{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5VJIE2AAIXSR66VXZDWHW3EZ2S","short_pith_number":"pith:5VJIE2AA","canonical_record":{"source":{"id":"1503.06481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-22T21:31:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6d1e5936afb1d82d800b1bce0140d1dc703fca24bb7f5ed1d785e779ef9026cd","abstract_canon_sha256":"8896ad5d0485388843f9a29dcd0f9016c83e565b06ff25427aafc94735baed3d"},"schema_version":"1.0"},"canonical_sha256":"ed5282680045e51f7ab7c8ec7b6c99d49defc57841187cf713170f7ea62184f3","source":{"kind":"arxiv","id":"1503.06481","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06481","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06481v2","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06481","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"5VJIE2AAIXSR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5VJIE2AAIXSR66VX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5VJIE2AA","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5VJIE2AAIXSR66VXZDWHW3EZ2S","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-22T21:31:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6d1e5936afb1d82d800b1bce0140d1dc703fca24bb7f5ed1d785e779ef9026cd","abstract_canon_sha256":"8896ad5d0485388843f9a29dcd0f9016c83e565b06ff25427aafc94735baed3d"},"schema_version":"1.0"},"canonical_sha256":"ed5282680045e51f7ab7c8ec7b6c99d49defc57841187cf713170f7ea62184f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:21.333591Z","signature_b64":"durD13YCjN5AX3u6g8STCI4gZJLFO7KhaVDyjPcXbC0X2hqxo0HDZEVBKxhDESF0kkWNgi7+q3YWdqcPw+ixDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed5282680045e51f7ab7c8ec7b6c99d49defc57841187cf713170f7ea62184f3","last_reissued_at":"2026-05-17T23:45:21.332961Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:21.332961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06481","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlEARwuLwGN6SSVFScrRUJYRQl7tDpavU7/2LC59j/wMPWyxdjiBcUBTE0Q8dvpkBCAb5cWyotSI++XV7nJsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:04:08.037471Z"},"content_sha256":"9df7a50e3a6efbdb95b0c8ec9de055bf1cc83167fb4a102b4f5cdfedf822e338","schema_version":"1.0","event_id":"sha256:9df7a50e3a6efbdb95b0c8ec9de055bf1cc83167fb4a102b4f5cdfedf822e338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5VJIE2AAIXSR66VXZDWHW3EZ2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surfaces containing two circles through each point and Pythagorean 6-tuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"M. Skopenkov, R. Krasauskas","submitted_at":"2015-03-22T21:31:10Z","abstract_excerpt":"We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darboux from XIXth century. We reduce finding all such surfaces to the algebraic problem of finding all Pythagorean 6-tuples of polynomials. The reduction is based on the Schicho parametrization of surfaces containing two conics through each point and a new approach using quaternionic rational parametrization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06481","kind":"arxiv","version":2},"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":"2026-05-17T23:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MABezj0dd/IfLJAvWOEWKpId6Zp+QE0ohtr1aoGRGqFZUTsaBlhwcc0NtC3jUiHMBoFxbuQ5yEAOmMmZnt0tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:04:08.037804Z"},"content_sha256":"fc2d5658a116dbdb8dc7e4c43651314b2b71a4e87938ae7602884c211cd4f506","schema_version":"1.0","event_id":"sha256:fc2d5658a116dbdb8dc7e4c43651314b2b71a4e87938ae7602884c211cd4f506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/bundle.json","state_url":"https://pith.science/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/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":"2026-06-25T18:04:08Z","links":{"resolver":"https://pith.science/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S","bundle":"https://pith.science/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/bundle.json","state":"https://pith.science/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VJIE2AAIXSR66VXZDWHW3EZ2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5VJIE2AAIXSR66VXZDWHW3EZ2S","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":"8896ad5d0485388843f9a29dcd0f9016c83e565b06ff25427aafc94735baed3d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-22T21:31:10Z","title_canon_sha256":"6d1e5936afb1d82d800b1bce0140d1dc703fca24bb7f5ed1d785e779ef9026cd"},"schema_version":"1.0","source":{"id":"1503.06481","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06481","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06481v2","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06481","created_at":"2026-05-17T23:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"5VJIE2AAIXSR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5VJIE2AAIXSR66VX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5VJIE2AA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:fc2d5658a116dbdb8dc7e4c43651314b2b71a4e87938ae7602884c211cd4f506","target":"graph","created_at":"2026-05-17T23:45:21Z","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 analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darboux from XIXth century. We reduce finding all such surfaces to the algebraic problem of finding all Pythagorean 6-tuples of polynomials. The reduction is based on the Schicho parametrization of surfaces containing two conics through each point and a new approach using quaternionic rational parametrization.","authors_text":"M. Skopenkov, R. Krasauskas","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-22T21:31:10Z","title":"Surfaces containing two circles through each point and Pythagorean 6-tuples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06481","kind":"arxiv","version":2},"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":"sha256:9df7a50e3a6efbdb95b0c8ec9de055bf1cc83167fb4a102b4f5cdfedf822e338","target":"record","created_at":"2026-05-17T23:45:21Z","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":"8896ad5d0485388843f9a29dcd0f9016c83e565b06ff25427aafc94735baed3d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-22T21:31:10Z","title_canon_sha256":"6d1e5936afb1d82d800b1bce0140d1dc703fca24bb7f5ed1d785e779ef9026cd"},"schema_version":"1.0","source":{"id":"1503.06481","kind":"arxiv","version":2}},"canonical_sha256":"ed5282680045e51f7ab7c8ec7b6c99d49defc57841187cf713170f7ea62184f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed5282680045e51f7ab7c8ec7b6c99d49defc57841187cf713170f7ea62184f3","first_computed_at":"2026-05-17T23:45:21.332961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:21.332961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"durD13YCjN5AX3u6g8STCI4gZJLFO7KhaVDyjPcXbC0X2hqxo0HDZEVBKxhDESF0kkWNgi7+q3YWdqcPw+ixDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:21.333591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06481","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df7a50e3a6efbdb95b0c8ec9de055bf1cc83167fb4a102b4f5cdfedf822e338","sha256:fc2d5658a116dbdb8dc7e4c43651314b2b71a4e87938ae7602884c211cd4f506"],"state_sha256":"5b67d108c9a3f765c3aa7d0beccc901b3f60cc3be7f31db51b7585b4bf369108"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VuFU0OojXnJu6XPPH3FhenyO1qytO/UItmy+8TirL62stEhKtNRvqHh8Gtg2CnfxtXlNzSresy20hJPGyyJNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:04:08.039591Z","bundle_sha256":"401c9abaff6d86ea51772c730b12ea7853bcf32fc4a54bc2182251b737fecc6b"}}