{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TO2WM7WXPJ2LKOYXUJ7QHWE5OQ","short_pith_number":"pith:TO2WM7WX","canonical_record":{"source":{"id":"1102.1066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-05T12:10:03Z","cross_cats_sorted":[],"title_canon_sha256":"0df269bb87410abeb151b1cf0196b34e328d4eed8564de9f42248fcdf2293e81","abstract_canon_sha256":"7ec9139ece2fcf09aa2fd7d2fda924db4ec2f10ffd6324899a810b4cc1b35263"},"schema_version":"1.0"},"canonical_sha256":"9bb5667ed77a74b53b17a27f03d89d7426353fab0ddb3c6286bec9f13e7d3866","source":{"kind":"arxiv","id":"1102.1066","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1066","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1066v3","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1066","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"TO2WM7WXPJ2L","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO2WM7WXPJ2LKOYX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO2WM7WX","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TO2WM7WXPJ2LKOYXUJ7QHWE5OQ","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-05T12:10:03Z","cross_cats_sorted":[],"title_canon_sha256":"0df269bb87410abeb151b1cf0196b34e328d4eed8564de9f42248fcdf2293e81","abstract_canon_sha256":"7ec9139ece2fcf09aa2fd7d2fda924db4ec2f10ffd6324899a810b4cc1b35263"},"schema_version":"1.0"},"canonical_sha256":"9bb5667ed77a74b53b17a27f03d89d7426353fab0ddb3c6286bec9f13e7d3866","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:52.642645Z","signature_b64":"eMwPE5GUuVrJVsqqZVdUghwtIGEtyEoqyX73Qulgz0HXv7kRsm72GUYUAq4dyYeftCx+T82tDhTeQfiEeiwzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bb5667ed77a74b53b17a27f03d89d7426353fab0ddb3c6286bec9f13e7d3866","last_reissued_at":"2026-05-18T02:17:52.641958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:52.641958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1066","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kJ4VnRivi6YX0LU8ARG4maD0YugtcELZe6+ZRX7Bd7UvVLhOuUPVNSH+ingxamYgAk0hJCkNwApxHJLNhMNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:15:03.327088Z"},"content_sha256":"f2125f99ff09eb828808190355258645d093c508906cad7b4e5e764f9cc312bf","schema_version":"1.0","event_id":"sha256:f2125f99ff09eb828808190355258645d093c508906cad7b4e5e764f9cc312bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TO2WM7WXPJ2LKOYXUJ7QHWE5OQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-T\\\"oplitz functions in KAM theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michela Procesi, Xindong Xu","submitted_at":"2011-02-05T12:10:03Z","abstract_excerpt":"We define and describe the class of Quasi-T\\\"oplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scr\\\"odinger equation on the torus $T^d$, thus proving existence and stability of quasi-periodic solutions and recovering the results of [10]. With respect to that paper we consider only the NLS which preserves the total Momentum and exploit this conserved quantity in order to simplify our treatment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1066","kind":"arxiv","version":3},"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":"2026-05-18T02:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/k86b3hqfIC7ZjGBVMJUlknZhE/pRybmp4r/g6xXvka4xEKBXRsw+gpJABsbClYSE4+lgjx/NhrWW4twaDrlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:15:03.327450Z"},"content_sha256":"2c3c7a0b141bbad736ea522b4e21ed6d9b007f2f64c317a2989434ed683074bd","schema_version":"1.0","event_id":"sha256:2c3c7a0b141bbad736ea522b4e21ed6d9b007f2f64c317a2989434ed683074bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/bundle.json","state_url":"https://pith.science/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/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":"2026-06-21T11:15:03Z","links":{"resolver":"https://pith.science/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ","bundle":"https://pith.science/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/bundle.json","state":"https://pith.science/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TO2WM7WXPJ2LKOYXUJ7QHWE5OQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TO2WM7WXPJ2LKOYXUJ7QHWE5OQ","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":"7ec9139ece2fcf09aa2fd7d2fda924db4ec2f10ffd6324899a810b4cc1b35263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-05T12:10:03Z","title_canon_sha256":"0df269bb87410abeb151b1cf0196b34e328d4eed8564de9f42248fcdf2293e81"},"schema_version":"1.0","source":{"id":"1102.1066","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1066","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1066v3","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1066","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"TO2WM7WXPJ2L","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO2WM7WXPJ2LKOYX","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO2WM7WX","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:2c3c7a0b141bbad736ea522b4e21ed6d9b007f2f64c317a2989434ed683074bd","target":"graph","created_at":"2026-05-18T02:17:52Z","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 define and describe the class of Quasi-T\\\"oplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scr\\\"odinger equation on the torus $T^d$, thus proving existence and stability of quasi-periodic solutions and recovering the results of [10]. With respect to that paper we consider only the NLS which preserves the total Momentum and exploit this conserved quantity in order to simplify our treatment.","authors_text":"Michela Procesi, Xindong Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-05T12:10:03Z","title":"Quasi-T\\\"oplitz functions in KAM theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1066","kind":"arxiv","version":3},"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:f2125f99ff09eb828808190355258645d093c508906cad7b4e5e764f9cc312bf","target":"record","created_at":"2026-05-18T02:17:52Z","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":"7ec9139ece2fcf09aa2fd7d2fda924db4ec2f10ffd6324899a810b4cc1b35263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-05T12:10:03Z","title_canon_sha256":"0df269bb87410abeb151b1cf0196b34e328d4eed8564de9f42248fcdf2293e81"},"schema_version":"1.0","source":{"id":"1102.1066","kind":"arxiv","version":3}},"canonical_sha256":"9bb5667ed77a74b53b17a27f03d89d7426353fab0ddb3c6286bec9f13e7d3866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb5667ed77a74b53b17a27f03d89d7426353fab0ddb3c6286bec9f13e7d3866","first_computed_at":"2026-05-18T02:17:52.641958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:52.641958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eMwPE5GUuVrJVsqqZVdUghwtIGEtyEoqyX73Qulgz0HXv7kRsm72GUYUAq4dyYeftCx+T82tDhTeQfiEeiwzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:52.642645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1066","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2125f99ff09eb828808190355258645d093c508906cad7b4e5e764f9cc312bf","sha256:2c3c7a0b141bbad736ea522b4e21ed6d9b007f2f64c317a2989434ed683074bd"],"state_sha256":"186eef7fa79616aae4461a3b98d3cde5dcca8f41933c5692310cd642d5da4c7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8r2DXqeuEkHMuEqLzX1cu+r7iDTU5KSmn2JvrDAImRYiNgHs8GxfTOpK/yQhdmap+7OP5Hwi1u2kYlQ7UDQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:15:03.329414Z","bundle_sha256":"e1be3ae65ede4d46f0d0e0ff589d062a927c07ceaa9c7cd094ef58badee63c38"}}