{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LDTKDLJYU3XWQGLXEG3WSQVYBZ","short_pith_number":"pith:LDTKDLJY","canonical_record":{"source":{"id":"0901.4652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-29T11:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"675f59ea6e942b992306ea4938852a63601a219ca6cb1fc7b5ad50bf17f98147","abstract_canon_sha256":"776408f1924a5024b814bfcef25a8fa2a9c64092228b896e6a9f847d629ac2ce"},"schema_version":"1.0"},"canonical_sha256":"58e6a1ad38a6ef68197721b76942b80e4e4d55a255b7e6aee08932b1a0e8fe1a","source":{"kind":"arxiv","id":"0901.4652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4652","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4652v1","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4652","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"LDTKDLJYU3XW","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LDTKDLJYU3XWQGLX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LDTKDLJY","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LDTKDLJYU3XWQGLXEG3WSQVYBZ","target":"record","payload":{"canonical_record":{"source":{"id":"0901.4652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-29T11:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"675f59ea6e942b992306ea4938852a63601a219ca6cb1fc7b5ad50bf17f98147","abstract_canon_sha256":"776408f1924a5024b814bfcef25a8fa2a9c64092228b896e6a9f847d629ac2ce"},"schema_version":"1.0"},"canonical_sha256":"58e6a1ad38a6ef68197721b76942b80e4e4d55a255b7e6aee08932b1a0e8fe1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:57.680423Z","signature_b64":"36nRWbF7CNQRcZCa4ZyKTulAne1T9h0xcJhMGPbtE8SO7zw5DJpj5J5SPyaGokNnxSzsvja8OZu+8Ou6E/TCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58e6a1ad38a6ef68197721b76942b80e4e4d55a255b7e6aee08932b1a0e8fe1a","last_reissued_at":"2026-05-18T03:02:57.679775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:57.679775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.4652","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":"2026-05-18T03:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4SsPgLTI0vWJ2HS2S1np3iy+qEg8mEDSVNp4gSFISY9k1LAtfcLgL1k1W/GGjOkqA4ysZ7Y8+1b58wMfNDXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:41:22.982910Z"},"content_sha256":"c52e0cdbb264027a831993843e07e4f01a1b8f5517958727f2a1b1c454cd737f","schema_version":"1.0","event_id":"sha256:c52e0cdbb264027a831993843e07e4f01a1b8f5517958727f2a1b1c454cd737f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LDTKDLJYU3XWQGLXEG3WSQVYBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational Conchoids of Algebraic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J.R. Sendra, J. Sendra","submitted_at":"2009-01-29T11:21:13Z","abstract_excerpt":"We study the rationality of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the isotropic lines, of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4652","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":"2026-05-18T03:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbsRAlV/p2iZwFYLL1C4k/tqXUJUONIdBLAKXxzQKMKzab5zTyGUuxymsh7pyVIg85bOLZpQAbozXsCs7bfwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:41:22.983253Z"},"content_sha256":"5bb595bf2ae5b6ddddad9fb1f8ead0018e803c0e67642ccae08e83b2ce6ecefe","schema_version":"1.0","event_id":"sha256:5bb595bf2ae5b6ddddad9fb1f8ead0018e803c0e67642ccae08e83b2ce6ecefe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/bundle.json","state_url":"https://pith.science/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/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":"2026-07-06T18:41:22Z","links":{"resolver":"https://pith.science/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ","bundle":"https://pith.science/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/bundle.json","state":"https://pith.science/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDTKDLJYU3XWQGLXEG3WSQVYBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LDTKDLJYU3XWQGLXEG3WSQVYBZ","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":"776408f1924a5024b814bfcef25a8fa2a9c64092228b896e6a9f847d629ac2ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-29T11:21:13Z","title_canon_sha256":"675f59ea6e942b992306ea4938852a63601a219ca6cb1fc7b5ad50bf17f98147"},"schema_version":"1.0","source":{"id":"0901.4652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4652","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4652v1","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4652","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"LDTKDLJYU3XW","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LDTKDLJYU3XWQGLX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LDTKDLJY","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:5bb595bf2ae5b6ddddad9fb1f8ead0018e803c0e67642ccae08e83b2ce6ecefe","target":"graph","created_at":"2026-05-18T03:02:57Z","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 rationality of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the isotropic lines, of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base ","authors_text":"J.R. Sendra, J. Sendra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-29T11:21:13Z","title":"Rational Conchoids of Algebraic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4652","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:c52e0cdbb264027a831993843e07e4f01a1b8f5517958727f2a1b1c454cd737f","target":"record","created_at":"2026-05-18T03:02:57Z","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":"776408f1924a5024b814bfcef25a8fa2a9c64092228b896e6a9f847d629ac2ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-29T11:21:13Z","title_canon_sha256":"675f59ea6e942b992306ea4938852a63601a219ca6cb1fc7b5ad50bf17f98147"},"schema_version":"1.0","source":{"id":"0901.4652","kind":"arxiv","version":1}},"canonical_sha256":"58e6a1ad38a6ef68197721b76942b80e4e4d55a255b7e6aee08932b1a0e8fe1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58e6a1ad38a6ef68197721b76942b80e4e4d55a255b7e6aee08932b1a0e8fe1a","first_computed_at":"2026-05-18T03:02:57.679775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:57.679775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"36nRWbF7CNQRcZCa4ZyKTulAne1T9h0xcJhMGPbtE8SO7zw5DJpj5J5SPyaGokNnxSzsvja8OZu+8Ou6E/TCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:57.680423Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c52e0cdbb264027a831993843e07e4f01a1b8f5517958727f2a1b1c454cd737f","sha256:5bb595bf2ae5b6ddddad9fb1f8ead0018e803c0e67642ccae08e83b2ce6ecefe"],"state_sha256":"c0fce2f04cff6b0a4ea6b21db45a942876858389093ffce080ddc8e9cd81516f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yo/lBh3B2PthOhi5o8B8FRwFgowstsSLEZRt38eVWsoFG4mKXraqoqxm0KLyfwvfIQCWFEDMXYLXogeTEKq+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:41:22.985095Z","bundle_sha256":"1fadff39a3047befcc803104a37a1469cd9995061c1b15c2f2420ff83bb74bd5"}}