{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EJJ6TQGSWANY7A3G5V2PJVNGIK","short_pith_number":"pith:EJJ6TQGS","canonical_record":{"source":{"id":"1304.5647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T16:34:21Z","cross_cats_sorted":[],"title_canon_sha256":"de648b13bda488599780e6611253046fb1117097ad334711ac93da54d7bc9c83","abstract_canon_sha256":"47e937c7b7f9eac910bf943447703917837ad4d66d1d14c79866ca612db8dea0"},"schema_version":"1.0"},"canonical_sha256":"2253e9c0d2b01b8f8366ed74f4d5a6428f79f6834d4570bf4b2f25b77503c005","source":{"kind":"arxiv","id":"1304.5647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5647","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5647v1","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5647","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"EJJ6TQGSWANY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EJJ6TQGSWANY7A3G","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EJJ6TQGS","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EJJ6TQGSWANY7A3G5V2PJVNGIK","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T16:34:21Z","cross_cats_sorted":[],"title_canon_sha256":"de648b13bda488599780e6611253046fb1117097ad334711ac93da54d7bc9c83","abstract_canon_sha256":"47e937c7b7f9eac910bf943447703917837ad4d66d1d14c79866ca612db8dea0"},"schema_version":"1.0"},"canonical_sha256":"2253e9c0d2b01b8f8366ed74f4d5a6428f79f6834d4570bf4b2f25b77503c005","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:24.519866Z","signature_b64":"kM4z5xWHXPUNVpJWGph5GPftCfYs/pkwSdaSC7CdNgNjmxcD2E5SkkOs6FxnJaL5+rbJSodIJYqi2ZfHh2LfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2253e9c0d2b01b8f8366ed74f4d5a6428f79f6834d4570bf4b2f25b77503c005","last_reissued_at":"2026-05-18T03:27:24.519151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:24.519151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5647","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":"2026-05-18T03:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0dl5U4oAMdS2WHUofmQu8kOy7izwASbvUkJ1yWe84Fy9gQiZSrzx46OggYf6/vGgZKw59Whj/oQPZdq3Hz/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:28:52.385216Z"},"content_sha256":"784267709c76b633d80da9b88ca5ace90503013b69b2cc477700dab00d506f5e","schema_version":"1.0","event_id":"sha256:784267709c76b633d80da9b88ca5ace90503013b69b2cc477700dab00d506f5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EJJ6TQGSWANY7A3G5V2PJVNGIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homoclinic orbits of first-order superquadratic Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril J. Batkam","submitted_at":"2013-04-20T16:34:21Z","abstract_excerpt":"In this article, we study the existence of homoclinic orbits for the first-order Hamiltonian system {equation*} J\\dot{u}(t)+\\nabla H(t,u(t))=0,\\quad t\\in\\mathbb{R}. {equation*} Under the Ambrosetti-Rabinowitz's superquadraticy condition, or no Ambrosetti-Rabinowitz's superquadracity condition, we present two results on the existence of infinitely many large energy homoclinic orbits when $H$ is even in $u$. We apply the generalized (variant) fountain theorems due to the author and Colin. Under no Ambrosetti-Rabinowitz's superquadracity condition, we also obtain the existence of a ground state h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5647","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":"2026-05-18T03:27:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqoG1ISDE2XroP/VnfcD5J/S+SfkbJIgpmqcReWddsOpuCVT6DNqpBn4VViIUmxgLQl2L6BmEOTMR/7IeCkRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:28:52.385577Z"},"content_sha256":"d756faa93ba032e907c29cfc757fce79036690724fc4753c27a304abe379cf96","schema_version":"1.0","event_id":"sha256:d756faa93ba032e907c29cfc757fce79036690724fc4753c27a304abe379cf96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/bundle.json","state_url":"https://pith.science/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/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":"2026-06-22T23:28:52Z","links":{"resolver":"https://pith.science/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK","bundle":"https://pith.science/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/bundle.json","state":"https://pith.science/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJJ6TQGSWANY7A3G5V2PJVNGIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EJJ6TQGSWANY7A3G5V2PJVNGIK","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":"47e937c7b7f9eac910bf943447703917837ad4d66d1d14c79866ca612db8dea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T16:34:21Z","title_canon_sha256":"de648b13bda488599780e6611253046fb1117097ad334711ac93da54d7bc9c83"},"schema_version":"1.0","source":{"id":"1304.5647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5647","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5647v1","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5647","created_at":"2026-05-18T03:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"EJJ6TQGSWANY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EJJ6TQGSWANY7A3G","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EJJ6TQGS","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:d756faa93ba032e907c29cfc757fce79036690724fc4753c27a304abe379cf96","target":"graph","created_at":"2026-05-18T03:27:24Z","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":"In this article, we study the existence of homoclinic orbits for the first-order Hamiltonian system {equation*} J\\dot{u}(t)+\\nabla H(t,u(t))=0,\\quad t\\in\\mathbb{R}. {equation*} Under the Ambrosetti-Rabinowitz's superquadraticy condition, or no Ambrosetti-Rabinowitz's superquadracity condition, we present two results on the existence of infinitely many large energy homoclinic orbits when $H$ is even in $u$. We apply the generalized (variant) fountain theorems due to the author and Colin. Under no Ambrosetti-Rabinowitz's superquadracity condition, we also obtain the existence of a ground state h","authors_text":"Cyril J. Batkam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T16:34:21Z","title":"Homoclinic orbits of first-order superquadratic Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5647","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":"sha256:784267709c76b633d80da9b88ca5ace90503013b69b2cc477700dab00d506f5e","target":"record","created_at":"2026-05-18T03:27:24Z","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":"47e937c7b7f9eac910bf943447703917837ad4d66d1d14c79866ca612db8dea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T16:34:21Z","title_canon_sha256":"de648b13bda488599780e6611253046fb1117097ad334711ac93da54d7bc9c83"},"schema_version":"1.0","source":{"id":"1304.5647","kind":"arxiv","version":1}},"canonical_sha256":"2253e9c0d2b01b8f8366ed74f4d5a6428f79f6834d4570bf4b2f25b77503c005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2253e9c0d2b01b8f8366ed74f4d5a6428f79f6834d4570bf4b2f25b77503c005","first_computed_at":"2026-05-18T03:27:24.519151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:24.519151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kM4z5xWHXPUNVpJWGph5GPftCfYs/pkwSdaSC7CdNgNjmxcD2E5SkkOs6FxnJaL5+rbJSodIJYqi2ZfHh2LfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:24.519866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:784267709c76b633d80da9b88ca5ace90503013b69b2cc477700dab00d506f5e","sha256:d756faa93ba032e907c29cfc757fce79036690724fc4753c27a304abe379cf96"],"state_sha256":"5044dbb752c9b28ce1c7a3f7f181a23eb7d613939c3ee3c3e30862b0d054d206"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaeURtklPwEEhztIqo31vuW8n6sI4mN7pf7RAet3ekgazn+DiZLSNV8YMARfGdAZJckC/ziHZ44qCVUd6ig4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:28:52.387699Z","bundle_sha256":"01dc34c8982bb7dd522543b385118ea9d2706628bd64f0319c1f3c9daa09a63c"}}