{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UYVGBCAZVDAY2XDK5D5KIK3VKN","short_pith_number":"pith:UYVGBCAZ","canonical_record":{"source":{"id":"1005.5120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T16:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"b9ff5d19ebb5b0e671a0f60f6e3104025b28d5542e014076829dd7e4a02fc3bd","abstract_canon_sha256":"ccdbc1c970580427e4dc4f238697cda17819928e22ab65e1b11e6531b5ac3e0e"},"schema_version":"1.0"},"canonical_sha256":"a62a608819a8c18d5c6ae8faa42b755350c7fb1279255e746e39da6bcd3da24f","source":{"kind":"arxiv","id":"1005.5120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5120","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5120v2","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5120","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"UYVGBCAZVDAY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UYVGBCAZVDAY2XDK","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UYVGBCAZ","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UYVGBCAZVDAY2XDK5D5KIK3VKN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.5120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T16:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"b9ff5d19ebb5b0e671a0f60f6e3104025b28d5542e014076829dd7e4a02fc3bd","abstract_canon_sha256":"ccdbc1c970580427e4dc4f238697cda17819928e22ab65e1b11e6531b5ac3e0e"},"schema_version":"1.0"},"canonical_sha256":"a62a608819a8c18d5c6ae8faa42b755350c7fb1279255e746e39da6bcd3da24f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:59.452288Z","signature_b64":"FzFL3y5X3knD15zvUQwiKr7O+Ewp4PKR+ZhSVulCtYaj1sl+Xxh68FFG8Ov7W4aH5SxT9KJu75RiGNby81aKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a62a608819a8c18d5c6ae8faa42b755350c7fb1279255e746e39da6bcd3da24f","last_reissued_at":"2026-05-18T04:05:59.451751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:59.451751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.5120","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":"2026-05-18T04:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/wbEzEpgGz9aZtenmbkr7dSKTD15wQ0AHd2qom92p9+vxPEJPpW4MAd4xqO098DuNNJp11dKd099aCy1Np9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:10:30.903716Z"},"content_sha256":"13e8aa2cf85da0a804fe690bee892ff0f9e1cc85d4319d52c0a0bbf744d23f67","schema_version":"1.0","event_id":"sha256:13e8aa2cf85da0a804fe690bee892ff0f9e1cc85d4319d52c0a0bbf744d23f67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UYVGBCAZVDAY2XDK5D5KIK3VKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chieh-Yu Chang, Matthew A. Papanikolas","submitted_at":"2010-05-27T16:56:11Z","abstract_excerpt":"Let rho be a Drinfeld A-module with generic characteristic defined over an algebraic function field. We prove that all of the algebraic relations among periods, quasi-periods, and logarithms of algebraic points on rho are those coming from linear relations induced by endomorphisms of rho."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5120","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":"2026-05-18T04:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F83I6FgWOXedBNTEFf/lvK5eIHlhsxHjbTetP9tJLpxxjcI1xEwmEcp2y0DmnL1+NGPq25+x41Ml69O9XZR0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:10:30.904059Z"},"content_sha256":"16b1e36b62495dc7694f086ee7904134ee818c3bafdc16ccb14a41ff6c8cc730","schema_version":"1.0","event_id":"sha256:16b1e36b62495dc7694f086ee7904134ee818c3bafdc16ccb14a41ff6c8cc730"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/bundle.json","state_url":"https://pith.science/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/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":"2026-06-02T02:10:30Z","links":{"resolver":"https://pith.science/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN","bundle":"https://pith.science/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/bundle.json","state":"https://pith.science/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UYVGBCAZVDAY2XDK5D5KIK3VKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UYVGBCAZVDAY2XDK5D5KIK3VKN","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":"ccdbc1c970580427e4dc4f238697cda17819928e22ab65e1b11e6531b5ac3e0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T16:56:11Z","title_canon_sha256":"b9ff5d19ebb5b0e671a0f60f6e3104025b28d5542e014076829dd7e4a02fc3bd"},"schema_version":"1.0","source":{"id":"1005.5120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5120","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5120v2","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5120","created_at":"2026-05-18T04:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"UYVGBCAZVDAY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UYVGBCAZVDAY2XDK","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UYVGBCAZ","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:16b1e36b62495dc7694f086ee7904134ee818c3bafdc16ccb14a41ff6c8cc730","target":"graph","created_at":"2026-05-18T04:05:59Z","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 rho be a Drinfeld A-module with generic characteristic defined over an algebraic function field. We prove that all of the algebraic relations among periods, quasi-periods, and logarithms of algebraic points on rho are those coming from linear relations induced by endomorphisms of rho.","authors_text":"Chieh-Yu Chang, Matthew A. Papanikolas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T16:56:11Z","title":"Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5120","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":"sha256:13e8aa2cf85da0a804fe690bee892ff0f9e1cc85d4319d52c0a0bbf744d23f67","target":"record","created_at":"2026-05-18T04:05:59Z","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":"ccdbc1c970580427e4dc4f238697cda17819928e22ab65e1b11e6531b5ac3e0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-27T16:56:11Z","title_canon_sha256":"b9ff5d19ebb5b0e671a0f60f6e3104025b28d5542e014076829dd7e4a02fc3bd"},"schema_version":"1.0","source":{"id":"1005.5120","kind":"arxiv","version":2}},"canonical_sha256":"a62a608819a8c18d5c6ae8faa42b755350c7fb1279255e746e39da6bcd3da24f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a62a608819a8c18d5c6ae8faa42b755350c7fb1279255e746e39da6bcd3da24f","first_computed_at":"2026-05-18T04:05:59.451751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:59.451751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FzFL3y5X3knD15zvUQwiKr7O+Ewp4PKR+ZhSVulCtYaj1sl+Xxh68FFG8Ov7W4aH5SxT9KJu75RiGNby81aKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:59.452288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13e8aa2cf85da0a804fe690bee892ff0f9e1cc85d4319d52c0a0bbf744d23f67","sha256:16b1e36b62495dc7694f086ee7904134ee818c3bafdc16ccb14a41ff6c8cc730"],"state_sha256":"09a91d7c50d410c026354de94dc7b75e005377200176f224618eee66e4347425"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oTbQIBb66XwF85bKsShB7JNsw1rW8/RUWuO0C4ZPi8CHOEg+MAB3EKQczddhn8dXcjmsONC/xTSDIgxo4ttkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:10:30.906002Z","bundle_sha256":"39fddc692663f416ebad71f649def68ba74b3aef94b6660acefedeb580169122"}}