{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:I64MVG5Y6JPFA7XVSUH6KMR2JX","short_pith_number":"pith:I64MVG5Y","canonical_record":{"source":{"id":"2408.11653","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-08-21T14:26:05Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f6d0d82443d9aeb5325bd2e4b7c09902656fb0b7ded99e6abcc5134701b8ce7e","abstract_canon_sha256":"5db4bf66c3b1438fe4b39362d42f24865e6a471000bdc52428a94a57887700c8"},"schema_version":"1.0"},"canonical_sha256":"47b8ca9bb8f25e507ef5950fe5323a4dfee915975828af06be52b192f7f9c8cd","source":{"kind":"arxiv","id":"2408.11653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11653","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11653v1","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11653","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"I64MVG5Y6JPF","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_16","alias_value":"I64MVG5Y6JPFA7XV","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_8","alias_value":"I64MVG5Y","created_at":"2026-07-05T08:57:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:I64MVG5Y6JPFA7XVSUH6KMR2JX","target":"record","payload":{"canonical_record":{"source":{"id":"2408.11653","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-08-21T14:26:05Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f6d0d82443d9aeb5325bd2e4b7c09902656fb0b7ded99e6abcc5134701b8ce7e","abstract_canon_sha256":"5db4bf66c3b1438fe4b39362d42f24865e6a471000bdc52428a94a57887700c8"},"schema_version":"1.0"},"canonical_sha256":"47b8ca9bb8f25e507ef5950fe5323a4dfee915975828af06be52b192f7f9c8cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:57:46.742879Z","signature_b64":"GvWOqrJBO/Mh63SeX+8VpIWYOj53daNMGWNDvGFJNXm+Ni3P56VTfhOj7XWD1bHW5hYd1TOS73SiiOROWMiwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47b8ca9bb8f25e507ef5950fe5323a4dfee915975828af06be52b192f7f9c8cd","last_reissued_at":"2026-07-05T08:57:46.742407Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:57:46.742407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.11653","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":"2026-07-05T08:57:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GLdFkONzS+3QywQ4LGNllGP4fz0jF16/wo8xm/H4IOxqG07Y8riTC6JYtMHKKgTEG8Xk14frbiZG4QIWrEJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:06:06.357003Z"},"content_sha256":"4e1635d528b896930057b089670801be88611a16bc3ced1c41651825d0f78754","schema_version":"1.0","event_id":"sha256:4e1635d528b896930057b089670801be88611a16bc3ced1c41651825d0f78754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:I64MVG5Y6JPFA7XVSUH6KMR2JX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional algorithmic Mordell","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Brian Lawrence, Levent Alp\\\"oge","submitted_at":"2024-08-21T14:26:05Z","abstract_excerpt":"We specify a Turing machine $T_{\\text{Mordell}}$ with the following properties.\n  1. On input $(K,C/K)$, with $K/\\mathbb{Q}$ a number field and $C/K$ a smooth projective hyperbolic curve, if $T_{\\text{Mordell}}$ terminates, then it outputs $C(K)$.\n  2. The Hodge, Tate, and Fontaine-Mazur conjectures imply that $T_{\\text{Mordell}}$ always terminates.\n  Similarly we specify a Turing machine $T_{\\text{Shafarevich}}$ with the following properties.\n  1. On input $(g, K,S, d)$, with $g, d \\in \\mathbb{Z}^+$, $K/\\mathbb{Q}$ a number field, and $S$ a finite set of places of $K$, if $T_{\\text{Shafarevic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11653","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.11653/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:57:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyNi7lFtKY4G0ComT/W7sGuo7BVP+jrJDdmT1tQDN2EsHWvc0U3Jpc+Y0YJowQJb2NNBJiSiGJsl/zqGmrLFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:06:06.357400Z"},"content_sha256":"2b6b24eeeb806c1f34f16259bf17fe88714860d4110072d1a7f4d63c0f27d303","schema_version":"1.0","event_id":"sha256:2b6b24eeeb806c1f34f16259bf17fe88714860d4110072d1a7f4d63c0f27d303"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/bundle.json","state_url":"https://pith.science/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/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":"2026-08-13T12:06:06Z","links":{"resolver":"https://pith.science/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX","bundle":"https://pith.science/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/bundle.json","state":"https://pith.science/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I64MVG5Y6JPFA7XVSUH6KMR2JX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I64MVG5Y6JPFA7XVSUH6KMR2JX","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":"5db4bf66c3b1438fe4b39362d42f24865e6a471000bdc52428a94a57887700c8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-08-21T14:26:05Z","title_canon_sha256":"f6d0d82443d9aeb5325bd2e4b7c09902656fb0b7ded99e6abcc5134701b8ce7e"},"schema_version":"1.0","source":{"id":"2408.11653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11653","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11653v1","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11653","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"I64MVG5Y6JPF","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_16","alias_value":"I64MVG5Y6JPFA7XV","created_at":"2026-07-05T08:57:46Z"},{"alias_kind":"pith_short_8","alias_value":"I64MVG5Y","created_at":"2026-07-05T08:57:46Z"}],"graph_snapshots":[{"event_id":"sha256:2b6b24eeeb806c1f34f16259bf17fe88714860d4110072d1a7f4d63c0f27d303","target":"graph","created_at":"2026-07-05T08:57:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.11653/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We specify a Turing machine $T_{\\text{Mordell}}$ with the following properties.\n  1. On input $(K,C/K)$, with $K/\\mathbb{Q}$ a number field and $C/K$ a smooth projective hyperbolic curve, if $T_{\\text{Mordell}}$ terminates, then it outputs $C(K)$.\n  2. The Hodge, Tate, and Fontaine-Mazur conjectures imply that $T_{\\text{Mordell}}$ always terminates.\n  Similarly we specify a Turing machine $T_{\\text{Shafarevich}}$ with the following properties.\n  1. On input $(g, K,S, d)$, with $g, d \\in \\mathbb{Z}^+$, $K/\\mathbb{Q}$ a number field, and $S$ a finite set of places of $K$, if $T_{\\text{Shafarevic","authors_text":"Brian Lawrence, Levent Alp\\\"oge","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-08-21T14:26:05Z","title":"Conditional algorithmic Mordell"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11653","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":"sha256:4e1635d528b896930057b089670801be88611a16bc3ced1c41651825d0f78754","target":"record","created_at":"2026-07-05T08:57:46Z","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":"5db4bf66c3b1438fe4b39362d42f24865e6a471000bdc52428a94a57887700c8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-08-21T14:26:05Z","title_canon_sha256":"f6d0d82443d9aeb5325bd2e4b7c09902656fb0b7ded99e6abcc5134701b8ce7e"},"schema_version":"1.0","source":{"id":"2408.11653","kind":"arxiv","version":1}},"canonical_sha256":"47b8ca9bb8f25e507ef5950fe5323a4dfee915975828af06be52b192f7f9c8cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47b8ca9bb8f25e507ef5950fe5323a4dfee915975828af06be52b192f7f9c8cd","first_computed_at":"2026-07-05T08:57:46.742407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:57:46.742407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GvWOqrJBO/Mh63SeX+8VpIWYOj53daNMGWNDvGFJNXm+Ni3P56VTfhOj7XWD1bHW5hYd1TOS73SiiOROWMiwBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:57:46.742879Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.11653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e1635d528b896930057b089670801be88611a16bc3ced1c41651825d0f78754","sha256:2b6b24eeeb806c1f34f16259bf17fe88714860d4110072d1a7f4d63c0f27d303"],"state_sha256":"be92af1bc217d6db0440f7642445e2906c8e9d4740e5cd9567e0f024c4b1bbf2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLKXDd/CsS1tFm+D1Vb/LDFDmhIAhuvtClWjmH1a+sXZG3Mji1FRyFgxNiFrcx8aHpEkNt+qCc9bAAp+O1XdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:06:06.360005Z","bundle_sha256":"4b5e3e68f90cd26369d89241c1c9ba441b80d528cedc0892673c0abbf050f617"}}