{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LHT63CDREIOCA4C5BRMLCPE53W","short_pith_number":"pith:LHT63CDR","canonical_record":{"source":{"id":"0911.4025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-20T12:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"3f73da19bb29ac26099b2f68b58aa8fba926a3640de19b8317fe257064c46e19","abstract_canon_sha256":"58b2cd60cee8831b3e4f15c629fc0d2edb2c0da6ed3c11019504b571d9490dc5"},"schema_version":"1.0"},"canonical_sha256":"59e7ed8871221c20705d0c58b13c9ddda9d74e183067949f74a8837a86131a47","source":{"kind":"arxiv","id":"0911.4025","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4025","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4025v2","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4025","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"LHT63CDREIOC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LHT63CDREIOCA4C5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LHT63CDR","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LHT63CDREIOCA4C5BRMLCPE53W","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-20T12:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"3f73da19bb29ac26099b2f68b58aa8fba926a3640de19b8317fe257064c46e19","abstract_canon_sha256":"58b2cd60cee8831b3e4f15c629fc0d2edb2c0da6ed3c11019504b571d9490dc5"},"schema_version":"1.0"},"canonical_sha256":"59e7ed8871221c20705d0c58b13c9ddda9d74e183067949f74a8837a86131a47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:54.336118Z","signature_b64":"9YHbWJcpKIYPTy2AzGdaejXK5ZxaqMYxrNEMNQgPeSkiS95u78uezJi2w+0Feg6HH3PXOKjsVnLW40V61UvlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e7ed8871221c20705d0c58b13c9ddda9d74e183067949f74a8837a86131a47","last_reissued_at":"2026-05-18T04:34:54.335628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:54.335628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4025","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":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUd13P9WLia21M0wX2d1ZL6iQioBLaeWZv7FlF1afUotDGMTmLb5mwPnllomccf424djV+LZ+lvkn8Xj1SNSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:00.997169Z"},"content_sha256":"afb59866fabf2f35ff93169e665cd2f6516577502f1485bbc70bcbde64a10895","schema_version":"1.0","event_id":"sha256:afb59866fabf2f35ff93169e665cd2f6516577502f1485bbc70bcbde64a10895"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LHT63CDREIOCA4C5BRMLCPE53W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gary McGuire, Vijaykumar Singh","submitted_at":"2009-11-20T12:14:17Z","abstract_excerpt":"We study the intersection of two particular Fermat hypersurfaces in $\\mathbb{P}^3$ over a finite field. Using the Kani-Rosen decomposition we study arithmetic properties of this curve in terms of its quotients. Explicit computation of the quotients is done using a Gr\\\"obner basis algorithm. We also study the $p$-rank, zeta function, and number of rational points, of the modulo $p$ reduction of the curve. We show that the Jacobian of the genus 2 quotient is $(4,4)$-split."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4025","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":"2026-05-18T04:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05N4ZCYx4PXYQEVjCE9Ay2Szqbd1i7ixKEU1GHSySUP8ojVPU78RaOMmjLDMuVTz2qGgKBM9bQTewMzVyWtqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:00.997525Z"},"content_sha256":"cf2f772273b59e2b17de28d78e507ffd66aa42a16228c241d537dcd6a0c076b7","schema_version":"1.0","event_id":"sha256:cf2f772273b59e2b17de28d78e507ffd66aa42a16228c241d537dcd6a0c076b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHT63CDREIOCA4C5BRMLCPE53W/bundle.json","state_url":"https://pith.science/pith/LHT63CDREIOCA4C5BRMLCPE53W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHT63CDREIOCA4C5BRMLCPE53W/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":"2026-06-22T14:23:00Z","links":{"resolver":"https://pith.science/pith/LHT63CDREIOCA4C5BRMLCPE53W","bundle":"https://pith.science/pith/LHT63CDREIOCA4C5BRMLCPE53W/bundle.json","state":"https://pith.science/pith/LHT63CDREIOCA4C5BRMLCPE53W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHT63CDREIOCA4C5BRMLCPE53W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LHT63CDREIOCA4C5BRMLCPE53W","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":"58b2cd60cee8831b3e4f15c629fc0d2edb2c0da6ed3c11019504b571d9490dc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-20T12:14:17Z","title_canon_sha256":"3f73da19bb29ac26099b2f68b58aa8fba926a3640de19b8317fe257064c46e19"},"schema_version":"1.0","source":{"id":"0911.4025","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4025","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4025v2","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4025","created_at":"2026-05-18T04:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"LHT63CDREIOC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LHT63CDREIOCA4C5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LHT63CDR","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:cf2f772273b59e2b17de28d78e507ffd66aa42a16228c241d537dcd6a0c076b7","target":"graph","created_at":"2026-05-18T04:34:54Z","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 intersection of two particular Fermat hypersurfaces in $\\mathbb{P}^3$ over a finite field. Using the Kani-Rosen decomposition we study arithmetic properties of this curve in terms of its quotients. Explicit computation of the quotients is done using a Gr\\\"obner basis algorithm. We also study the $p$-rank, zeta function, and number of rational points, of the modulo $p$ reduction of the curve. We show that the Jacobian of the genus 2 quotient is $(4,4)$-split.","authors_text":"Gary McGuire, Vijaykumar Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-20T12:14:17Z","title":"The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4025","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:afb59866fabf2f35ff93169e665cd2f6516577502f1485bbc70bcbde64a10895","target":"record","created_at":"2026-05-18T04:34:54Z","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":"58b2cd60cee8831b3e4f15c629fc0d2edb2c0da6ed3c11019504b571d9490dc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-20T12:14:17Z","title_canon_sha256":"3f73da19bb29ac26099b2f68b58aa8fba926a3640de19b8317fe257064c46e19"},"schema_version":"1.0","source":{"id":"0911.4025","kind":"arxiv","version":2}},"canonical_sha256":"59e7ed8871221c20705d0c58b13c9ddda9d74e183067949f74a8837a86131a47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59e7ed8871221c20705d0c58b13c9ddda9d74e183067949f74a8837a86131a47","first_computed_at":"2026-05-18T04:34:54.335628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:54.335628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9YHbWJcpKIYPTy2AzGdaejXK5ZxaqMYxrNEMNQgPeSkiS95u78uezJi2w+0Feg6HH3PXOKjsVnLW40V61UvlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:54.336118Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4025","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afb59866fabf2f35ff93169e665cd2f6516577502f1485bbc70bcbde64a10895","sha256:cf2f772273b59e2b17de28d78e507ffd66aa42a16228c241d537dcd6a0c076b7"],"state_sha256":"f08085d96f3b730800f642ae87cbe10160b08450edcfeadc2a6996808644da0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMtBzi1l6Cd/qhwL5kxWoBIoXz60XcRuATALqmyF1cB2BwruGIcUHPY2AMeo/QV1T8s1mkzLvDMXBr3dUjXnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:23:00.999587Z","bundle_sha256":"1386306d1dac3c928e244402776fda4116d51a6216939b38167de6cca66ba1b5"}}