{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ICCV53XD35JJCYA77W5K54L4DA","short_pith_number":"pith:ICCV53XD","canonical_record":{"source":{"id":"0908.1492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-08-11T11:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"70987b2671dd1bce6ef3a5123e25ec6538e1f119b926efe077ad06b8ac1ddb5a","abstract_canon_sha256":"be243dea101117491da058b4fd849bc6509d7f5fb1de2e74177882d214f16d9d"},"schema_version":"1.0"},"canonical_sha256":"40855eeee3df5291601ffdbaaef17c182fc28041de46b6aee08c2b907dcd5d45","source":{"kind":"arxiv","id":"0908.1492","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1492","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1492v1","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1492","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"ICCV53XD35JJ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"ICCV53XD35JJCYA7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"ICCV53XD","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ICCV53XD35JJCYA77W5K54L4DA","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-08-11T11:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"70987b2671dd1bce6ef3a5123e25ec6538e1f119b926efe077ad06b8ac1ddb5a","abstract_canon_sha256":"be243dea101117491da058b4fd849bc6509d7f5fb1de2e74177882d214f16d9d"},"schema_version":"1.0"},"canonical_sha256":"40855eeee3df5291601ffdbaaef17c182fc28041de46b6aee08c2b907dcd5d45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:35.624602Z","signature_b64":"aA5UhvBHt5l9qNVWoKoPsgIKahIMBW1VmxWHQnz3Uv1SovbH128WcS3GRw2QxStkRWt5r6mw1yAkfvFhtimCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40855eeee3df5291601ffdbaaef17c182fc28041de46b6aee08c2b907dcd5d45","last_reissued_at":"2026-05-18T02:12:35.623948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:35.623948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1492","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":"2026-05-18T02:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Cp61ynb+leq+pPJQcD054uwfgJn9zB+dS3PzrD7yDdtePbqJoG9ONu6tNW0gtaoytGRPv1B6qEL9rgiWkzwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:38:48.070338Z"},"content_sha256":"4d96a716bf2f15ea97f733da49d8dd2ca162749f2e41e65cb36ef64ff947f29b","schema_version":"1.0","event_id":"sha256:4d96a716bf2f15ea97f733da49d8dd2ca162749f2e41e65cb36ef64ff947f29b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ICCV53XD35JJCYA77W5K54L4DA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Paolo Maria Santini","submitted_at":"2009-08-11T11:10:26Z","abstract_excerpt":"We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the constru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1492","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":"2026-05-18T02:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qCNcWvBeAu+Y93QGcMya4yW3XTxIwHN1EBkMfMURW1JVHyEnTP9fYgWeLWMgvBX8ClOSrGZgAUNeHBHNqc9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:38:48.071026Z"},"content_sha256":"0a6f574ab86a355792b9dcd3c0675895ac4e32e78c8b701078f9b6bd3ae50c47","schema_version":"1.0","event_id":"sha256:0a6f574ab86a355792b9dcd3c0675895ac4e32e78c8b701078f9b6bd3ae50c47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICCV53XD35JJCYA77W5K54L4DA/bundle.json","state_url":"https://pith.science/pith/ICCV53XD35JJCYA77W5K54L4DA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICCV53XD35JJCYA77W5K54L4DA/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":"2026-05-31T05:38:48Z","links":{"resolver":"https://pith.science/pith/ICCV53XD35JJCYA77W5K54L4DA","bundle":"https://pith.science/pith/ICCV53XD35JJCYA77W5K54L4DA/bundle.json","state":"https://pith.science/pith/ICCV53XD35JJCYA77W5K54L4DA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICCV53XD35JJCYA77W5K54L4DA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ICCV53XD35JJCYA77W5K54L4DA","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":"be243dea101117491da058b4fd849bc6509d7f5fb1de2e74177882d214f16d9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-08-11T11:10:26Z","title_canon_sha256":"70987b2671dd1bce6ef3a5123e25ec6538e1f119b926efe077ad06b8ac1ddb5a"},"schema_version":"1.0","source":{"id":"0908.1492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1492","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1492v1","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1492","created_at":"2026-05-18T02:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"ICCV53XD35JJ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"ICCV53XD35JJCYA7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"ICCV53XD","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:0a6f574ab86a355792b9dcd3c0675895ac4e32e78c8b701078f9b6bd3ae50c47","target":"graph","created_at":"2026-05-18T02:12:35Z","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 propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the constru","authors_text":"Paolo Maria Santini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-08-11T11:10:26Z","title":"Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1492","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":"sha256:4d96a716bf2f15ea97f733da49d8dd2ca162749f2e41e65cb36ef64ff947f29b","target":"record","created_at":"2026-05-18T02:12:35Z","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":"be243dea101117491da058b4fd849bc6509d7f5fb1de2e74177882d214f16d9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-08-11T11:10:26Z","title_canon_sha256":"70987b2671dd1bce6ef3a5123e25ec6538e1f119b926efe077ad06b8ac1ddb5a"},"schema_version":"1.0","source":{"id":"0908.1492","kind":"arxiv","version":1}},"canonical_sha256":"40855eeee3df5291601ffdbaaef17c182fc28041de46b6aee08c2b907dcd5d45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40855eeee3df5291601ffdbaaef17c182fc28041de46b6aee08c2b907dcd5d45","first_computed_at":"2026-05-18T02:12:35.623948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:35.623948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aA5UhvBHt5l9qNVWoKoPsgIKahIMBW1VmxWHQnz3Uv1SovbH128WcS3GRw2QxStkRWt5r6mw1yAkfvFhtimCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:35.624602Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d96a716bf2f15ea97f733da49d8dd2ca162749f2e41e65cb36ef64ff947f29b","sha256:0a6f574ab86a355792b9dcd3c0675895ac4e32e78c8b701078f9b6bd3ae50c47"],"state_sha256":"fc31ce9c0c5eb8d862cf1822d28e181e027c8dba4f39e1b138f05f0ab2bb106e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7qCGuW/vhNEA5+Mzz6t4ZwAYIuuQeHm5VOyFA7BZcCtgORWpGUzf3+fzx0M5p2h6DLHA/AdrEhMmNGtA5tkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:38:48.074458Z","bundle_sha256":"ab71e9252b9cb48f73185d6a0b6550543ceec43ea1279540f87687bcc3f68f01"}}