{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:B4F4RPJLGHS4XTSEIOP7ZZMTX6","short_pith_number":"pith:B4F4RPJL","canonical_record":{"source":{"id":"0807.3157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-07-20T13:27:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3aa6a93d9eaa1ce17e843a96685a1d86846bdcecd9976d0094cb51236da46058","abstract_canon_sha256":"3e8207b63d3daf0ac3ae0025370e3d8aef00f9815a303e00df468fe68e5e8973"},"schema_version":"1.0"},"canonical_sha256":"0f0bc8bd2b31e5cbce44439ffce593bf9e0c758a44ebef74e77972a663faefb8","source":{"kind":"arxiv","id":"0807.3157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3157","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3157v1","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3157","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"B4F4RPJLGHS4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B4F4RPJLGHS4XTSE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B4F4RPJL","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:B4F4RPJLGHS4XTSEIOP7ZZMTX6","target":"record","payload":{"canonical_record":{"source":{"id":"0807.3157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-07-20T13:27:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3aa6a93d9eaa1ce17e843a96685a1d86846bdcecd9976d0094cb51236da46058","abstract_canon_sha256":"3e8207b63d3daf0ac3ae0025370e3d8aef00f9815a303e00df468fe68e5e8973"},"schema_version":"1.0"},"canonical_sha256":"0f0bc8bd2b31e5cbce44439ffce593bf9e0c758a44ebef74e77972a663faefb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:00.803544Z","signature_b64":"J17SCguNGFebj/Y9K9uMlSavSqyekw+/syq9Ar7LKcSntoo/lqo3U0r/sLKShzV+E14KgI8dj7H9heP0ZxrmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f0bc8bd2b31e5cbce44439ffce593bf9e0c758a44ebef74e77972a663faefb8","last_reissued_at":"2026-05-18T04:21:00.802966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:00.802966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.3157","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":"2026-05-18T04:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HjlJ4zhDezHctLFFwKTs3Isx7BWv9IAwEXQaqjYa1CMzRPP7epoNQW3P6aIOEO2+SCwad00fojacacZbZOpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:27:42.529341Z"},"content_sha256":"b3ebd748c05f417b8895f70aa29332f38f9610e418893463b63d7b7c4d6c478e","schema_version":"1.0","event_id":"sha256:b3ebd748c05f417b8895f70aa29332f38f9610e418893463b63d7b7c4d6c478e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:B4F4RPJLGHS4XTSEIOP7ZZMTX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic relations among periods and logarithms of rank 2 Drinfeld modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Chieh-Yu Chang, Matthew A. Papanikolas","submitted_at":"2008-07-20T13:27:02Z","abstract_excerpt":"For any rank 2 Drinfeld module rho defined over an algebraic function field, we consider its period matrix P, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of F_q is odd and rho is without complex multiplication. We show that the transcendence degree of the field generated by the entries of P over F_q(theta) is 4. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over F_q(theta)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3157","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":"2026-05-18T04:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w6E6YTK1yNV7idyUoL2I7vFv8F//pxG1J2mFCGgB4t6mhXYjfjaHMghUahU4hRAD1nV3vHsGvBYhhS0jTve5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:27:42.529689Z"},"content_sha256":"21f493bec245165ea820d28a239e33274f3745c974ea00de2c0cddec00c5fe85","schema_version":"1.0","event_id":"sha256:21f493bec245165ea820d28a239e33274f3745c974ea00de2c0cddec00c5fe85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/bundle.json","state_url":"https://pith.science/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/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":"2026-06-02T13:27:42Z","links":{"resolver":"https://pith.science/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6","bundle":"https://pith.science/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/bundle.json","state":"https://pith.science/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4F4RPJLGHS4XTSEIOP7ZZMTX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:B4F4RPJLGHS4XTSEIOP7ZZMTX6","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":"3e8207b63d3daf0ac3ae0025370e3d8aef00f9815a303e00df468fe68e5e8973","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-07-20T13:27:02Z","title_canon_sha256":"3aa6a93d9eaa1ce17e843a96685a1d86846bdcecd9976d0094cb51236da46058"},"schema_version":"1.0","source":{"id":"0807.3157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3157","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3157v1","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3157","created_at":"2026-05-18T04:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"B4F4RPJLGHS4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B4F4RPJLGHS4XTSE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B4F4RPJL","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:21f493bec245165ea820d28a239e33274f3745c974ea00de2c0cddec00c5fe85","target":"graph","created_at":"2026-05-18T04:21:00Z","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":"For any rank 2 Drinfeld module rho defined over an algebraic function field, we consider its period matrix P, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of F_q is odd and rho is without complex multiplication. We show that the transcendence degree of the field generated by the entries of P over F_q(theta) is 4. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over F_q(theta).","authors_text":"Chieh-Yu Chang, Matthew A. Papanikolas","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-07-20T13:27:02Z","title":"Algebraic relations among periods and logarithms of rank 2 Drinfeld modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3157","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:b3ebd748c05f417b8895f70aa29332f38f9610e418893463b63d7b7c4d6c478e","target":"record","created_at":"2026-05-18T04:21:00Z","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":"3e8207b63d3daf0ac3ae0025370e3d8aef00f9815a303e00df468fe68e5e8973","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-07-20T13:27:02Z","title_canon_sha256":"3aa6a93d9eaa1ce17e843a96685a1d86846bdcecd9976d0094cb51236da46058"},"schema_version":"1.0","source":{"id":"0807.3157","kind":"arxiv","version":1}},"canonical_sha256":"0f0bc8bd2b31e5cbce44439ffce593bf9e0c758a44ebef74e77972a663faefb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f0bc8bd2b31e5cbce44439ffce593bf9e0c758a44ebef74e77972a663faefb8","first_computed_at":"2026-05-18T04:21:00.802966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:00.802966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J17SCguNGFebj/Y9K9uMlSavSqyekw+/syq9Ar7LKcSntoo/lqo3U0r/sLKShzV+E14KgI8dj7H9heP0ZxrmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:00.803544Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.3157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3ebd748c05f417b8895f70aa29332f38f9610e418893463b63d7b7c4d6c478e","sha256:21f493bec245165ea820d28a239e33274f3745c974ea00de2c0cddec00c5fe85"],"state_sha256":"4057a22e752948b38396f0f1e6ac76ae88d010646c001fdbefbcd7bd41a05ac7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxySt4o8w4L6cQSjUCAqKr7cD/ZqjdJW0RmLIqzCO/2KXF6fHtGQ52FvoElornr6XNZhdOHaGVI0xHMJIuklBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:27:42.531620Z","bundle_sha256":"2e0f1ee078133d501b060eeb8490a0aafdb65802cd091058505727828a8be344"}}