{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7HP2K7TCZDPQGU2GCTDMOAZGCA","short_pith_number":"pith:7HP2K7TC","schema_version":"1.0","canonical_sha256":"f9dfa57e62c8df03534614c6c70326102f8ae9aef20198a3551e5bde8f56a46b","source":{"kind":"arxiv","id":"1908.03165","version":4},"attestation_state":"computed","paper":{"title":"Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SG","authors_text":"Niek Lamoree, Oliver Fabert","submitted_at":"2019-08-08T16:56:06Z","abstract_excerpt":"We extend the pseudoholomorphic curve methods from Floer theory to infinite-dimensional phase spaces and use our results to prove the existence of a forced time-periodic solution to a general Hamiltonian PDE with regularizing nonlinearity. In particular, when the nonlinearity is sufficiently regularizing, bounded and time-periodic, we prove an infinite-dimensional version of Gromov-Floer compactness by using ideas from the theory of Diophantine approximations to overcome the small divisor problem. Furthermore, in the case when the infinite-dimensional phase space is a product of a finite-dimen"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.03165","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2019-08-08T16:56:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"1d94be452cc4c6d7f8e041087d57974446278b90bd1518a52a9cf3641e972298","abstract_canon_sha256":"983c252b6a3c8a14153cff0d2383f25d2d6e85c9f5811bfc905b00be84ee4a14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:51.434854Z","signature_b64":"ABOJZ+op983BPwhw84vkHAw4DIDJ7R7JTO+aGjyL4MtqYzj9glj806d7ObjcyLb1JzsLcNFj2xcQ+U2OCJodBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9dfa57e62c8df03534614c6c70326102f8ae9aef20198a3551e5bde8f56a46b","last_reissued_at":"2026-07-05T05:57:51.434438Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:51.434438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SG","authors_text":"Niek Lamoree, Oliver Fabert","submitted_at":"2019-08-08T16:56:06Z","abstract_excerpt":"We extend the pseudoholomorphic curve methods from Floer theory to infinite-dimensional phase spaces and use our results to prove the existence of a forced time-periodic solution to a general Hamiltonian PDE with regularizing nonlinearity. In particular, when the nonlinearity is sufficiently regularizing, bounded and time-periodic, we prove an infinite-dimensional version of Gromov-Floer compactness by using ideas from the theory of Diophantine approximations to overcome the small divisor problem. Furthermore, in the case when the infinite-dimensional phase space is a product of a finite-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03165","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03165/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.03165","created_at":"2026-07-05T05:57:51.434496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03165v4","created_at":"2026-07-05T05:57:51.434496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03165","created_at":"2026-07-05T05:57:51.434496+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HP2K7TCZDPQ","created_at":"2026-07-05T05:57:51.434496+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HP2K7TCZDPQGU2G","created_at":"2026-07-05T05:57:51.434496+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HP2K7TC","created_at":"2026-07-05T05:57:51.434496+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA","json":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA.json","graph_json":"https://pith.science/api/pith-number/7HP2K7TCZDPQGU2GCTDMOAZGCA/graph.json","events_json":"https://pith.science/api/pith-number/7HP2K7TCZDPQGU2GCTDMOAZGCA/events.json","paper":"https://pith.science/paper/7HP2K7TC"},"agent_actions":{"view_html":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA","download_json":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA.json","view_paper":"https://pith.science/paper/7HP2K7TC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03165&json=true","fetch_graph":"https://pith.science/api/pith-number/7HP2K7TCZDPQGU2GCTDMOAZGCA/graph.json","fetch_events":"https://pith.science/api/pith-number/7HP2K7TCZDPQGU2GCTDMOAZGCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA/action/storage_attestation","attest_author":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA/action/author_attestation","sign_citation":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA/action/citation_signature","submit_replication":"https://pith.science/pith/7HP2K7TCZDPQGU2GCTDMOAZGCA/action/replication_record"}},"created_at":"2026-07-05T05:57:51.434496+00:00","updated_at":"2026-07-05T05:57:51.434496+00:00"}