{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EZNMURTLTEFV4QFL444BJSSRVC","short_pith_number":"pith:EZNMURTL","canonical_record":{"source":{"id":"1707.02532","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-09T06:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"befb6ce489c3669a3faf6c2eef9dd7883fccca8a8abbcd4a8569bb096cf99443","abstract_canon_sha256":"56a1a326cb0af79c31db0d89dec436c8e755f98f538d610b0669e8c0e911b93f"},"schema_version":"1.0"},"canonical_sha256":"265aca466b990b5e40abe73814ca51a8a891847fe1cb1a138f101754b7bd49cd","source":{"kind":"arxiv","id":"1707.02532","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02532","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02532v3","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02532","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"EZNMURTLTEFV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EZNMURTLTEFV4QFL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EZNMURTL","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EZNMURTLTEFV4QFL444BJSSRVC","target":"record","payload":{"canonical_record":{"source":{"id":"1707.02532","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-09T06:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"befb6ce489c3669a3faf6c2eef9dd7883fccca8a8abbcd4a8569bb096cf99443","abstract_canon_sha256":"56a1a326cb0af79c31db0d89dec436c8e755f98f538d610b0669e8c0e911b93f"},"schema_version":"1.0"},"canonical_sha256":"265aca466b990b5e40abe73814ca51a8a891847fe1cb1a138f101754b7bd49cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:51.543423Z","signature_b64":"gndCr54WrnlfQ+JD/XgBj9IeD+6W7gUuO/e1uPGqBQXelz2IrbPExZ2JSKppGPScuP5ii2eiWtBf9x+LaeIaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"265aca466b990b5e40abe73814ca51a8a891847fe1cb1a138f101754b7bd49cd","last_reissued_at":"2026-05-18T00:26:51.542718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:51.542718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.02532","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mdQKU8EnKZSEvKtj63IYWUbt/xSbjhF+I9O5pmOreIUR3HuzjfegbYk6d+yQCJ7BCA7SOAQicKd6kfjVem3hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:26:49.802696Z"},"content_sha256":"0ec0dff1f7b3349777d90f24d668254ce3ef4ea7e68197510a340e83539a52f2","schema_version":"1.0","event_id":"sha256:0ec0dff1f7b3349777d90f24d668254ce3ef4ea7e68197510a340e83539a52f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EZNMURTLTEFV4QFL444BJSSRVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jinlong Wei, Liang Ding, Shiqing Zhang","submitted_at":"2017-07-09T06:46:11Z","abstract_excerpt":"We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\\cite{AR,PS1,PS2,Qi,Wil}). Moreover, by our new mountain pass theorem, new existence of nontrivial periodic solutions for some nonlinear second-order discrete systems is obtained, which greatly improves the result in \\cite{Z04}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02532","kind":"arxiv","version":3},"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":"2026-05-18T00:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZEDLqDAWsjVG6s6lNue/6Rkz1+ZsmIi8K+MO4kCXWrjX+6GNFSsCTTKLEAEinYI8FKPp8V9Dh8A4tqDE4KxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:26:49.803340Z"},"content_sha256":"7dfa765e934819aacb02aaf135a5eda3b9a64a337b47108389ce08159807006f","schema_version":"1.0","event_id":"sha256:7dfa765e934819aacb02aaf135a5eda3b9a64a337b47108389ce08159807006f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZNMURTLTEFV4QFL444BJSSRVC/bundle.json","state_url":"https://pith.science/pith/EZNMURTLTEFV4QFL444BJSSRVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZNMURTLTEFV4QFL444BJSSRVC/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":"2026-06-05T02:26:49Z","links":{"resolver":"https://pith.science/pith/EZNMURTLTEFV4QFL444BJSSRVC","bundle":"https://pith.science/pith/EZNMURTLTEFV4QFL444BJSSRVC/bundle.json","state":"https://pith.science/pith/EZNMURTLTEFV4QFL444BJSSRVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZNMURTLTEFV4QFL444BJSSRVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EZNMURTLTEFV4QFL444BJSSRVC","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":"56a1a326cb0af79c31db0d89dec436c8e755f98f538d610b0669e8c0e911b93f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-09T06:46:11Z","title_canon_sha256":"befb6ce489c3669a3faf6c2eef9dd7883fccca8a8abbcd4a8569bb096cf99443"},"schema_version":"1.0","source":{"id":"1707.02532","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02532","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02532v3","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02532","created_at":"2026-05-18T00:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"EZNMURTLTEFV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EZNMURTLTEFV4QFL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EZNMURTL","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:7dfa765e934819aacb02aaf135a5eda3b9a64a337b47108389ce08159807006f","target":"graph","created_at":"2026-05-18T00:26:51Z","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 obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\\cite{AR,PS1,PS2,Qi,Wil}). Moreover, by our new mountain pass theorem, new existence of nontrivial periodic solutions for some nonlinear second-order discrete systems is obtained, which greatly improves the result in \\cite{Z04}.","authors_text":"Jinlong Wei, Liang Ding, Shiqing Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-09T06:46:11Z","title":"On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02532","kind":"arxiv","version":3},"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":"sha256:0ec0dff1f7b3349777d90f24d668254ce3ef4ea7e68197510a340e83539a52f2","target":"record","created_at":"2026-05-18T00:26:51Z","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":"56a1a326cb0af79c31db0d89dec436c8e755f98f538d610b0669e8c0e911b93f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-09T06:46:11Z","title_canon_sha256":"befb6ce489c3669a3faf6c2eef9dd7883fccca8a8abbcd4a8569bb096cf99443"},"schema_version":"1.0","source":{"id":"1707.02532","kind":"arxiv","version":3}},"canonical_sha256":"265aca466b990b5e40abe73814ca51a8a891847fe1cb1a138f101754b7bd49cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"265aca466b990b5e40abe73814ca51a8a891847fe1cb1a138f101754b7bd49cd","first_computed_at":"2026-05-18T00:26:51.542718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:51.542718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gndCr54WrnlfQ+JD/XgBj9IeD+6W7gUuO/e1uPGqBQXelz2IrbPExZ2JSKppGPScuP5ii2eiWtBf9x+LaeIaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:51.543423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02532","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ec0dff1f7b3349777d90f24d668254ce3ef4ea7e68197510a340e83539a52f2","sha256:7dfa765e934819aacb02aaf135a5eda3b9a64a337b47108389ce08159807006f"],"state_sha256":"dbeccbc41bfa737a8ff00b256bfa841eb83eae966f9eaa9a26fa3e83159b49e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R7K2aEqxIra7nyOdjKexDyPrBdQp9ZNr59zflZ8vvDPw5hSn2NuFH+QgPAQ9hfmu1Ws9KxdC28Vbwnq6O6iUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:26:49.806515Z","bundle_sha256":"eb93e5f74587c1c7f7b6680ebb2b8efcfa4788771a3bdceaeeb2243902969d35"}}