{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PFRP5S7XWJRIFXV3MPWLAMQJ5I","short_pith_number":"pith:PFRP5S7X","canonical_record":{"source":{"id":"1606.02946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-09T13:13:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0a62f66aaf443ffdd13b74d211b87fff85c87b84d0235a54afde4b7e39efb2f","abstract_canon_sha256":"43b7ff49162339e1f567837defdc042ffba052b5f46ed1fe631a902574fea2d2"},"schema_version":"1.0"},"canonical_sha256":"7962fecbf7b26282debb63ecb03209ea2da679ca95e811b135fc5f29fc9b7186","source":{"kind":"arxiv","id":"1606.02946","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02946","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02946v2","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02946","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"PFRP5S7XWJRI","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFRP5S7XWJRIFXV3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFRP5S7X","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PFRP5S7XWJRIFXV3MPWLAMQJ5I","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-09T13:13:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0a62f66aaf443ffdd13b74d211b87fff85c87b84d0235a54afde4b7e39efb2f","abstract_canon_sha256":"43b7ff49162339e1f567837defdc042ffba052b5f46ed1fe631a902574fea2d2"},"schema_version":"1.0"},"canonical_sha256":"7962fecbf7b26282debb63ecb03209ea2da679ca95e811b135fc5f29fc9b7186","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:23.186971Z","signature_b64":"s6dBQS6e0tzYCI/6zbg/vHYvoPPW6lkmK0fRXz1TtNlCk73ARUKzcybxQDN/Tj6yoodGQFPt0gDX1ZVX+KKPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7962fecbf7b26282debb63ecb03209ea2da679ca95e811b135fc5f29fc9b7186","last_reissued_at":"2026-05-18T01:10:23.186531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:23.186531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02946","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lw4RFuSvcy6JEY4GFFEkxh03/R0gwsWO28W9eKvSTtXO53D19nPf3Z2VjzL/DKUPk4+mFvyg8JX5kl71PykpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:54:42.838179Z"},"content_sha256":"726136d0d0b15a32431f976e5c1fdea718751e5df165c39d6b3fdf7a1da4b325","schema_version":"1.0","event_id":"sha256:726136d0d0b15a32431f976e5c1fdea718751e5df165c39d6b3fdf7a1da4b325"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PFRP5S7XWJRIFXV3MPWLAMQJ5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lectures on Classical Integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Alessandro Torrielli","submitted_at":"2016-06-09T13:13:36Z","abstract_excerpt":"We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schroedinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02946","kind":"arxiv","version":2},"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":"2026-05-18T01:10:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aWjKjXunRsh8NInEvD+kKzXtofinpo9G9BmttIhna2bq7ZMtujSNc/ixN12Ql5HXfdY2c1AJpzWr/MMQ9WJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:54:42.838869Z"},"content_sha256":"082a0f054771b2d4ae468816e3863c0d2f362dadc3052681372d6ed3ee00e2cd","schema_version":"1.0","event_id":"sha256:082a0f054771b2d4ae468816e3863c0d2f362dadc3052681372d6ed3ee00e2cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/bundle.json","state_url":"https://pith.science/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/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":"2026-05-22T03:54:42Z","links":{"resolver":"https://pith.science/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I","bundle":"https://pith.science/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/bundle.json","state":"https://pith.science/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFRP5S7XWJRIFXV3MPWLAMQJ5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PFRP5S7XWJRIFXV3MPWLAMQJ5I","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":"43b7ff49162339e1f567837defdc042ffba052b5f46ed1fe631a902574fea2d2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-09T13:13:36Z","title_canon_sha256":"c0a62f66aaf443ffdd13b74d211b87fff85c87b84d0235a54afde4b7e39efb2f"},"schema_version":"1.0","source":{"id":"1606.02946","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02946","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02946v2","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02946","created_at":"2026-05-18T01:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"PFRP5S7XWJRI","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PFRP5S7XWJRIFXV3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PFRP5S7X","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:082a0f054771b2d4ae468816e3863c0d2f362dadc3052681372d6ed3ee00e2cd","target":"graph","created_at":"2026-05-18T01:10:23Z","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 review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schroedinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classi","authors_text":"Alessandro Torrielli","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-09T13:13:36Z","title":"Lectures on Classical Integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02946","kind":"arxiv","version":2},"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":"sha256:726136d0d0b15a32431f976e5c1fdea718751e5df165c39d6b3fdf7a1da4b325","target":"record","created_at":"2026-05-18T01:10:23Z","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":"43b7ff49162339e1f567837defdc042ffba052b5f46ed1fe631a902574fea2d2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-06-09T13:13:36Z","title_canon_sha256":"c0a62f66aaf443ffdd13b74d211b87fff85c87b84d0235a54afde4b7e39efb2f"},"schema_version":"1.0","source":{"id":"1606.02946","kind":"arxiv","version":2}},"canonical_sha256":"7962fecbf7b26282debb63ecb03209ea2da679ca95e811b135fc5f29fc9b7186","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7962fecbf7b26282debb63ecb03209ea2da679ca95e811b135fc5f29fc9b7186","first_computed_at":"2026-05-18T01:10:23.186531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:23.186531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s6dBQS6e0tzYCI/6zbg/vHYvoPPW6lkmK0fRXz1TtNlCk73ARUKzcybxQDN/Tj6yoodGQFPt0gDX1ZVX+KKPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:23.186971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02946","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:726136d0d0b15a32431f976e5c1fdea718751e5df165c39d6b3fdf7a1da4b325","sha256:082a0f054771b2d4ae468816e3863c0d2f362dadc3052681372d6ed3ee00e2cd"],"state_sha256":"19ed8a769446b1682f0f6fb10b8b38f594dbeab7a3db21538d2a90b7a28b1a2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBMlmSl2mdPVEpuMmrTyRaofuWezUKOg4dVn6iZxatUFG+TCPLPeqw5asl6+6LQBFTgexLIiXTZ4nhm+wZQWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:54:42.842817Z","bundle_sha256":"d67e9d16b206764c221587bb4f61f95771fb8e980ffc83c45a3615e474ce7afd"}}