{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:455NKOJKFW5KTTJ2O6DJRB7JTT","short_pith_number":"pith:455NKOJK","canonical_record":{"source":{"id":"1301.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T22:20:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"abbdf5fdf8b435488d117ebf61fe50f74d5d953b1c04077cb19a47f9ff8bd6f9","abstract_canon_sha256":"1f76000b8a9ad3bb306a556fc10f6ac53ecf993b0b4b0e406e1b0ca9fdb22b7f"},"schema_version":"1.0"},"canonical_sha256":"e77ad5392a2dbaa9cd3a77869887e99cdfb69625f21fa75150ccde84fd87b036","source":{"kind":"arxiv","id":"1301.5029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5029","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5029v1","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5029","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"455NKOJKFW5K","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"455NKOJKFW5KTTJ2","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"455NKOJK","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:455NKOJKFW5KTTJ2O6DJRB7JTT","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T22:20:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"abbdf5fdf8b435488d117ebf61fe50f74d5d953b1c04077cb19a47f9ff8bd6f9","abstract_canon_sha256":"1f76000b8a9ad3bb306a556fc10f6ac53ecf993b0b4b0e406e1b0ca9fdb22b7f"},"schema_version":"1.0"},"canonical_sha256":"e77ad5392a2dbaa9cd3a77869887e99cdfb69625f21fa75150ccde84fd87b036","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:44.955903Z","signature_b64":"5LlZp/5W8BpcxTYkmwEMBz+AX+rVupS5Fh1tEzXW4UgrQI6EvoDIXz9ijzx70Lh/+zNpJPpGuPhSXwVM82M5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e77ad5392a2dbaa9cd3a77869887e99cdfb69625f21fa75150ccde84fd87b036","last_reissued_at":"2026-05-18T02:37:44.955198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:44.955198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5029","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":"2026-05-18T02:37:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k44GvyGwJQgelfli9BUZCYb1TTdMTJ4a1ZmFSVnzfsTYLzlM2hJR2wqSwNx/0Agc915rz/tmTyappzKpJQZeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:18:50.254760Z"},"content_sha256":"efc48b7d0a9874784bb46fdbf539e8d8e4517b119535d0ee97536e0b6fb45602","schema_version":"1.0","event_id":"sha256:efc48b7d0a9874784bb46fdbf539e8d8e4517b119535d0ee97536e0b6fb45602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:455NKOJKFW5KTTJ2O6DJRB7JTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markoff-Rosenberger triples in arithmetic progression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Jos\\'e M. Tornero","submitted_at":"2013-01-21T22:20:13Z","abstract_excerpt":"We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5029","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":"2026-05-18T02:37:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hti+xJ29lrxEcPK0udFIP3ivYycluGxXTodmAMzYIemoNK76wpp9Yd1YmqQoaVLiuvSMfZuWBPXU3Eo3nuRRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:18:50.255110Z"},"content_sha256":"2f7fd7501d009bc9ed23b3cc0dac636c92a0931f75aab35fc6a3734e861be6eb","schema_version":"1.0","event_id":"sha256:2f7fd7501d009bc9ed23b3cc0dac636c92a0931f75aab35fc6a3734e861be6eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/bundle.json","state_url":"https://pith.science/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/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":"2026-06-29T14:18:50Z","links":{"resolver":"https://pith.science/pith/455NKOJKFW5KTTJ2O6DJRB7JTT","bundle":"https://pith.science/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/bundle.json","state":"https://pith.science/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/455NKOJKFW5KTTJ2O6DJRB7JTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:455NKOJKFW5KTTJ2O6DJRB7JTT","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":"1f76000b8a9ad3bb306a556fc10f6ac53ecf993b0b4b0e406e1b0ca9fdb22b7f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T22:20:13Z","title_canon_sha256":"abbdf5fdf8b435488d117ebf61fe50f74d5d953b1c04077cb19a47f9ff8bd6f9"},"schema_version":"1.0","source":{"id":"1301.5029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5029","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5029v1","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5029","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"455NKOJKFW5K","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"455NKOJKFW5KTTJ2","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"455NKOJK","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:2f7fd7501d009bc9ed23b3cc0dac636c92a0931f75aab35fc6a3734e861be6eb","target":"graph","created_at":"2026-05-18T02:37:44Z","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":"We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and ","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Jos\\'e M. Tornero","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T22:20:13Z","title":"Markoff-Rosenberger triples in arithmetic progression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5029","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:efc48b7d0a9874784bb46fdbf539e8d8e4517b119535d0ee97536e0b6fb45602","target":"record","created_at":"2026-05-18T02:37:44Z","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":"1f76000b8a9ad3bb306a556fc10f6ac53ecf993b0b4b0e406e1b0ca9fdb22b7f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-21T22:20:13Z","title_canon_sha256":"abbdf5fdf8b435488d117ebf61fe50f74d5d953b1c04077cb19a47f9ff8bd6f9"},"schema_version":"1.0","source":{"id":"1301.5029","kind":"arxiv","version":1}},"canonical_sha256":"e77ad5392a2dbaa9cd3a77869887e99cdfb69625f21fa75150ccde84fd87b036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e77ad5392a2dbaa9cd3a77869887e99cdfb69625f21fa75150ccde84fd87b036","first_computed_at":"2026-05-18T02:37:44.955198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:44.955198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5LlZp/5W8BpcxTYkmwEMBz+AX+rVupS5Fh1tEzXW4UgrQI6EvoDIXz9ijzx70Lh/+zNpJPpGuPhSXwVM82M5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:44.955903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efc48b7d0a9874784bb46fdbf539e8d8e4517b119535d0ee97536e0b6fb45602","sha256:2f7fd7501d009bc9ed23b3cc0dac636c92a0931f75aab35fc6a3734e861be6eb"],"state_sha256":"d50250c8cb7134699a3c0060d701211edb3cde1b4f15e86569ac1d9ddadd8d43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+JWeJZ3azjMU0NH5KIOZEgDT5b0+hhnzYY/nGfKgd8pXvGG6+ANbiQnDeHj3xyfPQrFrheOSGHx+ZkbD1LUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:18:50.257061Z","bundle_sha256":"0878270a27df51ca9907021f7c8fc83b0681261af1df1041747b6b3b27584e58"}}