{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2NXHH5QD4YYAN24W4XX7SCBWF6","short_pith_number":"pith:2NXHH5QD","canonical_record":{"source":{"id":"1504.00564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T14:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"10bba03dd9ea341fba7940602c9eb0abcf5cedf294be475f35d93b8b315d87fa","abstract_canon_sha256":"d6cf8c3e9c95ec1f3e32145196c48b1a89a1291a9958067662566422eb7ffa3c"},"schema_version":"1.0"},"canonical_sha256":"d36e73f603e63006eb96e5eff908362f957dbbed8e2e24910351e52e7d15215d","source":{"kind":"arxiv","id":"1504.00564","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00564","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00564v1","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00564","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"2NXHH5QD4YYA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NXHH5QD4YYAN24W","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NXHH5QD","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2NXHH5QD4YYAN24W4XX7SCBWF6","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T14:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"10bba03dd9ea341fba7940602c9eb0abcf5cedf294be475f35d93b8b315d87fa","abstract_canon_sha256":"d6cf8c3e9c95ec1f3e32145196c48b1a89a1291a9958067662566422eb7ffa3c"},"schema_version":"1.0"},"canonical_sha256":"d36e73f603e63006eb96e5eff908362f957dbbed8e2e24910351e52e7d15215d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.884719Z","signature_b64":"YgFik5WHbw8BgIJbLaNO6vKri40NPe8/aKfwUOEeP730Et83crsXcGLFqwJmZzfkUzlyibFGjZ+vwrsQbNCyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d36e73f603e63006eb96e5eff908362f957dbbed8e2e24910351e52e7d15215d","last_reissued_at":"2026-05-18T00:35:55.884354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.884354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00564","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPgkRHQTTK4qKzwP7z3nrgi8kG/B1jHeR+eJeK5YICMXpXDG+lwDJtuW75RoiEns7sPzpKV/CCoYEj5ZxD7LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:19:28.141584Z"},"content_sha256":"16fd4889cfcf2a8c468dab0b606c2ee90631ae04f257685fe6e5230f4c6bf9af","schema_version":"1.0","event_id":"sha256:16fd4889cfcf2a8c468dab0b606c2ee90631ae04f257685fe6e5230f4c6bf9af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2NXHH5QD4YYAN24W4XX7SCBWF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reducible quasi-periodic solutions for the Non Linear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Procesi, Michela Procesi","submitted_at":"2015-04-02T14:08:56Z","abstract_excerpt":"The present paper is devoted to the construction of small reducible quasi--periodic solutions for the completely resonant NLS equations on a $d$--dimensional torus $\\T^d$. The main point is to prove that prove that the normal form is reducible, block diagonal and satisfies the second Melnikov condition block wise. From this we deduce the result by a KAM algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00564","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":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+MYH8JgzanuW0IakM3FigHuPI+cgoP8km5vVgaP94APwc4rg3Gem8w951ffcOBRoa45eMoifdFGIfBuhPGwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:19:28.142247Z"},"content_sha256":"8e5222f3c3c46738c476c049b0351e5006612e2260e1580b6259f2c1e54e0430","schema_version":"1.0","event_id":"sha256:8e5222f3c3c46738c476c049b0351e5006612e2260e1580b6259f2c1e54e0430"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/bundle.json","state_url":"https://pith.science/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/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":"2026-05-31T01:19:28Z","links":{"resolver":"https://pith.science/pith/2NXHH5QD4YYAN24W4XX7SCBWF6","bundle":"https://pith.science/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/bundle.json","state":"https://pith.science/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NXHH5QD4YYAN24W4XX7SCBWF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NXHH5QD4YYAN24W4XX7SCBWF6","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":"d6cf8c3e9c95ec1f3e32145196c48b1a89a1291a9958067662566422eb7ffa3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T14:08:56Z","title_canon_sha256":"10bba03dd9ea341fba7940602c9eb0abcf5cedf294be475f35d93b8b315d87fa"},"schema_version":"1.0","source":{"id":"1504.00564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00564","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00564v1","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00564","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"2NXHH5QD4YYA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NXHH5QD4YYAN24W","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NXHH5QD","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:8e5222f3c3c46738c476c049b0351e5006612e2260e1580b6259f2c1e54e0430","target":"graph","created_at":"2026-05-18T00:35:55Z","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":"The present paper is devoted to the construction of small reducible quasi--periodic solutions for the completely resonant NLS equations on a $d$--dimensional torus $\\T^d$. The main point is to prove that prove that the normal form is reducible, block diagonal and satisfies the second Melnikov condition block wise. From this we deduce the result by a KAM algorithm.","authors_text":"Claudio Procesi, Michela Procesi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T14:08:56Z","title":"Reducible quasi-periodic solutions for the Non Linear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00564","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":"sha256:16fd4889cfcf2a8c468dab0b606c2ee90631ae04f257685fe6e5230f4c6bf9af","target":"record","created_at":"2026-05-18T00:35:55Z","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":"d6cf8c3e9c95ec1f3e32145196c48b1a89a1291a9958067662566422eb7ffa3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-02T14:08:56Z","title_canon_sha256":"10bba03dd9ea341fba7940602c9eb0abcf5cedf294be475f35d93b8b315d87fa"},"schema_version":"1.0","source":{"id":"1504.00564","kind":"arxiv","version":1}},"canonical_sha256":"d36e73f603e63006eb96e5eff908362f957dbbed8e2e24910351e52e7d15215d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d36e73f603e63006eb96e5eff908362f957dbbed8e2e24910351e52e7d15215d","first_computed_at":"2026-05-18T00:35:55.884354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.884354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YgFik5WHbw8BgIJbLaNO6vKri40NPe8/aKfwUOEeP730Et83crsXcGLFqwJmZzfkUzlyibFGjZ+vwrsQbNCyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.884719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16fd4889cfcf2a8c468dab0b606c2ee90631ae04f257685fe6e5230f4c6bf9af","sha256:8e5222f3c3c46738c476c049b0351e5006612e2260e1580b6259f2c1e54e0430"],"state_sha256":"d0ca267a1a6ff7f3f177592c6a2ae5953f9129a773a16b1b6329085ac738f32d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ny1i8Lon+ilgTw5ne1WgM7UYIFZLU3rIHeIPgXFnrnkB4rspNsgyRdq4dkd+i5JBgDE1Qa567/aViffdwG+lAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:19:28.145809Z","bundle_sha256":"baf3d60739c8f589a3513d2db71faf02b4a5bcb9d9129ab2baa9df2db04c3967"}}