{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:APLE55RATAC5QCVLPA5KIAAZBM","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":"1e3ad14181ee7ba1bee87094fd6253eafa2bbfb82b6a4db5ca59b0ba1d2a4eb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-04-13T15:23:10Z","title_canon_sha256":"e44bf2544e124345ee5b51b1d4b256b99931e74e357e7ee2a753cd83f590397c"},"schema_version":"1.0","source":{"id":"2404.09025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.09025","created_at":"2026-07-05T08:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"2404.09025v1","created_at":"2026-07-05T08:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.09025","created_at":"2026-07-05T08:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"APLE55RATAC5","created_at":"2026-07-05T08:07:43Z"},{"alias_kind":"pith_short_16","alias_value":"APLE55RATAC5QCVL","created_at":"2026-07-05T08:07:43Z"},{"alias_kind":"pith_short_8","alias_value":"APLE55RA","created_at":"2026-07-05T08:07:43Z"}],"graph_snapshots":[{"event_id":"sha256:4b4cc738ebc3593e5fef9554dbe6e1ed5db136535aad56a31d5983b2e5d3e89d","target":"graph","created_at":"2026-07-05T08:07:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.09025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of discussing in a simple case the analyticity properties to be required on the perturbation of the integrable system in order to ensure the persistence of a large measure set of invariant tori with finite energy. The proof we provide of the persistence of the invariant tori implements the Renormalization Group scheme based on the tree formalism -- i.e. the graphical re","authors_text":"Guido Gentile, Livia Corsi, Michela Procesi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-04-13T15:23:10Z","title":"Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09025","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":"sha256:1abe707c1f635b0a165f93441fc9614192e5c73bca98dd224de456c99e539d68","target":"record","created_at":"2026-07-05T08:07:43Z","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":"1e3ad14181ee7ba1bee87094fd6253eafa2bbfb82b6a4db5ca59b0ba1d2a4eb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-04-13T15:23:10Z","title_canon_sha256":"e44bf2544e124345ee5b51b1d4b256b99931e74e357e7ee2a753cd83f590397c"},"schema_version":"1.0","source":{"id":"2404.09025","kind":"arxiv","version":1}},"canonical_sha256":"03d64ef6209805d80aab783aa400190b3492f3e0e16adcaeda74995c0c49bd91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d64ef6209805d80aab783aa400190b3492f3e0e16adcaeda74995c0c49bd91","first_computed_at":"2026-07-05T08:07:43.892490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:07:43.892490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"leS4fnzR4omp//2VDiZGdjK7qDCTXGPnxy1V3ysH7mOeNjnCv1wUKUbRx2YWhdY+i6qGSdbhR0SlFBoWDwprAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:07:43.893042Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.09025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1abe707c1f635b0a165f93441fc9614192e5c73bca98dd224de456c99e539d68","sha256:4b4cc738ebc3593e5fef9554dbe6e1ed5db136535aad56a31d5983b2e5d3e89d"],"state_sha256":"c2f7b61b4815e44cc9c045f8a757cf7298037ac726fd2a253a141a31271b7357"}