{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:777HFBTSHEZGJLTMGW3MF3C53J","short_pith_number":"pith:777HFBTS","canonical_record":{"source":{"id":"math/0107150","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-07-20T16:34:29Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"631ceaca571ef35fb9f2b7f59acc3f60a4910c71e6bd431791fe9194f83d59ee","abstract_canon_sha256":"4699153b918a01f3d9f8569188923594fe0786cc044b8a717b3502cf18958492"},"schema_version":"1.0"},"canonical_sha256":"fffe728672393264ae6c35b6c2ec5dda7700ed033084b6f8a9a7cbec80b890b9","source":{"kind":"arxiv","id":"math/0107150","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107150","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107150v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107150","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"777HFBTSHEZG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"777HFBTSHEZGJLTM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"777HFBTS","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:777HFBTSHEZGJLTMGW3MF3C53J","target":"record","payload":{"canonical_record":{"source":{"id":"math/0107150","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-07-20T16:34:29Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"631ceaca571ef35fb9f2b7f59acc3f60a4910c71e6bd431791fe9194f83d59ee","abstract_canon_sha256":"4699153b918a01f3d9f8569188923594fe0786cc044b8a717b3502cf18958492"},"schema_version":"1.0"},"canonical_sha256":"fffe728672393264ae6c35b6c2ec5dda7700ed033084b6f8a9a7cbec80b890b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.807441Z","signature_b64":"pXKWDZN8fYa9YPnXUFb3hU1WfwQQjkwAvePtZJBOru4cQYMFyB4JS+I9QYGTtA/2FBP3jyk+/ng0okK6E2KHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fffe728672393264ae6c35b6c2ec5dda7700ed033084b6f8a9a7cbec80b890b9","last_reissued_at":"2026-05-18T01:37:47.806961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.806961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0107150","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMZEC7I16kbJy3q3h+AEuoMYTEDxz5+BKKZArVSNwRBfWjL3JKZqKrwPiTyBlox7BzQA9WQYCNjWWBpPvR2NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:27:48.217761Z"},"content_sha256":"5634c783b3929d1986993c003d8e80bd3570ac7f81026472ab9222d66c75ce50","schema_version":"1.0","event_id":"sha256:5634c783b3929d1986993c003d8e80bd3570ac7f81026472ab9222d66c75ce50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:777HFBTSHEZGJLTMGW3MF3C53J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Weil-Barsotti formula for Drinfeld modules","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Matthew A. Papanikolas, Niranjan Ramachandran","submitted_at":"2001-07-20T16:34:29Z","abstract_excerpt":"We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107150","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cS1ilrNhOWtXQotFG3yCyndllnyOJQoqU/dl2j0nGZoREzSVhJL/JL4S2ggarnTHDzrIUhaDqffZHCLWWDRfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:27:48.218100Z"},"content_sha256":"57a47c5c9c0313c166066d9bc6b874c1942e93973b4ded268dba1c8a215338d2","schema_version":"1.0","event_id":"sha256:57a47c5c9c0313c166066d9bc6b874c1942e93973b4ded268dba1c8a215338d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/777HFBTSHEZGJLTMGW3MF3C53J/bundle.json","state_url":"https://pith.science/pith/777HFBTSHEZGJLTMGW3MF3C53J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/777HFBTSHEZGJLTMGW3MF3C53J/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":"2026-06-02T01:27:48Z","links":{"resolver":"https://pith.science/pith/777HFBTSHEZGJLTMGW3MF3C53J","bundle":"https://pith.science/pith/777HFBTSHEZGJLTMGW3MF3C53J/bundle.json","state":"https://pith.science/pith/777HFBTSHEZGJLTMGW3MF3C53J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/777HFBTSHEZGJLTMGW3MF3C53J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:777HFBTSHEZGJLTMGW3MF3C53J","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":"4699153b918a01f3d9f8569188923594fe0786cc044b8a717b3502cf18958492","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2001-07-20T16:34:29Z","title_canon_sha256":"631ceaca571ef35fb9f2b7f59acc3f60a4910c71e6bd431791fe9194f83d59ee"},"schema_version":"1.0","source":{"id":"math/0107150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107150","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107150v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107150","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"777HFBTSHEZG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"777HFBTSHEZGJLTM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"777HFBTS","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:57a47c5c9c0313c166066d9bc6b874c1942e93973b4ded268dba1c8a215338d2","target":"graph","created_at":"2026-05-18T01:37:47Z","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 group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves.","authors_text":"Matthew A. Papanikolas, Niranjan Ramachandran","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-07-20T16:34:29Z","title":"A Weil-Barsotti formula for Drinfeld modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107150","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":"sha256:5634c783b3929d1986993c003d8e80bd3570ac7f81026472ab9222d66c75ce50","target":"record","created_at":"2026-05-18T01:37:47Z","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":"4699153b918a01f3d9f8569188923594fe0786cc044b8a717b3502cf18958492","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2001-07-20T16:34:29Z","title_canon_sha256":"631ceaca571ef35fb9f2b7f59acc3f60a4910c71e6bd431791fe9194f83d59ee"},"schema_version":"1.0","source":{"id":"math/0107150","kind":"arxiv","version":2}},"canonical_sha256":"fffe728672393264ae6c35b6c2ec5dda7700ed033084b6f8a9a7cbec80b890b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fffe728672393264ae6c35b6c2ec5dda7700ed033084b6f8a9a7cbec80b890b9","first_computed_at":"2026-05-18T01:37:47.806961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:47.806961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pXKWDZN8fYa9YPnXUFb3hU1WfwQQjkwAvePtZJBOru4cQYMFyB4JS+I9QYGTtA/2FBP3jyk+/ng0okK6E2KHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:47.807441Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5634c783b3929d1986993c003d8e80bd3570ac7f81026472ab9222d66c75ce50","sha256:57a47c5c9c0313c166066d9bc6b874c1942e93973b4ded268dba1c8a215338d2"],"state_sha256":"e0507ca55206ddc9e4059334f7158482d0d58fab5130c3e7ed30a3a665a1000a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6hPCoeKcvvSLB7Z8SRriQ2SXY3yWe54My1ZXKKwSfmoT9jNfKSe2qCYd6uOEpwKfsxae+qUBYBuHmnh1xAVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:27:48.219958Z","bundle_sha256":"5ba4a84229c10abf779cd3a05a08736d4d36193e98a8552114f08aaa69860dd7"}}