{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NVM3OSQOJWZV6JCUTULUFOZCAW","short_pith_number":"pith:NVM3OSQO","canonical_record":{"source":{"id":"1210.5038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a9a0dd4447fce3ff8cb31e1ebaa0609fe50079c3bc93be955ddfcc52b77719fe","abstract_canon_sha256":"387e4546353e4a9737e67d62ea020cb45c88cada96330a8bfab07fde2cacdaa8"},"schema_version":"1.0"},"canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","source":{"kind":"arxiv","id":"1210.5038","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5038","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5038v1","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5038","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"NVM3OSQOJWZV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NVM3OSQOJWZV6JCU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NVM3OSQO","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NVM3OSQOJWZV6JCUTULUFOZCAW","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a9a0dd4447fce3ff8cb31e1ebaa0609fe50079c3bc93be955ddfcc52b77719fe","abstract_canon_sha256":"387e4546353e4a9737e67d62ea020cb45c88cada96330a8bfab07fde2cacdaa8"},"schema_version":"1.0"},"canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:54.468089Z","signature_b64":"dDceruyRZoXt5gYuA8MoTn9U3KwUpuhjtsF57Rl8UtyH+NOXkA4gn6YQoCkpN7i2AJ+3LBLHcgG3x0LNhOO1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","last_reissued_at":"2026-05-18T03:42:54.467519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:54.467519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5038","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":"2026-05-18T03:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYrZUiXp+JYNmBcgLJ6iPBCG9Tclma/jRHHtkerktQoLBMzmUp4oSglX7pQ9N61DBvqGqXOUY+3bDRd5C8ncCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:44:34.475555Z"},"content_sha256":"7aa67910826d3090e212e7ce720d7560b6df3f35f2da6b5fcb187ab1c37666ab","schema_version":"1.0","event_id":"sha256:7aa67910826d3090e212e7ce720d7560b6df3f35f2da6b5fcb187ab1c37666ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NVM3OSQOJWZV6JCUTULUFOZCAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular solution and lattice miura transformation of bigraded Toda Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Chuanzhong Li, Jingsong He","submitted_at":"2012-10-18T07:24:34Z","abstract_excerpt":"In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the $(1,2)$-BTH with $3\\times 3$-sized Lax matrix, and discuss some geometric structure of the solution from which the difference between $(1,2)$-BTH and original Toda hierarchy is shown. After this, we construct another kind of Lax representation of $(N,1)$-bigraded Toda hierarchy($(N,1)$-BTH) which does not use the fractional operator of Lax operator. Then we introduce lattice Miura transformation o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5038","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":"2026-05-18T03:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9x4F1MU+biCuz4vDxyNQTejv0RLrXDwqbkEydzzA52blJJCs0LuU7cIy0pePxYGHOtOPjwHgx6EPLQ7fJlqQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:44:34.475898Z"},"content_sha256":"40a29ea961b8d58057fc991a8b83d30e6305022a56f4a3751f030587e79380dc","schema_version":"1.0","event_id":"sha256:40a29ea961b8d58057fc991a8b83d30e6305022a56f4a3751f030587e79380dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/bundle.json","state_url":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/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":"2026-06-03T14:44:34Z","links":{"resolver":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW","bundle":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/bundle.json","state":"https://pith.science/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVM3OSQOJWZV6JCUTULUFOZCAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NVM3OSQOJWZV6JCUTULUFOZCAW","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":"387e4546353e4a9737e67d62ea020cb45c88cada96330a8bfab07fde2cacdaa8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","title_canon_sha256":"a9a0dd4447fce3ff8cb31e1ebaa0609fe50079c3bc93be955ddfcc52b77719fe"},"schema_version":"1.0","source":{"id":"1210.5038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5038","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5038v1","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5038","created_at":"2026-05-18T03:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"NVM3OSQOJWZV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NVM3OSQOJWZV6JCU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NVM3OSQO","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:40a29ea961b8d58057fc991a8b83d30e6305022a56f4a3751f030587e79380dc","target":"graph","created_at":"2026-05-18T03:42:54Z","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":"In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the $(1,2)$-BTH with $3\\times 3$-sized Lax matrix, and discuss some geometric structure of the solution from which the difference between $(1,2)$-BTH and original Toda hierarchy is shown. After this, we construct another kind of Lax representation of $(N,1)$-bigraded Toda hierarchy($(N,1)$-BTH) which does not use the fractional operator of Lax operator. Then we introduce lattice Miura transformation o","authors_text":"Chuanzhong Li, Jingsong He","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","title":"Regular solution and lattice miura transformation of bigraded Toda Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5038","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":"sha256:7aa67910826d3090e212e7ce720d7560b6df3f35f2da6b5fcb187ab1c37666ab","target":"record","created_at":"2026-05-18T03:42:54Z","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":"387e4546353e4a9737e67d62ea020cb45c88cada96330a8bfab07fde2cacdaa8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-10-18T07:24:34Z","title_canon_sha256":"a9a0dd4447fce3ff8cb31e1ebaa0609fe50079c3bc93be955ddfcc52b77719fe"},"schema_version":"1.0","source":{"id":"1210.5038","kind":"arxiv","version":1}},"canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d59b74a0e4db35f24549d1742bb2205af35b27dd4f4ca981e1d5c435e4ccdb0","first_computed_at":"2026-05-18T03:42:54.467519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:54.467519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dDceruyRZoXt5gYuA8MoTn9U3KwUpuhjtsF57Rl8UtyH+NOXkA4gn6YQoCkpN7i2AJ+3LBLHcgG3x0LNhOO1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:54.468089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa67910826d3090e212e7ce720d7560b6df3f35f2da6b5fcb187ab1c37666ab","sha256:40a29ea961b8d58057fc991a8b83d30e6305022a56f4a3751f030587e79380dc"],"state_sha256":"41af3b46840fe0c1152cbcde1652c3be2d9e8ed2664cc6bad55d43da4781cce2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"70/yYBLlXMYSbyXdxoMx1tx3i8PnFgoADDXzRQd4o1MaAItheVQ9lPPLRGkwnd8ezS72QkiIBvS/MKu2vM0nBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:44:34.477864Z","bundle_sha256":"5e5f371f2783abe51d66d7362fe85ab1bf9b6b928d495c301bf6184052d891e0"}}