{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7WPW5Q53BCIGC5S3ULB5NLHPP6","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":"cf05470dd78d1310914b22e7ef43bcf8b318b67e8acfd7d3b6023c0892043bb3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-03-10T15:26:47Z","title_canon_sha256":"125df0e19bb2485f03c2168b936242bf6e566e6039fa8dc2f39a665b0e10de3e"},"schema_version":"1.0","source":{"id":"0803.1439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1439","created_at":"2026-05-18T01:20:31Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1439v1","created_at":"2026-05-18T01:20:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1439","created_at":"2026-05-18T01:20:31Z"},{"alias_kind":"pith_short_12","alias_value":"7WPW5Q53BCIG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7WPW5Q53BCIGC5S3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7WPW5Q53","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:c2359a2f2ff9372dbb7659a278a9f0cb8c1fed1960fa068cc1f5a844778c315f","target":"graph","created_at":"2026-05-18T01:20:31Z","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":"A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are difference counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.","authors_text":"Blazej M. Szablikowski, Burcu Silindir, Maciej Blaszak","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-03-10T15:26:47Z","title":"R-matrix approach to integrable systems on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1439","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":"sha256:79121ece4b72bba35897d127b32c4c7ed849ddd4e8ca3399446fc949be93a840","target":"record","created_at":"2026-05-18T01:20:31Z","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":"cf05470dd78d1310914b22e7ef43bcf8b318b67e8acfd7d3b6023c0892043bb3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-03-10T15:26:47Z","title_canon_sha256":"125df0e19bb2485f03c2168b936242bf6e566e6039fa8dc2f39a665b0e10de3e"},"schema_version":"1.0","source":{"id":"0803.1439","kind":"arxiv","version":1}},"canonical_sha256":"fd9f6ec3bb089061765ba2c3d6acef7f956ad65ef9280df8a256abcda444a8c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd9f6ec3bb089061765ba2c3d6acef7f956ad65ef9280df8a256abcda444a8c4","first_computed_at":"2026-05-18T01:20:31.907058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:31.907058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hnq6mJ/g81a6ty4jISp7vXqcYlxbG8+CavJP06Oa5WckGXJWzdx2B4OJPVFc24hA7UpNYCYEsVJ6CP7pAqAwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:31.907464Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79121ece4b72bba35897d127b32c4c7ed849ddd4e8ca3399446fc949be93a840","sha256:c2359a2f2ff9372dbb7659a278a9f0cb8c1fed1960fa068cc1f5a844778c315f"],"state_sha256":"d5fb92057aff86bbddf00449a37ab53c1d2777d05fed7ddd8cf349702088cfbb"}