{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DVGYUH37FHM4K6LU2HBIVMVZJJ","short_pith_number":"pith:DVGYUH37","canonical_record":{"source":{"id":"1312.4465","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-16T19:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"8c0328a0d7e874136f10922b906e3282757b1469d3f3b368bdefb72a3dc9be13","abstract_canon_sha256":"e91adf10fd8d3f39fc52242fba66654db251c18b671a507a103288c9d5928e42"},"schema_version":"1.0"},"canonical_sha256":"1d4d8a1f7f29d9c57974d1c28ab2b94a6f39ce9bf0e67eb2c583396628d644e2","source":{"kind":"arxiv","id":"1312.4465","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4465","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4465v5","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4465","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"DVGYUH37FHM4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DVGYUH37FHM4K6LU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DVGYUH37","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DVGYUH37FHM4K6LU2HBIVMVZJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4465","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-16T19:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"8c0328a0d7e874136f10922b906e3282757b1469d3f3b368bdefb72a3dc9be13","abstract_canon_sha256":"e91adf10fd8d3f39fc52242fba66654db251c18b671a507a103288c9d5928e42"},"schema_version":"1.0"},"canonical_sha256":"1d4d8a1f7f29d9c57974d1c28ab2b94a6f39ce9bf0e67eb2c583396628d644e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:05.096635Z","signature_b64":"bx1eyaKOVs9B97rW900zlP3XSiK8H3s7jTixul+973LDGPG3xA8Rh+nyu6InMk/ZS/R1MtWe3vxiw2DoL3lCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d4d8a1f7f29d9c57974d1c28ab2b94a6f39ce9bf0e67eb2c583396628d644e2","last_reissued_at":"2026-05-17T23:45:05.096107Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:05.096107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4465","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cjqq7epcRyiwLygcrSA2Z/kgp1VfTcFm/jE4PXSAyF6hhaTnTbVUdn/iXg/LMVSUM6M8jrGlL/elBDzdnC0YDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:07.925019Z"},"content_sha256":"8715cc7246261cae23d87f98a084281895759fe4566f315bf3582f56bc032df0","schema_version":"1.0","event_id":"sha256:8715cc7246261cae23d87f98a084281895759fe4566f315bf3582f56bc032df0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DVGYUH37FHM4K6LU2HBIVMVZJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit smoothed prime ideals theorems under GRH","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giuseppe Molteni, Lo\\\"ic Greni\\'e","submitted_at":"2013-12-16T19:10:48Z","abstract_excerpt":"Let $\\psi_{\\mathbb K}$ be the Chebyshev function of a number field $\\mathbb K$. Let $\\psi^{(1)}_{\\mathbb K}(x):=\\int_{0}^{x}\\psi_{\\mathbb K}(t)\\,d t$ and $\\psi^{(2)}_{\\mathbb K}(x):=2\\int_{0}^{x}\\psi^{(1)}_{\\mathbb K}(t)\\,d t$. We prove under GRH explicit inequalities for the differences $|\\psi^{(1)}_{\\mathbb K}(x) - \\tfrac{x^2}{2}|$ and $|\\psi^{(2)}_{\\mathbb K}(x) - \\tfrac{x^3}{3}|$. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4465","kind":"arxiv","version":5},"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":"2026-05-17T23:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpQFlIumrpwabxFL9rrauViMb1ClqPeMfdEBBCj0Q0dSBjeEGQF0yYnBWKV/DJvyG5JFdgedqp4lFp48Hec5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:02:07.925664Z"},"content_sha256":"48f9abf3280c835ea3ed9c0fb9eb31aa9751cb03887d299a018f1285f7e63a7e","schema_version":"1.0","event_id":"sha256:48f9abf3280c835ea3ed9c0fb9eb31aa9751cb03887d299a018f1285f7e63a7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/bundle.json","state_url":"https://pith.science/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/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":"2026-06-02T06:02:07Z","links":{"resolver":"https://pith.science/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ","bundle":"https://pith.science/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/bundle.json","state":"https://pith.science/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVGYUH37FHM4K6LU2HBIVMVZJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DVGYUH37FHM4K6LU2HBIVMVZJJ","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":"e91adf10fd8d3f39fc52242fba66654db251c18b671a507a103288c9d5928e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-16T19:10:48Z","title_canon_sha256":"8c0328a0d7e874136f10922b906e3282757b1469d3f3b368bdefb72a3dc9be13"},"schema_version":"1.0","source":{"id":"1312.4465","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4465","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4465v5","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4465","created_at":"2026-05-17T23:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"DVGYUH37FHM4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DVGYUH37FHM4K6LU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DVGYUH37","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:48f9abf3280c835ea3ed9c0fb9eb31aa9751cb03887d299a018f1285f7e63a7e","target":"graph","created_at":"2026-05-17T23:45:05Z","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":"Let $\\psi_{\\mathbb K}$ be the Chebyshev function of a number field $\\mathbb K$. Let $\\psi^{(1)}_{\\mathbb K}(x):=\\int_{0}^{x}\\psi_{\\mathbb K}(t)\\,d t$ and $\\psi^{(2)}_{\\mathbb K}(x):=2\\int_{0}^{x}\\psi^{(1)}_{\\mathbb K}(t)\\,d t$. We prove under GRH explicit inequalities for the differences $|\\psi^{(1)}_{\\mathbb K}(x) - \\tfrac{x^2}{2}|$ and $|\\psi^{(2)}_{\\mathbb K}(x) - \\tfrac{x^3}{3}|$. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals.","authors_text":"Giuseppe Molteni, Lo\\\"ic Greni\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-16T19:10:48Z","title":"Explicit smoothed prime ideals theorems under GRH"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4465","kind":"arxiv","version":5},"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":"sha256:8715cc7246261cae23d87f98a084281895759fe4566f315bf3582f56bc032df0","target":"record","created_at":"2026-05-17T23:45:05Z","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":"e91adf10fd8d3f39fc52242fba66654db251c18b671a507a103288c9d5928e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-16T19:10:48Z","title_canon_sha256":"8c0328a0d7e874136f10922b906e3282757b1469d3f3b368bdefb72a3dc9be13"},"schema_version":"1.0","source":{"id":"1312.4465","kind":"arxiv","version":5}},"canonical_sha256":"1d4d8a1f7f29d9c57974d1c28ab2b94a6f39ce9bf0e67eb2c583396628d644e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d4d8a1f7f29d9c57974d1c28ab2b94a6f39ce9bf0e67eb2c583396628d644e2","first_computed_at":"2026-05-17T23:45:05.096107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:05.096107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bx1eyaKOVs9B97rW900zlP3XSiK8H3s7jTixul+973LDGPG3xA8Rh+nyu6InMk/ZS/R1MtWe3vxiw2DoL3lCAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:05.096635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4465","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8715cc7246261cae23d87f98a084281895759fe4566f315bf3582f56bc032df0","sha256:48f9abf3280c835ea3ed9c0fb9eb31aa9751cb03887d299a018f1285f7e63a7e"],"state_sha256":"35076242d48d58bbef6f0424351738c0cccf5b0dabebcf9ac5f2320c9c7389fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uguyaRtVLfdH3WpInkzMe+NPJVlx/ueGz9U9bXSQSumq8kLtZizTQBrUzNbLMcNKlYNx/9LLRLd6JCJzH4MaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:02:07.928804Z","bundle_sha256":"059800c96d2a0497bb9871acf1fc9707c708d608e3d629a1defcbcb3b1d43d55"}}