoPrcx8jSxpGxpMFyuEALdvtfifO5H11eudwCojZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d012e6d5f53403fba3eb66ad1d556e99dddc6be3a1c9bca368aac44d85552c7e","last_reissued_at":"2026-05-18T04:40:54.388608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:54.388608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3302","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":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txpGUlsIJW9IJfhLkxVgL/TLeygNh5Y5wubwJcwDQtNWV4lKUI6pqJD8EWdW5GiB6DCsyHaMyRD50C02wE+qBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:26:19.522280Z"},"content_sha256":"35a2b45965eb34412341fcdbfcb06cb9b6db82468d8221df74e7437103592285","schema_version":"1.0","event_id":"sha256:35a2b45965eb34412341fcdbfcb06cb9b6db82468d8221df74e7437103592285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2AJONVPVGQB7XI7LM2WR2VLOTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive periodic solutions of singular systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Haiyan Wang","submitted_at":"2010-07-19T22:43:32Z","abstract_excerpt":"The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our results provide a unified treatment for the problem and significantly improve several results in the literature. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3302","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":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NNQ7lMx06f+Zaeg3GTWZEZQqXgyLPiLtET7AGHEGFJ8O/AL8Bm6JoVQNrvnoaHR9std5tQFfuqcDl75NAl+ZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:26:19.522987Z"},"content_sha256":"f63ec5f7fb464cc1a45d25fd3ebba6cae67264708e1c25e6430cdfc399c83f01","schema_version":"1.0","event_id":"sha256:f63ec5f7fb464cc1a45d25fd3ebba6cae67264708e1c25e6430cdfc399c83f01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/bundle.json","state_url":"https://pith.science/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/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":"2026-05-29T22:26:19Z","links":{"resolver":"https://pith.science/pith/2AJONVPVGQB7XI7LM2WR2VLOTH","bundle":"https://pith.science/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/bundle.json","state":"https://pith.science/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AJONVPVGQB7XI7LM2WR2VLOTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2AJONVPVGQB7XI7LM2WR2VLOTH","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":"afcd189082f5ce668506b0b4880e234e9f57268a4fa7bf2f7163bba481726dcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-19T22:43:32Z","title_canon_sha256":"76e4481e30222e1e7cc510e8f40bc8a994febaef3c00a6cb19438736549f9eaa"},"schema_version":"1.0","source":{"id":"1007.3302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3302","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3302v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3302","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"2AJONVPVGQB7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2AJONVPVGQB7XI7L","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2AJONVPV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:f63ec5f7fb464cc1a45d25fd3ebba6cae67264708e1c25e6430cdfc399c83f01","target":"graph","created_at":"2026-05-18T04:40:54Z","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":"The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our results provide a unified treatment for the problem and significantly improve several results in the literature. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone.","authors_text":"Haiyan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-19T22:43:32Z","title":"Positive periodic solutions of singular systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3302","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":"sha256:35a2b45965eb34412341fcdbfcb06cb9b6db82468d8221df74e7437103592285","target":"record","created_at":"2026-05-18T04:40:54Z","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":"afcd189082f5ce668506b0b4880e234e9f57268a4fa7bf2f7163bba481726dcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-19T22:43:32Z","title_canon_sha256":"76e4481e30222e1e7cc510e8f40bc8a994febaef3c00a6cb19438736549f9eaa"},"schema_version":"1.0","source":{"id":"1007.3302","kind":"arxiv","version":1}},"canonical_sha256":"d012e6d5f53403fba3eb66ad1d556e99dddc6be3a1c9bca368aac44d85552c7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d012e6d5f53403fba3eb66ad1d556e99dddc6be3a1c9bca368aac44d85552c7e","first_computed_at":"2026-05-18T04:40:54.388608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.388608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uO64mLhv+qs9bezJ1vDMB1EneWzf4C9BQ5G8qhZIzBHqLoPrcx8jSxpGxpMFyuEALdvtfifO5H11eudwCojZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.389142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a2b45965eb34412341fcdbfcb06cb9b6db82468d8221df74e7437103592285","sha256:f63ec5f7fb464cc1a45d25fd3ebba6cae67264708e1c25e6430cdfc399c83f01"],"state_sha256":"73e89856284ff562119d831d0553dc1058dd8e7f95fc2883ef721e9e36b25e4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCxK7eKSfi28bNPz93krFdkP5vFnD2n27RFwPMcB0fWDwpy2Y0GakyN8wZY7b6dlOARORU0mpkJXfMzlB7oFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T22:26:19.526580Z","bundle_sha256":"ec2c47bb3f52540f6db4b38990fb18be5a5b4783957d2a676772a4540fc6a7c8"}}