{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6465GFEIDF2UDSJP44QFCNDHCO","short_pith_number":"pith:6465GFEI","canonical_record":{"source":{"id":"1211.2125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-09T13:34:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"78fb08651caf5e6bd2e554407a8562a21f599463d7cda3d88459ddfc8e0e5da0","abstract_canon_sha256":"d058fbd74b97d5ccf1be906e6edd01545f71d1c6622610df2e1e69031238e57a"},"schema_version":"1.0"},"canonical_sha256":"f73dd31488197541c92fe720513467138e0d7a20a08e5c10280d43eaa9107226","source":{"kind":"arxiv","id":"1211.2125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2125","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2125v1","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2125","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"pith_short_12","alias_value":"6465GFEIDF2U","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6465GFEIDF2UDSJP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6465GFEI","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6465GFEIDF2UDSJP44QFCNDHCO","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-09T13:34:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"78fb08651caf5e6bd2e554407a8562a21f599463d7cda3d88459ddfc8e0e5da0","abstract_canon_sha256":"d058fbd74b97d5ccf1be906e6edd01545f71d1c6622610df2e1e69031238e57a"},"schema_version":"1.0"},"canonical_sha256":"f73dd31488197541c92fe720513467138e0d7a20a08e5c10280d43eaa9107226","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:27.522101Z","signature_b64":"Lewz1Gmj6q+lqB8pCGZgW5kUi4E7mwFye+wqA+0rnPeiSPjceqzlSzyhMk3Wkuf3lfSmNyid7DuP2c6NCt8bCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f73dd31488197541c92fe720513467138e0d7a20a08e5c10280d43eaa9107226","last_reissued_at":"2026-05-18T02:48:27.521395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:27.521395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2125","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":"2026-05-18T02:48:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+vhpqmZGj4ae726C81BykysoQ1odUhL0NmnVENOLbSP7FdfXUOPB72j2LcMEEqyAeEp+tYOwfYoVG/svy7gCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:42:37.518992Z"},"content_sha256":"eeefa1ba0621fc10abcbf925c4ce88a3278163cdb84e9cd64f25094bfe81e681","schema_version":"1.0","event_id":"sha256:eeefa1ba0621fc10abcbf925c4ce88a3278163cdb84e9cd64f25094bfe81e681"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6465GFEIDF2UDSJP44QFCNDHCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergent series for quasi-periodically forced strongly dissipative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Guido Gentile, Livia Corsi, Roberto Feola","submitted_at":"2012-11-09T13:34:05Z","abstract_excerpt":"We study the ordinary differential equation ${\\varepsilon}\\ddot x+\\dot x + {\\varepsilon} g(x) = {\\varepsilon} f(\\omega t)$, with $f$ and $g$ analytic and $f$ quasi-periodic in $t$ with frequency vector $\\omega\\in R^{d}$. We show that if there exists $c_0\\in R$ such that $g(c_0)$ equals the average of $f$ and the first non-zero derivative of $g$ at $c_0$ is of odd order $n$, then, for ${\\varepsilon}$ small enough and under very mild Diophantine conditions on $\\omega$, there exists a quasi-periodic solution close to $c_0$, with the same frequency vector as $f$. In particular if $f$ is a trigonom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2125","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":"2026-05-18T02:48:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPBHnFSHfmPhP11HVc4bQGTkXA2a4NVKKDLd8B2GLwvhkLIyD5Sgj7TSFXMwX2SNoH3wgucg4AOhmJ6Kn/goAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:42:37.519431Z"},"content_sha256":"f8344e6764b753f40ce98fe58b32a7d1a66e47975b1ddeff933cf50494002238","schema_version":"1.0","event_id":"sha256:f8344e6764b753f40ce98fe58b32a7d1a66e47975b1ddeff933cf50494002238"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6465GFEIDF2UDSJP44QFCNDHCO/bundle.json","state_url":"https://pith.science/pith/6465GFEIDF2UDSJP44QFCNDHCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6465GFEIDF2UDSJP44QFCNDHCO/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":"2026-06-05T16:42:37Z","links":{"resolver":"https://pith.science/pith/6465GFEIDF2UDSJP44QFCNDHCO","bundle":"https://pith.science/pith/6465GFEIDF2UDSJP44QFCNDHCO/bundle.json","state":"https://pith.science/pith/6465GFEIDF2UDSJP44QFCNDHCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6465GFEIDF2UDSJP44QFCNDHCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6465GFEIDF2UDSJP44QFCNDHCO","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":"d058fbd74b97d5ccf1be906e6edd01545f71d1c6622610df2e1e69031238e57a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-09T13:34:05Z","title_canon_sha256":"78fb08651caf5e6bd2e554407a8562a21f599463d7cda3d88459ddfc8e0e5da0"},"schema_version":"1.0","source":{"id":"1211.2125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2125","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2125v1","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2125","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"pith_short_12","alias_value":"6465GFEIDF2U","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6465GFEIDF2UDSJP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6465GFEI","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:f8344e6764b753f40ce98fe58b32a7d1a66e47975b1ddeff933cf50494002238","target":"graph","created_at":"2026-05-18T02:48:27Z","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 study the ordinary differential equation ${\\varepsilon}\\ddot x+\\dot x + {\\varepsilon} g(x) = {\\varepsilon} f(\\omega t)$, with $f$ and $g$ analytic and $f$ quasi-periodic in $t$ with frequency vector $\\omega\\in R^{d}$. We show that if there exists $c_0\\in R$ such that $g(c_0)$ equals the average of $f$ and the first non-zero derivative of $g$ at $c_0$ is of odd order $n$, then, for ${\\varepsilon}$ small enough and under very mild Diophantine conditions on $\\omega$, there exists a quasi-periodic solution close to $c_0$, with the same frequency vector as $f$. In particular if $f$ is a trigonom","authors_text":"Guido Gentile, Livia Corsi, Roberto Feola","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-09T13:34:05Z","title":"Convergent series for quasi-periodically forced strongly dissipative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2125","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:eeefa1ba0621fc10abcbf925c4ce88a3278163cdb84e9cd64f25094bfe81e681","target":"record","created_at":"2026-05-18T02:48:27Z","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":"d058fbd74b97d5ccf1be906e6edd01545f71d1c6622610df2e1e69031238e57a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-09T13:34:05Z","title_canon_sha256":"78fb08651caf5e6bd2e554407a8562a21f599463d7cda3d88459ddfc8e0e5da0"},"schema_version":"1.0","source":{"id":"1211.2125","kind":"arxiv","version":1}},"canonical_sha256":"f73dd31488197541c92fe720513467138e0d7a20a08e5c10280d43eaa9107226","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f73dd31488197541c92fe720513467138e0d7a20a08e5c10280d43eaa9107226","first_computed_at":"2026-05-18T02:48:27.521395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:27.521395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lewz1Gmj6q+lqB8pCGZgW5kUi4E7mwFye+wqA+0rnPeiSPjceqzlSzyhMk3Wkuf3lfSmNyid7DuP2c6NCt8bCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:27.522101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeefa1ba0621fc10abcbf925c4ce88a3278163cdb84e9cd64f25094bfe81e681","sha256:f8344e6764b753f40ce98fe58b32a7d1a66e47975b1ddeff933cf50494002238"],"state_sha256":"428b3ea1f2e5a1c0a8b2d862e68254de37790ee349af6df2342e92a2f9d7e544"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UEoKLWSRQoN+1bAof4RqvTiBmVmoh2WrZ/0UDVG43ZjztWctdb8i8egRr4IuN9ku5MKy17ySYTYLSpaai9n3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:42:37.521521Z","bundle_sha256":"9885366158fc5f5958c7eba65757a065e1b6e666bcd33dfdcfdce1105093058f"}}