{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PJERIFTIKPDITJPISO7ZOAD4Q2","short_pith_number":"pith:PJERIFTI","canonical_record":{"source":{"id":"1210.3059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-10T20:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"ffdee0214d5fdefed19a8aa8312faffe6603f5b0344c34a51158d66282a0039e","abstract_canon_sha256":"54e2ecdc4287290817fa632538f067d806148aa3e8907a7d85ee36efc428e591"},"schema_version":"1.0"},"canonical_sha256":"7a4914166853c689a5e893bf97007c86ba6a3f47345b7722b1b3ee89392389e2","source":{"kind":"arxiv","id":"1210.3059","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3059","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3059v2","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3059","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"PJERIFTIKPDI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PJERIFTIKPDITJPI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PJERIFTI","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PJERIFTIKPDITJPISO7ZOAD4Q2","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-10T20:54:28Z","cross_cats_sorted":[],"title_canon_sha256":"ffdee0214d5fdefed19a8aa8312faffe6603f5b0344c34a51158d66282a0039e","abstract_canon_sha256":"54e2ecdc4287290817fa632538f067d806148aa3e8907a7d85ee36efc428e591"},"schema_version":"1.0"},"canonical_sha256":"7a4914166853c689a5e893bf97007c86ba6a3f47345b7722b1b3ee89392389e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:29.079620Z","signature_b64":"lh4sAMkp9w4ck01LwXqTA42qHIDqVisOPLhjN0+YlmneXYOQbvEKJYymm5oT8GMAiULTquiG1JE2DJQxV/bYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4914166853c689a5e893bf97007c86ba6a3f47345b7722b1b3ee89392389e2","last_reissued_at":"2026-05-18T03:16:29.079093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:29.079093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3059","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":"2026-05-18T03:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93yWvgrSqtwS74RbBSvztl5+wcKsCxpw3WfkLD1CtqJvrER2XrERPnmBoxfuSEVTGRm2/Cdj1XIb/uVj+4w9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:22:47.709776Z"},"content_sha256":"a842a4f574647d1f7acaabf6dd61928cf75ec945b7f8d1042374eeb8ff98f79b","schema_version":"1.0","event_id":"sha256:a842a4f574647d1f7acaabf6dd61928cf75ec945b7f8d1042374eeb8ff98f79b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PJERIFTIKPDITJPISO7ZOAD4Q2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The filled Julia set of a Drinfeld module and uniform bounds for torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Ingram","submitted_at":"2012-10-10T20:54:28Z","abstract_excerpt":"If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a characterisation of the component module J/J^0 which is analogous to the Kodaira-Neron characterisation of the special fibre of a Neron model of an elliptic curve over a non-archimedean field. In particular, if L is the fraction field of a discrete valuation ring, then the component module is finite, and moreover trivial in the case of good reduction.\n  In the context o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3059","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":"2026-05-18T03:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLdeUOUF2xB64/tG35xSScEPy1/agRsQHB8VVmWG7B7DFsoQxl7O4ZxceXdkBQepFBzehj40FnN7D+eaufzDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:22:47.710221Z"},"content_sha256":"d20143afc25bfe767dfa59a4c302ab36bf8994fd6eee51b22f6f3f909faf8208","schema_version":"1.0","event_id":"sha256:d20143afc25bfe767dfa59a4c302ab36bf8994fd6eee51b22f6f3f909faf8208"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/bundle.json","state_url":"https://pith.science/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/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":"2026-06-05T20:22:47Z","links":{"resolver":"https://pith.science/pith/PJERIFTIKPDITJPISO7ZOAD4Q2","bundle":"https://pith.science/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/bundle.json","state":"https://pith.science/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJERIFTIKPDITJPISO7ZOAD4Q2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PJERIFTIKPDITJPISO7ZOAD4Q2","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":"54e2ecdc4287290817fa632538f067d806148aa3e8907a7d85ee36efc428e591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-10T20:54:28Z","title_canon_sha256":"ffdee0214d5fdefed19a8aa8312faffe6603f5b0344c34a51158d66282a0039e"},"schema_version":"1.0","source":{"id":"1210.3059","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3059","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3059v2","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3059","created_at":"2026-05-18T03:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"PJERIFTIKPDI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PJERIFTIKPDITJPI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PJERIFTI","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:d20143afc25bfe767dfa59a4c302ab36bf8994fd6eee51b22f6f3f909faf8208","target":"graph","created_at":"2026-05-18T03:16:29Z","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":"If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a characterisation of the component module J/J^0 which is analogous to the Kodaira-Neron characterisation of the special fibre of a Neron model of an elliptic curve over a non-archimedean field. In particular, if L is the fraction field of a discrete valuation ring, then the component module is finite, and moreover trivial in the case of good reduction.\n  In the context o","authors_text":"Patrick Ingram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-10T20:54:28Z","title":"The filled Julia set of a Drinfeld module and uniform bounds for torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3059","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:a842a4f574647d1f7acaabf6dd61928cf75ec945b7f8d1042374eeb8ff98f79b","target":"record","created_at":"2026-05-18T03:16:29Z","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":"54e2ecdc4287290817fa632538f067d806148aa3e8907a7d85ee36efc428e591","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-10T20:54:28Z","title_canon_sha256":"ffdee0214d5fdefed19a8aa8312faffe6603f5b0344c34a51158d66282a0039e"},"schema_version":"1.0","source":{"id":"1210.3059","kind":"arxiv","version":2}},"canonical_sha256":"7a4914166853c689a5e893bf97007c86ba6a3f47345b7722b1b3ee89392389e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4914166853c689a5e893bf97007c86ba6a3f47345b7722b1b3ee89392389e2","first_computed_at":"2026-05-18T03:16:29.079093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:29.079093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lh4sAMkp9w4ck01LwXqTA42qHIDqVisOPLhjN0+YlmneXYOQbvEKJYymm5oT8GMAiULTquiG1JE2DJQxV/bYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:29.079620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3059","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a842a4f574647d1f7acaabf6dd61928cf75ec945b7f8d1042374eeb8ff98f79b","sha256:d20143afc25bfe767dfa59a4c302ab36bf8994fd6eee51b22f6f3f909faf8208"],"state_sha256":"6a3661a0a2ae7570ffa7a74d9c0b55ac0001ac1ea2846bcc0f879fd461961759"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i09TiyOKkxzXS3PiZq2LCFb3Mp/mQRI4yVDDtz3MzNAFVBSiTFwGfWZNAbW9+u7zDwhNt/1wCu1GbxdwsdvhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:22:47.714260Z","bundle_sha256":"f873e4b069cc0fa11e65c293abf1ac431629944ec0795b58c3cd0c6e6c64ad59"}}