{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:I2L7OCPXDZHYJCXKMQOA3FVS7P","short_pith_number":"pith:I2L7OCPX","canonical_record":{"source":{"id":"1806.01158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"56b6c388d469370131f5a80754eac2afd32655969113f6bdac734c67ea63d364","abstract_canon_sha256":"602438873e949836e85146cf00a5e48a92131764fe41e4f88662dd337f41dea3"},"schema_version":"1.0"},"canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","source":{"kind":"arxiv","id":"1806.01158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01158","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01158v1","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01158","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"I2L7OCPXDZHY","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I2L7OCPXDZHYJCXK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I2L7OCPX","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:I2L7OCPXDZHYJCXKMQOA3FVS7P","target":"record","payload":{"canonical_record":{"source":{"id":"1806.01158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"56b6c388d469370131f5a80754eac2afd32655969113f6bdac734c67ea63d364","abstract_canon_sha256":"602438873e949836e85146cf00a5e48a92131764fe41e4f88662dd337f41dea3"},"schema_version":"1.0"},"canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:17.283492Z","signature_b64":"1oqM3YrVlC3X+wBNS1A9L7bLYMEhMrvUqos2yBHYgDjGnbvtpVtXb1czze+gyi8sa5z6N5SzJYu43BQXtlByBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","last_reissued_at":"2026-05-18T00:14:17.282764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:17.282764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.01158","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":"2026-05-18T00:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UPdo4R7OohPQGDnr6CTxzksionIxSpUQ7O2xoTe78WJxx6aFTl0Kw9PO5N+Tzq0YQ5Aukg9+xWTgRhh0/x8IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:47:45.151969Z"},"content_sha256":"1eff07f0b143dfc69f2a994655a106dcebe86537a33008dd8b1a74df1316072d","schema_version":"1.0","event_id":"sha256:1eff07f0b143dfc69f2a994655a106dcebe86537a33008dd8b1a74df1316072d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:I2L7OCPXDZHYJCXKMQOA3FVS7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic Curves Containing Sequences of Consecutive Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gamze Sava\\c{s} \\c{C}elik, G\\\"okhan Soydan","submitted_at":"2018-06-04T15:17:51Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ described by $y^2= x^3+ Kx+ L$ where $K, L \\in \\mathbb{Q}$. A set of rational points $(x_i,y_i) \\in E(\\mathbb{Q})$ for $i=1, 2, \\cdots, k$, is said to be a sequence of consecutive cubes on $E$ if the $x-$coordinates of the points $x_i$'s for $i=1, 2, \\cdots$ form consecutive cubes. In this note, we show the existence of an infinite family of elliptic curves containing a length-$5$-term sequence of consecutive cubes. Morever, these five rational points in $E (\\mathbb{Q})$ are linearly independent and the rank $r$ of $E(\\mathbb{Q})$ is at least $5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01158","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":"2026-05-18T00:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GW4Vn82YPFRKS08s4UaIFVSIt/CjdFIDls++rnZjkPeU3QUsrqAHL+i03yhFkd+UZYLu4+c6QbHX+hiuF40yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:47:45.152673Z"},"content_sha256":"740ad048ae555e4ffafa8c3c051e3a124eade17fa3650a96efde485962d85772","schema_version":"1.0","event_id":"sha256:740ad048ae555e4ffafa8c3c051e3a124eade17fa3650a96efde485962d85772"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/bundle.json","state_url":"https://pith.science/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/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":"2026-06-07T09:47:45Z","links":{"resolver":"https://pith.science/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P","bundle":"https://pith.science/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/bundle.json","state":"https://pith.science/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2L7OCPXDZHYJCXKMQOA3FVS7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I2L7OCPXDZHYJCXKMQOA3FVS7P","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":"602438873e949836e85146cf00a5e48a92131764fe41e4f88662dd337f41dea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","title_canon_sha256":"56b6c388d469370131f5a80754eac2afd32655969113f6bdac734c67ea63d364"},"schema_version":"1.0","source":{"id":"1806.01158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01158","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01158v1","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01158","created_at":"2026-05-18T00:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"I2L7OCPXDZHY","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I2L7OCPXDZHYJCXK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I2L7OCPX","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:740ad048ae555e4ffafa8c3c051e3a124eade17fa3650a96efde485962d85772","target":"graph","created_at":"2026-05-18T00:14:17Z","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":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ described by $y^2= x^3+ Kx+ L$ where $K, L \\in \\mathbb{Q}$. A set of rational points $(x_i,y_i) \\in E(\\mathbb{Q})$ for $i=1, 2, \\cdots, k$, is said to be a sequence of consecutive cubes on $E$ if the $x-$coordinates of the points $x_i$'s for $i=1, 2, \\cdots$ form consecutive cubes. In this note, we show the existence of an infinite family of elliptic curves containing a length-$5$-term sequence of consecutive cubes. Morever, these five rational points in $E (\\mathbb{Q})$ are linearly independent and the rank $r$ of $E(\\mathbb{Q})$ is at least $5$.","authors_text":"Gamze Sava\\c{s} \\c{C}elik, G\\\"okhan Soydan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","title":"Elliptic Curves Containing Sequences of Consecutive Cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01158","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":"sha256:1eff07f0b143dfc69f2a994655a106dcebe86537a33008dd8b1a74df1316072d","target":"record","created_at":"2026-05-18T00:14:17Z","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":"602438873e949836e85146cf00a5e48a92131764fe41e4f88662dd337f41dea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","title_canon_sha256":"56b6c388d469370131f5a80754eac2afd32655969113f6bdac734c67ea63d364"},"schema_version":"1.0","source":{"id":"1806.01158","kind":"arxiv","version":1}},"canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","first_computed_at":"2026-05-18T00:14:17.282764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:17.282764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1oqM3YrVlC3X+wBNS1A9L7bLYMEhMrvUqos2yBHYgDjGnbvtpVtXb1czze+gyi8sa5z6N5SzJYu43BQXtlByBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:17.283492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eff07f0b143dfc69f2a994655a106dcebe86537a33008dd8b1a74df1316072d","sha256:740ad048ae555e4ffafa8c3c051e3a124eade17fa3650a96efde485962d85772"],"state_sha256":"e90b7dcba49d2781d26257d3db0bd43321a05ee8ace948d1071e1a180340b839"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/qJPcGu5khtSviuyc6aY8rIWC3atex8F3IIlDVQwXAMTQ9L4k8B2BR7tFMab0eGxIceAQ84360B9F7M+c/w/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:47:45.156599Z","bundle_sha256":"dd54619667a4d6312366a079c05a577a243fe892b789390c4700afe36c7e9735"}}