{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:I6NKVRDXSI4MHVGDTBRZDCUGRV","short_pith_number":"pith:I6NKVRDX","canonical_record":{"source":{"id":"1803.11043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-29T13:10:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6e5e834648ee5a2d6afaad90097194b3f8fda8ed2fb3587e7af4e01fed346c71","abstract_canon_sha256":"b1db4c573a8c4821c4b8973ddd0db5bd86c09e96b1a62972cd0ec51eb682773a"},"schema_version":"1.0"},"canonical_sha256":"479aaac4779238c3d4c39863918a868d5a7f37f4ad77f1b07e1ea96ccb831ce0","source":{"kind":"arxiv","id":"1803.11043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.11043","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1803.11043v1","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11043","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"I6NKVRDXSI4M","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I6NKVRDXSI4MHVGD","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I6NKVRDX","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:I6NKVRDXSI4MHVGDTBRZDCUGRV","target":"record","payload":{"canonical_record":{"source":{"id":"1803.11043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-29T13:10:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6e5e834648ee5a2d6afaad90097194b3f8fda8ed2fb3587e7af4e01fed346c71","abstract_canon_sha256":"b1db4c573a8c4821c4b8973ddd0db5bd86c09e96b1a62972cd0ec51eb682773a"},"schema_version":"1.0"},"canonical_sha256":"479aaac4779238c3d4c39863918a868d5a7f37f4ad77f1b07e1ea96ccb831ce0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:46.774543Z","signature_b64":"lGBe30aL1Vv/MKMzlHB4Jt62NDgBC/UwDG7TrFFwXu9w4FrA6ZlSd4G2qRouUNWnjnM3kvVUgxIw5ptdBTWSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"479aaac4779238c3d4c39863918a868d5a7f37f4ad77f1b07e1ea96ccb831ce0","last_reissued_at":"2026-05-18T00:19:46.773799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:46.773799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.11043","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":"2026-05-18T00:19:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HF0XT1vVFfr3U2c3CjNK9MLcPj46khihYw3S7OW5a5OJRGQoItv94JJwe8bRKIyZFBzryhVITocrLkAECfLQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:18:13.194553Z"},"content_sha256":"714148fa508ba1a0292b3bb50ac8fb8d0d0c7e204e9328e53481acdaab43a11f","schema_version":"1.0","event_id":"sha256:714148fa508ba1a0292b3bb50ac8fb8d0d0c7e204e9328e53481acdaab43a11f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:I6NKVRDXSI4MHVGDTBRZDCUGRV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jakub Maksymiuk, Magdalena Chmara","submitted_at":"2018-03-29T13:10:07Z","abstract_excerpt":"Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part $K-W$ and a forcing term. We consider two situations: $G$ satisfying $\\Delta_2\\cap\\nabla_2$ in infinity and globally. We give conditions on the growth of the potential near zero for both situations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11043","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":"2026-05-18T00:19:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"loqhc6s0HFZB0ohX59fU42dXBMFD0hC8RleKC1vnqpuW7JXGjAYK0PtS6e+Qbm6JhYXzV26HcNJVWjjmaDNCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:18:13.194908Z"},"content_sha256":"8b50268afc1867c5490afac8602fc29c7531aa46dcabf1fb04e61a7fc5d05950","schema_version":"1.0","event_id":"sha256:8b50268afc1867c5490afac8602fc29c7531aa46dcabf1fb04e61a7fc5d05950"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/bundle.json","state_url":"https://pith.science/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/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":"2026-06-30T20:18:13Z","links":{"resolver":"https://pith.science/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV","bundle":"https://pith.science/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/bundle.json","state":"https://pith.science/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6NKVRDXSI4MHVGDTBRZDCUGRV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I6NKVRDXSI4MHVGDTBRZDCUGRV","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":"b1db4c573a8c4821c4b8973ddd0db5bd86c09e96b1a62972cd0ec51eb682773a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-29T13:10:07Z","title_canon_sha256":"6e5e834648ee5a2d6afaad90097194b3f8fda8ed2fb3587e7af4e01fed346c71"},"schema_version":"1.0","source":{"id":"1803.11043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.11043","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"arxiv_version","alias_value":"1803.11043v1","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11043","created_at":"2026-05-18T00:19:46Z"},{"alias_kind":"pith_short_12","alias_value":"I6NKVRDXSI4M","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I6NKVRDXSI4MHVGD","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I6NKVRDX","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:8b50268afc1867c5490afac8602fc29c7531aa46dcabf1fb04e61a7fc5d05950","target":"graph","created_at":"2026-05-18T00:19:46Z","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":"Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part $K-W$ and a forcing term. We consider two situations: $G$ satisfying $\\Delta_2\\cap\\nabla_2$ in infinity and globally. We give conditions on the growth of the potential near zero for both situations.","authors_text":"Jakub Maksymiuk, Magdalena Chmara","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-29T13:10:07Z","title":"Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11043","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":"sha256:714148fa508ba1a0292b3bb50ac8fb8d0d0c7e204e9328e53481acdaab43a11f","target":"record","created_at":"2026-05-18T00:19:46Z","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":"b1db4c573a8c4821c4b8973ddd0db5bd86c09e96b1a62972cd0ec51eb682773a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-29T13:10:07Z","title_canon_sha256":"6e5e834648ee5a2d6afaad90097194b3f8fda8ed2fb3587e7af4e01fed346c71"},"schema_version":"1.0","source":{"id":"1803.11043","kind":"arxiv","version":1}},"canonical_sha256":"479aaac4779238c3d4c39863918a868d5a7f37f4ad77f1b07e1ea96ccb831ce0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"479aaac4779238c3d4c39863918a868d5a7f37f4ad77f1b07e1ea96ccb831ce0","first_computed_at":"2026-05-18T00:19:46.773799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:46.773799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGBe30aL1Vv/MKMzlHB4Jt62NDgBC/UwDG7TrFFwXu9w4FrA6ZlSd4G2qRouUNWnjnM3kvVUgxIw5ptdBTWSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:46.774543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.11043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:714148fa508ba1a0292b3bb50ac8fb8d0d0c7e204e9328e53481acdaab43a11f","sha256:8b50268afc1867c5490afac8602fc29c7531aa46dcabf1fb04e61a7fc5d05950"],"state_sha256":"4ddec81b4bcc81c451bf2f0910ee128bd7f12759a62321a18b73802c33f4d4ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1U5yByU8ykxUlc44MSO/ON7D84aGOSD0KevsBoHSBXKS9PpTTPzO3xC9f9VquqR9szsJs1TZNLFmkW25epDjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:18:13.197351Z","bundle_sha256":"c25989b29e52e4ea0d6418e16639008bed7e167df024457c9df69025ec3be783"}}