{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ANNRSLDXIDIFT45EBI7QBHLIDH","short_pith_number":"pith:ANNRSLDX","canonical_record":{"source":{"id":"0708.3168","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T13:00:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bb3fba22de51eb7b2b541677335ff024a279a26a678375b2ea2a5abdd9f9ea03","abstract_canon_sha256":"82a3bfd49c0781d87a2deee7f8df6c0a90efd8bbf12b8dc4cf4d1e608ace276f"},"schema_version":"1.0"},"canonical_sha256":"035b192c7740d059f3a40a3f009d6819ca0879bc815efa2e88370228920184d5","source":{"kind":"arxiv","id":"0708.3168","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.3168","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"0708.3168v2","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.3168","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"ANNRSLDXIDIF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ANNRSLDXIDIFT45E","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ANNRSLDX","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ANNRSLDXIDIFT45EBI7QBHLIDH","target":"record","payload":{"canonical_record":{"source":{"id":"0708.3168","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T13:00:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bb3fba22de51eb7b2b541677335ff024a279a26a678375b2ea2a5abdd9f9ea03","abstract_canon_sha256":"82a3bfd49c0781d87a2deee7f8df6c0a90efd8bbf12b8dc4cf4d1e608ace276f"},"schema_version":"1.0"},"canonical_sha256":"035b192c7740d059f3a40a3f009d6819ca0879bc815efa2e88370228920184d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:31.255781Z","signature_b64":"49vGI+VE6+E4VWGfCSN6DjGWxwA/xOu2IU/f6952png7kodkCO3soI1z7Ca+fdqNqSkVU6EzJGznbVzhCPeqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"035b192c7740d059f3a40a3f009d6819ca0879bc815efa2e88370228920184d5","last_reissued_at":"2026-05-18T01:24:31.255230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:31.255230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.3168","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5O9Q6soq13/XzqQ20BwzXHSODeBKYLhbTTnuN5ys4Hkis5h6BVaSMrazD3TbImgV4RV1K1NFGLw8WiAoNz8fCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:57:55.478759Z"},"content_sha256":"4849947f98ed5f998ccceb12a4d6f8e6cd459bc381f0bbad060510388f4ea0f3","schema_version":"1.0","event_id":"sha256:4849947f98ed5f998ccceb12a4d6f8e6cd459bc381f0bbad060510388f4ea0f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ANNRSLDXIDIFT45EBI7QBHLIDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generic Approach to Searching for Jacobians","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Andrew V. Sutherland","submitted_at":"2007-08-23T13:00:25Z","abstract_excerpt":"We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.3168","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fo1QJmYsRG6mCeC/JjYoJ/KgIuRg6zOz/tZmLY5XONe+KGXtu16sx7jXu6fhYkr8Ji3UsqH8IW3YOKVIPzRpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:57:55.479391Z"},"content_sha256":"9daf635c9b415d24f00acf1de7e28c83dafa2ed56b9223ad784a4e449de0e33e","schema_version":"1.0","event_id":"sha256:9daf635c9b415d24f00acf1de7e28c83dafa2ed56b9223ad784a4e449de0e33e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/bundle.json","state_url":"https://pith.science/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/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":"2026-06-05T19:57:55Z","links":{"resolver":"https://pith.science/pith/ANNRSLDXIDIFT45EBI7QBHLIDH","bundle":"https://pith.science/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/bundle.json","state":"https://pith.science/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANNRSLDXIDIFT45EBI7QBHLIDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ANNRSLDXIDIFT45EBI7QBHLIDH","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":"82a3bfd49c0781d87a2deee7f8df6c0a90efd8bbf12b8dc4cf4d1e608ace276f","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T13:00:25Z","title_canon_sha256":"bb3fba22de51eb7b2b541677335ff024a279a26a678375b2ea2a5abdd9f9ea03"},"schema_version":"1.0","source":{"id":"0708.3168","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.3168","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"0708.3168v2","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.3168","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"ANNRSLDXIDIF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ANNRSLDXIDIFT45E","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ANNRSLDX","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:9daf635c9b415d24f00acf1de7e28c83dafa2ed56b9223ad784a4e449de0e33e","target":"graph","created_at":"2026-05-18T01:24:31Z","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 consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fi","authors_text":"Andrew V. Sutherland","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T13:00:25Z","title":"A Generic Approach to Searching for Jacobians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.3168","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":"sha256:4849947f98ed5f998ccceb12a4d6f8e6cd459bc381f0bbad060510388f4ea0f3","target":"record","created_at":"2026-05-18T01:24:31Z","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":"82a3bfd49c0781d87a2deee7f8df6c0a90efd8bbf12b8dc4cf4d1e608ace276f","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2007-08-23T13:00:25Z","title_canon_sha256":"bb3fba22de51eb7b2b541677335ff024a279a26a678375b2ea2a5abdd9f9ea03"},"schema_version":"1.0","source":{"id":"0708.3168","kind":"arxiv","version":2}},"canonical_sha256":"035b192c7740d059f3a40a3f009d6819ca0879bc815efa2e88370228920184d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"035b192c7740d059f3a40a3f009d6819ca0879bc815efa2e88370228920184d5","first_computed_at":"2026-05-18T01:24:31.255230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:31.255230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49vGI+VE6+E4VWGfCSN6DjGWxwA/xOu2IU/f6952png7kodkCO3soI1z7Ca+fdqNqSkVU6EzJGznbVzhCPeqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:31.255781Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.3168","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4849947f98ed5f998ccceb12a4d6f8e6cd459bc381f0bbad060510388f4ea0f3","sha256:9daf635c9b415d24f00acf1de7e28c83dafa2ed56b9223ad784a4e449de0e33e"],"state_sha256":"7f1a220aac4fd65954d92888d7ecc70e4427356efac82b0e420d0411d147f1e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UPfVVyU6gMvHYWJNVAlPVuIoqLyZCSeuqrH9la6uQwyH4PreZ87YWF06bHqH8otm7gHTUDTx/hamj4mpix6nAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:57:55.483164Z","bundle_sha256":"4d4df27456b9bb519c8811c8c4bedba8a196c570bd209b1c1cb199d7471929ea"}}