{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZYV5W5IDKE7L6NYYFTSPIMYN7F","short_pith_number":"pith:ZYV5W5ID","canonical_record":{"source":{"id":"1602.01011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-02T17:09:44Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c51579b9c4879a50b71c2b13a4f96af32ac3f014a31bb841dcf7b347902ef65f","abstract_canon_sha256":"afd71e65e4c4f75167da5e1b884baf4cce106066901707c7e0a1b3bd9730ee57"},"schema_version":"1.0"},"canonical_sha256":"ce2bdb7503513ebf37182ce4f4330df96fb51e685484edaf9dc3d2e915840106","source":{"kind":"arxiv","id":"1602.01011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01011","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01011v1","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01011","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZYV5W5IDKE7L","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZYV5W5IDKE7L6NYY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZYV5W5ID","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZYV5W5IDKE7L6NYYFTSPIMYN7F","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-02T17:09:44Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c51579b9c4879a50b71c2b13a4f96af32ac3f014a31bb841dcf7b347902ef65f","abstract_canon_sha256":"afd71e65e4c4f75167da5e1b884baf4cce106066901707c7e0a1b3bd9730ee57"},"schema_version":"1.0"},"canonical_sha256":"ce2bdb7503513ebf37182ce4f4330df96fb51e685484edaf9dc3d2e915840106","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:48.977140Z","signature_b64":"BdgvDKGRrp3EI8BkL2khVq9JH9gfBw9u96nxDS5/p+kce5Icm9Moh4R4DMpqk1cj33OGkBIwL4HB3AcbzjQfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2bdb7503513ebf37182ce4f4330df96fb51e685484edaf9dc3d2e915840106","last_reissued_at":"2026-05-18T00:35:48.976462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:48.976462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01011","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":"2026-05-18T00:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpCiiuz3Hk68ecMMeTPymmWpmpeoofu/UNLqEOl+obAmB1Lk5GPkzl1SAW9GdoOoO7FImbvHeHq8WV7KyVKPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:04:55.124443Z"},"content_sha256":"eb1ee67e675888c49262d59760bf376df536a4e498f6d7a992b41425dc648a76","schema_version":"1.0","event_id":"sha256:eb1ee67e675888c49262d59760bf376df536a4e498f6d7a992b41425dc648a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZYV5W5IDKE7L6NYYFTSPIMYN7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diophantine equations via cluster transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Philipp Lampe","submitted_at":"2016-02-02T17:09:44Z","abstract_excerpt":"Motivated by Fomin and Zelevinsky's theory of cluster algebras we introduce a variant of the Markov equation; we show that all natural solutions of the equation arise from an initial solution by cluster transformations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01011","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":"2026-05-18T00:35:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTJpOPw1skhgE0hrmIGYQVoe4gcftGUhTpYTnf+0inVMkLq4KJ1OKPHzRddENMbMCbaGUGxlw+ZpsrjrMojwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:04:55.124792Z"},"content_sha256":"56a5ed8633be8666c2e62cd8514ac4cbf24980ef34a7b559c17a0b610f53aaa6","schema_version":"1.0","event_id":"sha256:56a5ed8633be8666c2e62cd8514ac4cbf24980ef34a7b559c17a0b610f53aaa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/bundle.json","state_url":"https://pith.science/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/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":"2026-07-01T21:04:55Z","links":{"resolver":"https://pith.science/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F","bundle":"https://pith.science/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/bundle.json","state":"https://pith.science/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYV5W5IDKE7L6NYYFTSPIMYN7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZYV5W5IDKE7L6NYYFTSPIMYN7F","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":"afd71e65e4c4f75167da5e1b884baf4cce106066901707c7e0a1b3bd9730ee57","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-02T17:09:44Z","title_canon_sha256":"c51579b9c4879a50b71c2b13a4f96af32ac3f014a31bb841dcf7b347902ef65f"},"schema_version":"1.0","source":{"id":"1602.01011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01011","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01011v1","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01011","created_at":"2026-05-18T00:35:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZYV5W5IDKE7L","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZYV5W5IDKE7L6NYY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZYV5W5ID","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:56a5ed8633be8666c2e62cd8514ac4cbf24980ef34a7b559c17a0b610f53aaa6","target":"graph","created_at":"2026-05-18T00:35:48Z","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":"Motivated by Fomin and Zelevinsky's theory of cluster algebras we introduce a variant of the Markov equation; we show that all natural solutions of the equation arise from an initial solution by cluster transformations.","authors_text":"Philipp Lampe","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-02T17:09:44Z","title":"Diophantine equations via cluster transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01011","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:eb1ee67e675888c49262d59760bf376df536a4e498f6d7a992b41425dc648a76","target":"record","created_at":"2026-05-18T00:35:48Z","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":"afd71e65e4c4f75167da5e1b884baf4cce106066901707c7e0a1b3bd9730ee57","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-02T17:09:44Z","title_canon_sha256":"c51579b9c4879a50b71c2b13a4f96af32ac3f014a31bb841dcf7b347902ef65f"},"schema_version":"1.0","source":{"id":"1602.01011","kind":"arxiv","version":1}},"canonical_sha256":"ce2bdb7503513ebf37182ce4f4330df96fb51e685484edaf9dc3d2e915840106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce2bdb7503513ebf37182ce4f4330df96fb51e685484edaf9dc3d2e915840106","first_computed_at":"2026-05-18T00:35:48.976462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:48.976462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BdgvDKGRrp3EI8BkL2khVq9JH9gfBw9u96nxDS5/p+kce5Icm9Moh4R4DMpqk1cj33OGkBIwL4HB3AcbzjQfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:48.977140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb1ee67e675888c49262d59760bf376df536a4e498f6d7a992b41425dc648a76","sha256:56a5ed8633be8666c2e62cd8514ac4cbf24980ef34a7b559c17a0b610f53aaa6"],"state_sha256":"034c8e25f3a2b5045a3bf7b4743738d316c9137707e2568c082c8b0344e73f38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1SPw9rBqX+LuuuIWMNrFHwm32ufHeWMeTzf8h3dKCwMNAunwGmwa4AH+KecwFGVZJV5dI3sDwE/UcZQfM7tCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:04:55.126789Z","bundle_sha256":"f3b89f601f80e858b5df4a8b9c4c93ea45fa1ad585b7fb4bf9d59624a5a5c054"}}