{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:NQFN6N6LWOGHBAOJVCGM647NKT","short_pith_number":"pith:NQFN6N6L","canonical_record":{"source":{"id":"0808.3038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-22T08:00:36Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"40a9b70dc6727e153d6944e659c11e90e801143401c20331ca889f0a0431d9a6","abstract_canon_sha256":"7799c1066f6c47dacaf159d408cc66da0812b2c6d7a96e5d55d69a4ec9794544"},"schema_version":"1.0"},"canonical_sha256":"6c0adf37cbb38c7081c9a88ccf73ed54d6f55a135bea9e3907a47111339b8ff4","source":{"kind":"arxiv","id":"0808.3038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3038","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3038v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3038","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"NQFN6N6LWOGH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NQFN6N6LWOGHBAOJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NQFN6N6L","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:NQFN6N6LWOGHBAOJVCGM647NKT","target":"record","payload":{"canonical_record":{"source":{"id":"0808.3038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-22T08:00:36Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"40a9b70dc6727e153d6944e659c11e90e801143401c20331ca889f0a0431d9a6","abstract_canon_sha256":"7799c1066f6c47dacaf159d408cc66da0812b2c6d7a96e5d55d69a4ec9794544"},"schema_version":"1.0"},"canonical_sha256":"6c0adf37cbb38c7081c9a88ccf73ed54d6f55a135bea9e3907a47111339b8ff4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:22.480181Z","signature_b64":"6JitT2XCl8ezOBv6zTeRulc8mSOQnrTzULkbHX8iUURixJB28DvyHeD/H9aHa9HxMK6kVzJAmInHDspWt3cvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c0adf37cbb38c7081c9a88ccf73ed54d6f55a135bea9e3907a47111339b8ff4","last_reissued_at":"2026-05-18T04:20:22.479460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:22.479460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.3038","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":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uejzps+UP4x27eBnyHD88nV+ed9dNMXYGyBKg7H1VwqIV5OD22Uy7GtEdSpWhoLh8Ktea7Eh6gQuhNi4lOaoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:32:12.740763Z"},"content_sha256":"982552f529a2e9fbf5de0cdd73dda3635baee66f2cb3ea36623b6c9723c53bce","schema_version":"1.0","event_id":"sha256:982552f529a2e9fbf5de0cdd73dda3635baee66f2cb3ea36623b6c9723c53bce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:NQFN6N6LWOGHBAOJVCGM647NKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tschirnhaus-Weierstrass curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"David Sevilla, Josef Schicho","submitted_at":"2008-08-22T08:00:36Z","abstract_excerpt":"We define the concept of Tschirnhaus-Weierstrass curve, named after the Weierstrass form of an elliptic curve and Tschirnhaus transformations. Every pointed curve has a Tschirnhaus-Weierstrass form, and this representation is unique up to a scaling of variables. This is useful for computing isomorphisms between curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3038","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":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxZrNUMMpjgqTrtV9lh66lH80rs/gtOXt6IOU31lF36W+92xdef2jplSFCvMt8kZ0CXlbTth2Y/WFsv8L5dBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:32:12.741167Z"},"content_sha256":"2763e1c5ecb05a61e9648be1d3eee58b12cebbe88c8e67e28d2bdbcb675fe351","schema_version":"1.0","event_id":"sha256:2763e1c5ecb05a61e9648be1d3eee58b12cebbe88c8e67e28d2bdbcb675fe351"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQFN6N6LWOGHBAOJVCGM647NKT/bundle.json","state_url":"https://pith.science/pith/NQFN6N6LWOGHBAOJVCGM647NKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQFN6N6LWOGHBAOJVCGM647NKT/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":"2026-05-27T02:32:12Z","links":{"resolver":"https://pith.science/pith/NQFN6N6LWOGHBAOJVCGM647NKT","bundle":"https://pith.science/pith/NQFN6N6LWOGHBAOJVCGM647NKT/bundle.json","state":"https://pith.science/pith/NQFN6N6LWOGHBAOJVCGM647NKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQFN6N6LWOGHBAOJVCGM647NKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:NQFN6N6LWOGHBAOJVCGM647NKT","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":"7799c1066f6c47dacaf159d408cc66da0812b2c6d7a96e5d55d69a4ec9794544","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-22T08:00:36Z","title_canon_sha256":"40a9b70dc6727e153d6944e659c11e90e801143401c20331ca889f0a0431d9a6"},"schema_version":"1.0","source":{"id":"0808.3038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3038","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3038v2","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3038","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"NQFN6N6LWOGH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NQFN6N6LWOGHBAOJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NQFN6N6L","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:2763e1c5ecb05a61e9648be1d3eee58b12cebbe88c8e67e28d2bdbcb675fe351","target":"graph","created_at":"2026-05-18T04:20:22Z","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 define the concept of Tschirnhaus-Weierstrass curve, named after the Weierstrass form of an elliptic curve and Tschirnhaus transformations. Every pointed curve has a Tschirnhaus-Weierstrass form, and this representation is unique up to a scaling of variables. This is useful for computing isomorphisms between curves.","authors_text":"David Sevilla, Josef Schicho","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-22T08:00:36Z","title":"Tschirnhaus-Weierstrass curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3038","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":"sha256:982552f529a2e9fbf5de0cdd73dda3635baee66f2cb3ea36623b6c9723c53bce","target":"record","created_at":"2026-05-18T04:20:22Z","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":"7799c1066f6c47dacaf159d408cc66da0812b2c6d7a96e5d55d69a4ec9794544","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-22T08:00:36Z","title_canon_sha256":"40a9b70dc6727e153d6944e659c11e90e801143401c20331ca889f0a0431d9a6"},"schema_version":"1.0","source":{"id":"0808.3038","kind":"arxiv","version":2}},"canonical_sha256":"6c0adf37cbb38c7081c9a88ccf73ed54d6f55a135bea9e3907a47111339b8ff4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c0adf37cbb38c7081c9a88ccf73ed54d6f55a135bea9e3907a47111339b8ff4","first_computed_at":"2026-05-18T04:20:22.479460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:22.479460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JitT2XCl8ezOBv6zTeRulc8mSOQnrTzULkbHX8iUURixJB28DvyHeD/H9aHa9HxMK6kVzJAmInHDspWt3cvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:22.480181Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.3038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:982552f529a2e9fbf5de0cdd73dda3635baee66f2cb3ea36623b6c9723c53bce","sha256:2763e1c5ecb05a61e9648be1d3eee58b12cebbe88c8e67e28d2bdbcb675fe351"],"state_sha256":"59b13bb4b91e47e1a5f5e40e5eca602facd31fd642da394c177deeec042bbf0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIYK4EhDjCJf9XkG2u1siA2g+6Af7qLOvCM/2X3PnCekolpdXO9ZOiu3AhBrwXz9VoTlmilnJIs3Ui+EE9OpDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:32:12.743723Z","bundle_sha256":"e516c08b89b9672ebb88324d5e5fed2b9053886adf6a72791b80930558327582"}}