{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:LFY3Q3KNL5TKJ7TYI5J4XYFENZ","short_pith_number":"pith:LFY3Q3KN","canonical_record":{"source":{"id":"math-ph/9801207","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-01-01T00:00:00Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ca2ec5fe6941998eeef62e2254342c799bd84f37e201eabb43bae96636917988","abstract_canon_sha256":"1d6a34da502682920b891b5d5a0f3cda930ba2849241402cf71a55f915f34b9a"},"schema_version":"1.0"},"canonical_sha256":"5971b86d4d5f66a4fe784753cbe0a46e55dc899a6d623e61fd7bdc8be23276dd","source":{"kind":"arxiv","id":"math-ph/9801207","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9801207","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9801207v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9801207","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"LFY3Q3KNL5TK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"LFY3Q3KNL5TKJ7TY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"LFY3Q3KN","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:LFY3Q3KNL5TKJ7TYI5J4XYFENZ","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/9801207","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-01-01T00:00:00Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ca2ec5fe6941998eeef62e2254342c799bd84f37e201eabb43bae96636917988","abstract_canon_sha256":"1d6a34da502682920b891b5d5a0f3cda930ba2849241402cf71a55f915f34b9a"},"schema_version":"1.0"},"canonical_sha256":"5971b86d4d5f66a4fe784753cbe0a46e55dc899a6d623e61fd7bdc8be23276dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:30.811738Z","signature_b64":"ji/S32E6387Dhj00iBSfZjDzBAg+8b0Q7N1rcztm1zyQ2mOX0s9puD/PhIdUPmAU5MJYYkCHWo/o5NY6W/+sCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5971b86d4d5f66a4fe784753cbe0a46e55dc899a6d623e61fd7bdc8be23276dd","last_reissued_at":"2026-05-18T01:38:30.811243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:30.811243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/9801207","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgRnJfYewoOCmmcTbxOaMzPcDDVGKUpFjt2xhIv+y8YNvjbSOgP2mygGcQvNLQtDx/WbSl3tQ4P75gEjR1T9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:39:52.044840Z"},"content_sha256":"bf658c72beeb445779b0faf600671f8f29e22f0202b25a7cb7740980e3596138","schema_version":"1.0","event_id":"sha256:bf658c72beeb445779b0faf600671f8f29e22f0202b25a7cb7740980e3596138"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:LFY3Q3KNL5TKJ7TYI5J4XYFENZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified approach to Miura, B\\\"acklund and Darboux transformations for nonlinear partial differential equations","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Esther Conde, P. G. Est\\'evez, Pilar R. Gordoa","submitted_at":"1998-01-01T00:00:00Z","abstract_excerpt":"This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlev\\'e Property systematically used as a tool for obtaining clear cut answers to almost all the questions related with Nonlinear Partial Differential Equations: Lax pairs, Miura, B\\\"acklund or Darboux Transformations as well as $\\tau$-functions, in a unified way. Besides to present the basics of the Method we exemplify this approach by applying it to four equations in $(1+1)$-dimensions. Two of them are related with the other two through Miura transformations that are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9801207","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e13t6oM2affAm5AlNiGx6K3PlNOsgbREdNU93GnSDE8nqPvVFZU0OzSM2R8lV8+PcCSmxHwn4KKSM07qIJXlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:39:52.045197Z"},"content_sha256":"21619c8e1d9074c53d7c33cdeb8acc8b9be42c8f80b59f16a6aac5a0f83fb77a","schema_version":"1.0","event_id":"sha256:21619c8e1d9074c53d7c33cdeb8acc8b9be42c8f80b59f16a6aac5a0f83fb77a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/bundle.json","state_url":"https://pith.science/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/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":"2026-06-21T08:39:52Z","links":{"resolver":"https://pith.science/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ","bundle":"https://pith.science/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/bundle.json","state":"https://pith.science/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFY3Q3KNL5TKJ7TYI5J4XYFENZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:LFY3Q3KNL5TKJ7TYI5J4XYFENZ","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":"1d6a34da502682920b891b5d5a0f3cda930ba2849241402cf71a55f915f34b9a","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-01-01T00:00:00Z","title_canon_sha256":"ca2ec5fe6941998eeef62e2254342c799bd84f37e201eabb43bae96636917988"},"schema_version":"1.0","source":{"id":"math-ph/9801207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9801207","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9801207v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9801207","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"LFY3Q3KNL5TK","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"LFY3Q3KNL5TKJ7TY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"LFY3Q3KN","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:21619c8e1d9074c53d7c33cdeb8acc8b9be42c8f80b59f16a6aac5a0f83fb77a","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlev\\'e Property systematically used as a tool for obtaining clear cut answers to almost all the questions related with Nonlinear Partial Differential Equations: Lax pairs, Miura, B\\\"acklund or Darboux Transformations as well as $\\tau$-functions, in a unified way. Besides to present the basics of the Method we exemplify this approach by applying it to four equations in $(1+1)$-dimensions. Two of them are related with the other two through Miura transformations that are ","authors_text":"Esther Conde, P. G. Est\\'evez, Pilar R. Gordoa","cross_cats":["math.AP","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1998-01-01T00:00:00Z","title":"Unified approach to Miura, B\\\"acklund and Darboux transformations for nonlinear partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9801207","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:bf658c72beeb445779b0faf600671f8f29e22f0202b25a7cb7740980e3596138","target":"record","created_at":"2026-05-18T01:38:30Z","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":"1d6a34da502682920b891b5d5a0f3cda930ba2849241402cf71a55f915f34b9a","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-01-01T00:00:00Z","title_canon_sha256":"ca2ec5fe6941998eeef62e2254342c799bd84f37e201eabb43bae96636917988"},"schema_version":"1.0","source":{"id":"math-ph/9801207","kind":"arxiv","version":1}},"canonical_sha256":"5971b86d4d5f66a4fe784753cbe0a46e55dc899a6d623e61fd7bdc8be23276dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5971b86d4d5f66a4fe784753cbe0a46e55dc899a6d623e61fd7bdc8be23276dd","first_computed_at":"2026-05-18T01:38:30.811243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.811243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ji/S32E6387Dhj00iBSfZjDzBAg+8b0Q7N1rcztm1zyQ2mOX0s9puD/PhIdUPmAU5MJYYkCHWo/o5NY6W/+sCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.811738Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9801207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf658c72beeb445779b0faf600671f8f29e22f0202b25a7cb7740980e3596138","sha256:21619c8e1d9074c53d7c33cdeb8acc8b9be42c8f80b59f16a6aac5a0f83fb77a"],"state_sha256":"2f2ad9d36aa8c556bf56f7fe5832af1a711ad29aaa628fbe78f1916585a96ebd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8t+IAwQB/jmo0FgWcCz32DwIlbUr37HqOjAqtOkOvo2etsjXKIVuBVLc0TVOGVq0tK9cIabnnqHVfC2IrpgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:39:52.047328Z","bundle_sha256":"2887c12ef788b0416967e1f4c5df5c4237c6c47212d17838b249d73b966ceabc"}}