{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z7BJ3F7XXYYTVFRM7A7YIZNCBJ","short_pith_number":"pith:Z7BJ3F7X","canonical_record":{"source":{"id":"1409.7519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-26T09:54:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"67bee1494d61c1bc2d13574594b807af05f4b32edc3268a28e688191c6754db9","abstract_canon_sha256":"d825b763d630efb32fc356a48abfad0305a7a18c62aaaa03fca799623362b4ad"},"schema_version":"1.0"},"canonical_sha256":"cfc29d97f7be313a962cf83f8465a20a6d56474b3d36817d0b0c7580a7fd9edd","source":{"kind":"arxiv","id":"1409.7519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7519","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7519v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7519","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"Z7BJ3F7XXYYT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z7BJ3F7XXYYTVFRM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z7BJ3F7X","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z7BJ3F7XXYYTVFRM7A7YIZNCBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-26T09:54:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"67bee1494d61c1bc2d13574594b807af05f4b32edc3268a28e688191c6754db9","abstract_canon_sha256":"d825b763d630efb32fc356a48abfad0305a7a18c62aaaa03fca799623362b4ad"},"schema_version":"1.0"},"canonical_sha256":"cfc29d97f7be313a962cf83f8465a20a6d56474b3d36817d0b0c7580a7fd9edd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.489362Z","signature_b64":"f4kmDd0vlbGjZpIVFJzsfk7i269Wpdn296fKNtc2Ip3b8N2OgE8Zx/VfnN1Z+IrFFaadI2DNCKWEjHwBdF9IDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfc29d97f7be313a962cf83f8465a20a6d56474b3d36817d0b0c7580a7fd9edd","last_reissued_at":"2026-05-18T02:41:52.488686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.488686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7519","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vW8/EA2BpjgoSOUiJIo1+R/OYjdKsFsfyykX0esS3iBu1+xV1ef/NkMHR9lI+NW9G7+8eJyLZLr2pigP2IW5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:43:26.000495Z"},"content_sha256":"0b25aac94ec53efebd0ecd88340067ac7eef61303c9b8d757b0a09c0fce209f7","schema_version":"1.0","event_id":"sha256:0b25aac94ec53efebd0ecd88340067ac7eef61303c9b8d757b0a09c0fce209f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z7BJ3F7XXYYTVFRM7A7YIZNCBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit points on $y^2 + xy - t^d y = x^3$ and related character sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Christopher Davis, Tommy Occhipinti","submitted_at":"2014-09-26T09:54:38Z","abstract_excerpt":"Let $\\mathbb{F}_q$ denote a finite field of characteristic $p \\geq 5$ and let $d = q+1$. Let $E_d$ denote the elliptic curve over the function field $\\mathbb{F}_{q^2}(t)$ defined by the equation $y^2 + xy - t^d y = x^3$. Its rank is $q$ when $q \\equiv 1 \\bmod 3$ and its rank is $q-2$ when $q \\equiv 2 \\bmod 3$. We describe an explicit method for producing points on this elliptic curve. In case $q \\not\\equiv 11 \\bmod 12$, our method produces points which generate a full-rank subgroup. Our strategy for producing rational points on $E_d$ makes use of a dominant map from the degree $d$ Fermat surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7519","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p86rJPYyVDV+GMfjrEVYor1hpNapB6kmsa9LuTCTbw3xcnjR8rVbBoc/rdt4Mh7jiG8KU0WpELRuMWr11oIoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:43:26.000834Z"},"content_sha256":"70456cefe9ae8013c1ed1618945d88b947563300e2fcb5367e12aaf61f972e5d","schema_version":"1.0","event_id":"sha256:70456cefe9ae8013c1ed1618945d88b947563300e2fcb5367e12aaf61f972e5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/bundle.json","state_url":"https://pith.science/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/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":"2026-06-22T16:43:26Z","links":{"resolver":"https://pith.science/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ","bundle":"https://pith.science/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/bundle.json","state":"https://pith.science/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7BJ3F7XXYYTVFRM7A7YIZNCBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z7BJ3F7XXYYTVFRM7A7YIZNCBJ","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":"d825b763d630efb32fc356a48abfad0305a7a18c62aaaa03fca799623362b4ad","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-26T09:54:38Z","title_canon_sha256":"67bee1494d61c1bc2d13574594b807af05f4b32edc3268a28e688191c6754db9"},"schema_version":"1.0","source":{"id":"1409.7519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7519","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7519v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7519","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"Z7BJ3F7XXYYT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z7BJ3F7XXYYTVFRM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z7BJ3F7X","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:70456cefe9ae8013c1ed1618945d88b947563300e2fcb5367e12aaf61f972e5d","target":"graph","created_at":"2026-05-18T02:41:52Z","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 $\\mathbb{F}_q$ denote a finite field of characteristic $p \\geq 5$ and let $d = q+1$. Let $E_d$ denote the elliptic curve over the function field $\\mathbb{F}_{q^2}(t)$ defined by the equation $y^2 + xy - t^d y = x^3$. Its rank is $q$ when $q \\equiv 1 \\bmod 3$ and its rank is $q-2$ when $q \\equiv 2 \\bmod 3$. We describe an explicit method for producing points on this elliptic curve. In case $q \\not\\equiv 11 \\bmod 12$, our method produces points which generate a full-rank subgroup. Our strategy for producing rational points on $E_d$ makes use of a dominant map from the degree $d$ Fermat surfa","authors_text":"Christopher Davis, Tommy Occhipinti","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-26T09:54:38Z","title":"Explicit points on $y^2 + xy - t^d y = x^3$ and related character sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7519","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":"sha256:0b25aac94ec53efebd0ecd88340067ac7eef61303c9b8d757b0a09c0fce209f7","target":"record","created_at":"2026-05-18T02:41:52Z","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":"d825b763d630efb32fc356a48abfad0305a7a18c62aaaa03fca799623362b4ad","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-26T09:54:38Z","title_canon_sha256":"67bee1494d61c1bc2d13574594b807af05f4b32edc3268a28e688191c6754db9"},"schema_version":"1.0","source":{"id":"1409.7519","kind":"arxiv","version":1}},"canonical_sha256":"cfc29d97f7be313a962cf83f8465a20a6d56474b3d36817d0b0c7580a7fd9edd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfc29d97f7be313a962cf83f8465a20a6d56474b3d36817d0b0c7580a7fd9edd","first_computed_at":"2026-05-18T02:41:52.488686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.488686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4kmDd0vlbGjZpIVFJzsfk7i269Wpdn296fKNtc2Ip3b8N2OgE8Zx/VfnN1Z+IrFFaadI2DNCKWEjHwBdF9IDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.489362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b25aac94ec53efebd0ecd88340067ac7eef61303c9b8d757b0a09c0fce209f7","sha256:70456cefe9ae8013c1ed1618945d88b947563300e2fcb5367e12aaf61f972e5d"],"state_sha256":"888743195c13ec96b42de1b8f44ce0385992cc830e81b8260c12e67b046d8cb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqu+3z8TNEwvmTDAeOTPILFo2IJKrQzrnaRnMcm2gQXhtYb2fBTW1UEw9iRQILeLMKL6jmsoGH2sFSVVjQtyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:43:26.002733Z","bundle_sha256":"30c4c6a6e5752ca28f699bfc37267e5a1250b2edf719d8947d0f110fc8a602fc"}}