{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:I6XDRPNDOQ4UIUHOVCMWGDKN6T","short_pith_number":"pith:I6XDRPND","canonical_record":{"source":{"id":"1210.2340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-08T17:00:48Z","cross_cats_sorted":[],"title_canon_sha256":"b923cfcb699f37d96aa33df43f94d47c019c3d672f95bb14bcddf74999f70aca","abstract_canon_sha256":"074a5829f6e453d89cbb4b4a23fe1b45f8e88c833198e157803358e444652ac3"},"schema_version":"1.0"},"canonical_sha256":"47ae38bda374394450eea899630d4df4d3e590dca4ecd3ccc543ebd7a748aab3","source":{"kind":"arxiv","id":"1210.2340","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2340","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2340v3","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2340","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"I6XDRPNDOQ4U","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I6XDRPNDOQ4UIUHO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I6XDRPND","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:I6XDRPNDOQ4UIUHOVCMWGDKN6T","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2340","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-08T17:00:48Z","cross_cats_sorted":[],"title_canon_sha256":"b923cfcb699f37d96aa33df43f94d47c019c3d672f95bb14bcddf74999f70aca","abstract_canon_sha256":"074a5829f6e453d89cbb4b4a23fe1b45f8e88c833198e157803358e444652ac3"},"schema_version":"1.0"},"canonical_sha256":"47ae38bda374394450eea899630d4df4d3e590dca4ecd3ccc543ebd7a748aab3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:40.785339Z","signature_b64":"4ulXnuLjRBVirFWRfyeAffY98gmbDlRfIaW6rrWBr5B1/XlzkcE0rNY5QQXehJn5S5apYHNyH3AFiiGyQ5NMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47ae38bda374394450eea899630d4df4d3e590dca4ecd3ccc543ebd7a748aab3","last_reissued_at":"2026-05-18T03:37:40.784829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:40.784829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2340","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoHYZ6Y1TGosG3wFii6bQ1IAqqLxwCv5q87QOFp9r3TptQ94CzIjDqXCRsFSJdk2vPmL9oKlLyq+1vU61OYLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:29:32.132582Z"},"content_sha256":"3891dd2f203676d4202186c5bad677ccf2233a248428e5e935e476b0442e2cb4","schema_version":"1.0","event_id":"sha256:3891dd2f203676d4202186c5bad677ccf2233a248428e5e935e476b0442e2cb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:I6XDRPNDOQ4UIUHOVCMWGDKN6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound for the canonical height associated to a Drinfeld module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Ingram","submitted_at":"2012-10-08T17:00:48Z","abstract_excerpt":"Denis associated to each Drinfeld module M over a global function function field L a canonical height function, which plays a role analogous to that of the Neron-Tate height in the context of elliptic curves. We prove that there exist constants \\epsilon>0 and C, depending only on the number of places at which M has bad reduction, such that either x in M is a torsion point of bounded order, or else the canonical height of x is bound below by \\epsilon max{h(j_M), deg(D_M)}, where j_M is a certain invariant of the isomorphism class of M, and D_M is the minimal discriminant of M. As an application"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2340","kind":"arxiv","version":3},"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":"2026-05-18T03:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+GkS6/IcaajVD1XamMKXeGKheSwrfU/ACduqBh1CfkgDGRPAujVSMyL5K7VLu1bgJqgQ9cuOzM8IC654pisCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:29:32.133532Z"},"content_sha256":"6bce87277e9e823f647fbc25bc376a99ee01700f69655027496fd292c2dae29d","schema_version":"1.0","event_id":"sha256:6bce87277e9e823f647fbc25bc376a99ee01700f69655027496fd292c2dae29d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/bundle.json","state_url":"https://pith.science/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/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":"2026-06-05T20:29:32Z","links":{"resolver":"https://pith.science/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T","bundle":"https://pith.science/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/bundle.json","state":"https://pith.science/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6XDRPNDOQ4UIUHOVCMWGDKN6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I6XDRPNDOQ4UIUHOVCMWGDKN6T","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":"074a5829f6e453d89cbb4b4a23fe1b45f8e88c833198e157803358e444652ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-08T17:00:48Z","title_canon_sha256":"b923cfcb699f37d96aa33df43f94d47c019c3d672f95bb14bcddf74999f70aca"},"schema_version":"1.0","source":{"id":"1210.2340","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2340","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2340v3","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2340","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"I6XDRPNDOQ4U","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I6XDRPNDOQ4UIUHO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I6XDRPND","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:6bce87277e9e823f647fbc25bc376a99ee01700f69655027496fd292c2dae29d","target":"graph","created_at":"2026-05-18T03:37:40Z","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":"Denis associated to each Drinfeld module M over a global function function field L a canonical height function, which plays a role analogous to that of the Neron-Tate height in the context of elliptic curves. We prove that there exist constants \\epsilon>0 and C, depending only on the number of places at which M has bad reduction, such that either x in M is a torsion point of bounded order, or else the canonical height of x is bound below by \\epsilon max{h(j_M), deg(D_M)}, where j_M is a certain invariant of the isomorphism class of M, and D_M is the minimal discriminant of M. As an application","authors_text":"Patrick Ingram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-08T17:00:48Z","title":"A lower bound for the canonical height associated to a Drinfeld module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2340","kind":"arxiv","version":3},"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":"sha256:3891dd2f203676d4202186c5bad677ccf2233a248428e5e935e476b0442e2cb4","target":"record","created_at":"2026-05-18T03:37:40Z","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":"074a5829f6e453d89cbb4b4a23fe1b45f8e88c833198e157803358e444652ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-08T17:00:48Z","title_canon_sha256":"b923cfcb699f37d96aa33df43f94d47c019c3d672f95bb14bcddf74999f70aca"},"schema_version":"1.0","source":{"id":"1210.2340","kind":"arxiv","version":3}},"canonical_sha256":"47ae38bda374394450eea899630d4df4d3e590dca4ecd3ccc543ebd7a748aab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47ae38bda374394450eea899630d4df4d3e590dca4ecd3ccc543ebd7a748aab3","first_computed_at":"2026-05-18T03:37:40.784829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:40.784829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ulXnuLjRBVirFWRfyeAffY98gmbDlRfIaW6rrWBr5B1/XlzkcE0rNY5QQXehJn5S5apYHNyH3AFiiGyQ5NMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:40.785339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2340","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3891dd2f203676d4202186c5bad677ccf2233a248428e5e935e476b0442e2cb4","sha256:6bce87277e9e823f647fbc25bc376a99ee01700f69655027496fd292c2dae29d"],"state_sha256":"233133c2e5b488c3f1f048f1b00865720ec3501dea5c36c9b542576258d3ad35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ykE5K8PopwsUWmhL+txwt5P8uStpj/F1/vMIL+TYCqUPDUJBQRiFooH6TbRjsBldt/9duHj/Ji2vBN7FHYNaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:29:32.138088Z","bundle_sha256":"65f7917b1d55167acd23e559de073cf25b11ac70d72a12d7d23bd83e45cceb35"}}