{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:35M26MXEKKQR4VITADRYHPYSYN","short_pith_number":"pith:35M26MXE","canonical_record":{"source":{"id":"1504.03847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-15T10:06:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d13ea20468b92d51e0cdca982ff1d9bccae3c5fb4963de4b2e232a78c67750a2","abstract_canon_sha256":"f8f2433de094d7dc141dbe691193f4073031931a5c25b5b075827ffb50389753"},"schema_version":"1.0"},"canonical_sha256":"df59af32e452a11e551300e383bf12c369865202deec012553e3d0229a38d893","source":{"kind":"arxiv","id":"1504.03847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03847","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03847v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03847","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"35M26MXEKKQR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"35M26MXEKKQR4VIT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"35M26MXE","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:35M26MXEKKQR4VITADRYHPYSYN","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-15T10:06:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d13ea20468b92d51e0cdca982ff1d9bccae3c5fb4963de4b2e232a78c67750a2","abstract_canon_sha256":"f8f2433de094d7dc141dbe691193f4073031931a5c25b5b075827ffb50389753"},"schema_version":"1.0"},"canonical_sha256":"df59af32e452a11e551300e383bf12c369865202deec012553e3d0229a38d893","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:41.907991Z","signature_b64":"wVKV56IWaU6AY2YY47fitiTNcahQdfKxVreQMR+Ltl1Vnk/bLnv4k67qQBSQTmAoCHDg3TJlyhoEBTXsTfwNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df59af32e452a11e551300e383bf12c369865202deec012553e3d0229a38d893","last_reissued_at":"2026-05-18T02:18:41.907432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:41.907432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03847","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjjxghtC89xY/czM/yfETWavaAOaH6L4U4q5HewvoffQpLg8Ik8wZWca0Xzbu8pj6RvzMMY3kLHlaxERqA4uBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:45:01.299971Z"},"content_sha256":"f9c60be56b3d5e36eeb3caee202f3e6210b22063c7c606de9b4f2058ff7c2a2f","schema_version":"1.0","event_id":"sha256:f9c60be56b3d5e36eeb3caee202f3e6210b22063c7c606de9b4f2058ff7c2a2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:35M26MXEKKQR4VITADRYHPYSYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetries and Reduction of Discrete Painleve Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mensah Folly-Gbetoula","submitted_at":"2015-04-15T10:06:08Z","abstract_excerpt":"The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and we obtain a number of symmetries. These symmetries are used to construct exact solutions in some cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03847","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAk/J16nMOYwWA5dYZR23apzj6ojyaoglSLz7czaO092NlC+RRlWO6OyswnG7lFTqJDx/rpaXx2FDDoZAR8bAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:45:01.300688Z"},"content_sha256":"67f6d52f6e9d1d8745d7c0683276fa0861de0c3160244ddb4d2779f176e34bbd","schema_version":"1.0","event_id":"sha256:67f6d52f6e9d1d8745d7c0683276fa0861de0c3160244ddb4d2779f176e34bbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35M26MXEKKQR4VITADRYHPYSYN/bundle.json","state_url":"https://pith.science/pith/35M26MXEKKQR4VITADRYHPYSYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35M26MXEKKQR4VITADRYHPYSYN/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":"2026-07-02T02:45:01Z","links":{"resolver":"https://pith.science/pith/35M26MXEKKQR4VITADRYHPYSYN","bundle":"https://pith.science/pith/35M26MXEKKQR4VITADRYHPYSYN/bundle.json","state":"https://pith.science/pith/35M26MXEKKQR4VITADRYHPYSYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35M26MXEKKQR4VITADRYHPYSYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:35M26MXEKKQR4VITADRYHPYSYN","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":"f8f2433de094d7dc141dbe691193f4073031931a5c25b5b075827ffb50389753","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-15T10:06:08Z","title_canon_sha256":"d13ea20468b92d51e0cdca982ff1d9bccae3c5fb4963de4b2e232a78c67750a2"},"schema_version":"1.0","source":{"id":"1504.03847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03847","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03847v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03847","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"35M26MXEKKQR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"35M26MXEKKQR4VIT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"35M26MXE","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:67f6d52f6e9d1d8745d7c0683276fa0861de0c3160244ddb4d2779f176e34bbd","target":"graph","created_at":"2026-05-18T02:18:41Z","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":"The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and we obtain a number of symmetries. These symmetries are used to construct exact solutions in some cases.","authors_text":"Mensah Folly-Gbetoula","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-15T10:06:08Z","title":"Symmetries and Reduction of Discrete Painleve Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03847","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:f9c60be56b3d5e36eeb3caee202f3e6210b22063c7c606de9b4f2058ff7c2a2f","target":"record","created_at":"2026-05-18T02:18:41Z","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":"f8f2433de094d7dc141dbe691193f4073031931a5c25b5b075827ffb50389753","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-15T10:06:08Z","title_canon_sha256":"d13ea20468b92d51e0cdca982ff1d9bccae3c5fb4963de4b2e232a78c67750a2"},"schema_version":"1.0","source":{"id":"1504.03847","kind":"arxiv","version":1}},"canonical_sha256":"df59af32e452a11e551300e383bf12c369865202deec012553e3d0229a38d893","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df59af32e452a11e551300e383bf12c369865202deec012553e3d0229a38d893","first_computed_at":"2026-05-18T02:18:41.907432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:41.907432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wVKV56IWaU6AY2YY47fitiTNcahQdfKxVreQMR+Ltl1Vnk/bLnv4k67qQBSQTmAoCHDg3TJlyhoEBTXsTfwNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:41.907991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9c60be56b3d5e36eeb3caee202f3e6210b22063c7c606de9b4f2058ff7c2a2f","sha256:67f6d52f6e9d1d8745d7c0683276fa0861de0c3160244ddb4d2779f176e34bbd"],"state_sha256":"2398cc3510dce6d7e275fd2d11223bb65d1d0353401eab7f65515ddfd3eb431d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PYuyGoJKV5t0Gq9dVo0r58fklT5QSft2hO4DyWLgPci42OzhBS+k+DCT7D3amAk040GoPSOnXUEvbxGe8ylOBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T02:45:01.309084Z","bundle_sha256":"e97fbdb88cd6675eb5f033fe80253f97eb603e85425cb5cf983d0d3410fe0e4d"}}