{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LRXZ6NBDZ4W3X2T2IJRXERX5XT","short_pith_number":"pith:LRXZ6NBD","canonical_record":{"source":{"id":"2406.01443","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T15:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"8adbcbe063a7ac042743ce3d69755e6bb5e7a26c66916f77d9a0e0f85403e7b8","abstract_canon_sha256":"9b9cbbfc680f1f33a204e83159bec7b63d51b50b2cc335a8fe0c013cc8897581"},"schema_version":"1.0"},"canonical_sha256":"5c6f9f3423cf2dbbea7a42637246fdbcdfc943ee800ea5e80118f37f379d08d5","source":{"kind":"arxiv","id":"2406.01443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01443","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01443v1","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01443","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"LRXZ6NBDZ4W3","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"LRXZ6NBDZ4W3X2T2","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"LRXZ6NBD","created_at":"2026-07-05T08:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LRXZ6NBDZ4W3X2T2IJRXERX5XT","target":"record","payload":{"canonical_record":{"source":{"id":"2406.01443","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T15:33:36Z","cross_cats_sorted":[],"title_canon_sha256":"8adbcbe063a7ac042743ce3d69755e6bb5e7a26c66916f77d9a0e0f85403e7b8","abstract_canon_sha256":"9b9cbbfc680f1f33a204e83159bec7b63d51b50b2cc335a8fe0c013cc8897581"},"schema_version":"1.0"},"canonical_sha256":"5c6f9f3423cf2dbbea7a42637246fdbcdfc943ee800ea5e80118f37f379d08d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:39.899910Z","signature_b64":"5pS8dYQTFVFiZUe2IXv8AVQHXfxBoSRgZpt2q2DC1SLXd5JtmOy7Ln/7aO0YsMglx5YDeNDLYFJNSYcGSeo0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c6f9f3423cf2dbbea7a42637246fdbcdfc943ee800ea5e80118f37f379d08d5","last_reissued_at":"2026-07-05T08:26:39.899480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:39.899480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.01443","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":"2026-07-05T08:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktPjlx8QPic6IPz2W8MXe1BgDH2PUdStJX2Q8qnZGoxlW2c+9JDRBpFq0jL7SB6kTa/64pflMy1tduSTwFSUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:26:15.089277Z"},"content_sha256":"a5e4a3e9b3d76e9a889246bcc682c52d6b731cf5e90acb5e68eefb302018fb58","schema_version":"1.0","event_id":"sha256:a5e4a3e9b3d76e9a889246bcc682c52d6b731cf5e90acb5e68eefb302018fb58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LRXZ6NBDZ4W3X2T2IJRXERX5XT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert's tenth problem for families of $ \\mathbb{Z}_p $-extensions of imaginary quadratic fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anwesh Ray, Katharina M\\\"uller","submitted_at":"2024-06-03T15:33:36Z","abstract_excerpt":"Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $\\mathbb{Z}_p$-towers of imaginary quadratic fields $K$. For a odd prime $p$, the lines $(a,b) \\in \\mathbb{P}^1(\\mathbb{Z}_p)$ are identified with $\\mathbb{Z}_p$-extensions $ K_{a,b}/K $. Under certain conditions on $ K $ that involve explicit elliptic curves, we identify a line $(a_0,b_0) \\in \\mathbb{P}^1(\\mathbb{Z}/p\\mathbb{Z})$ such that for all $(a,b) \\in \\mathbb{P}^1(\\mathbb{Z}_p)$ with $(a, b)\\not\\equiv (a_0, b_0)\\pmod{p}$, Hilbert's tenth problem has a negative answer in all finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01443","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/2406.01443/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":"2026-07-05T08:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NPrUch9lt6tR+04IW3PjZJOM+HPclup4VtH+dmQrBb4isGwhCsF9usN7y78XP2wZfnq7yP9ePD2g4TvfdqFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:26:15.090460Z"},"content_sha256":"cafa3093c8219a7719ee6ee44ea113800aebf7deac25edbb72bc7434003398e7","schema_version":"1.0","event_id":"sha256:cafa3093c8219a7719ee6ee44ea113800aebf7deac25edbb72bc7434003398e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/bundle.json","state_url":"https://pith.science/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/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":"2026-08-09T20:26:15Z","links":{"resolver":"https://pith.science/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT","bundle":"https://pith.science/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/bundle.json","state":"https://pith.science/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRXZ6NBDZ4W3X2T2IJRXERX5XT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LRXZ6NBDZ4W3X2T2IJRXERX5XT","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":"9b9cbbfc680f1f33a204e83159bec7b63d51b50b2cc335a8fe0c013cc8897581","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T15:33:36Z","title_canon_sha256":"8adbcbe063a7ac042743ce3d69755e6bb5e7a26c66916f77d9a0e0f85403e7b8"},"schema_version":"1.0","source":{"id":"2406.01443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01443","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01443v1","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01443","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"LRXZ6NBDZ4W3","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"LRXZ6NBDZ4W3X2T2","created_at":"2026-07-05T08:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"LRXZ6NBD","created_at":"2026-07-05T08:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:cafa3093c8219a7719ee6ee44ea113800aebf7deac25edbb72bc7434003398e7","target":"graph","created_at":"2026-07-05T08:26:39Z","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/2406.01443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $\\mathbb{Z}_p$-towers of imaginary quadratic fields $K$. For a odd prime $p$, the lines $(a,b) \\in \\mathbb{P}^1(\\mathbb{Z}_p)$ are identified with $\\mathbb{Z}_p$-extensions $ K_{a,b}/K $. Under certain conditions on $ K $ that involve explicit elliptic curves, we identify a line $(a_0,b_0) \\in \\mathbb{P}^1(\\mathbb{Z}/p\\mathbb{Z})$ such that for all $(a,b) \\in \\mathbb{P}^1(\\mathbb{Z}_p)$ with $(a, b)\\not\\equiv (a_0, b_0)\\pmod{p}$, Hilbert's tenth problem has a negative answer in all finite","authors_text":"Anwesh Ray, Katharina M\\\"uller","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T15:33:36Z","title":"Hilbert's tenth problem for families of $ \\mathbb{Z}_p $-extensions of imaginary quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01443","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:a5e4a3e9b3d76e9a889246bcc682c52d6b731cf5e90acb5e68eefb302018fb58","target":"record","created_at":"2026-07-05T08:26:39Z","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":"9b9cbbfc680f1f33a204e83159bec7b63d51b50b2cc335a8fe0c013cc8897581","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-06-03T15:33:36Z","title_canon_sha256":"8adbcbe063a7ac042743ce3d69755e6bb5e7a26c66916f77d9a0e0f85403e7b8"},"schema_version":"1.0","source":{"id":"2406.01443","kind":"arxiv","version":1}},"canonical_sha256":"5c6f9f3423cf2dbbea7a42637246fdbcdfc943ee800ea5e80118f37f379d08d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c6f9f3423cf2dbbea7a42637246fdbcdfc943ee800ea5e80118f37f379d08d5","first_computed_at":"2026-07-05T08:26:39.899480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:39.899480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5pS8dYQTFVFiZUe2IXv8AVQHXfxBoSRgZpt2q2DC1SLXd5JtmOy7Ln/7aO0YsMglx5YDeNDLYFJNSYcGSeo0BA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:39.899910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.01443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e4a3e9b3d76e9a889246bcc682c52d6b731cf5e90acb5e68eefb302018fb58","sha256:cafa3093c8219a7719ee6ee44ea113800aebf7deac25edbb72bc7434003398e7"],"state_sha256":"a2c6eaf7287ce36eb8d880d96443218237aa73bc249626b49324ec15a3693ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRy+Mr45kzWA6xAD5byX+tU+TpzEvlwvXiTSMnuDr4lGIIghGXCqhcSUCy08Vqg5ePlND+HFsaLnR3LqSRNgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:26:15.098661Z","bundle_sha256":"dfc29baba32cbe53555d7cd51e3ffd837275403f37b5604915dcb009e87ef889"}}