{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6UOGPPKSRTCIJHVL4KGGG2IOFV","short_pith_number":"pith:6UOGPPKS","canonical_record":{"source":{"id":"1210.7840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:02:28Z","cross_cats_sorted":[],"title_canon_sha256":"728dc3597c01212ce53f2f99272e1badc56425bf922ccccd356bb27e6557894c","abstract_canon_sha256":"0e7da262ae0df54ed8d779f5d329e697ed7c42b50aa0e31ffac3339bfd2dcfe5"},"schema_version":"1.0"},"canonical_sha256":"f51c67bd528cc4849eabe28c63690e2d5ddb2139b56287dd0f18440d35030266","source":{"kind":"arxiv","id":"1210.7840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7840","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7840v1","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7840","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6UOGPPKSRTCI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6UOGPPKSRTCIJHVL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6UOGPPKS","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6UOGPPKSRTCIJHVL4KGGG2IOFV","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:02:28Z","cross_cats_sorted":[],"title_canon_sha256":"728dc3597c01212ce53f2f99272e1badc56425bf922ccccd356bb27e6557894c","abstract_canon_sha256":"0e7da262ae0df54ed8d779f5d329e697ed7c42b50aa0e31ffac3339bfd2dcfe5"},"schema_version":"1.0"},"canonical_sha256":"f51c67bd528cc4849eabe28c63690e2d5ddb2139b56287dd0f18440d35030266","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:58.020078Z","signature_b64":"ejBFnHKKIA595leoRk7lXft6p6g3BRclYTezi4xMurEvyCpsvOSm9kHPf1D0MHEicr33edr6OcEq/9S4t7c5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f51c67bd528cc4849eabe28c63690e2d5ddb2139b56287dd0f18440d35030266","last_reissued_at":"2026-05-18T03:41:58.019221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:58.019221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7840","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":"2026-05-18T03:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9Brat/Y7SRIngWxzus4SAR/e4Hg8BGoOYHHkCKSLtBFAc1gQ9XNj2JvpZJoaUkNmZ0/FbXqCwThbsI4huBdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:16:18.457477Z"},"content_sha256":"b944b9cb87f3c57443e9850e5b99ce0347edd1fb03131f15dbca09cb95cf3d53","schema_version":"1.0","event_id":"sha256:b944b9cb87f3c57443e9850e5b99ce0347edd1fb03131f15dbca09cb95cf3d53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6UOGPPKSRTCIJHVL4KGGG2IOFV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bound on the Norm of Shortest Vectors in Lattices Arising from CM Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jacob McNamara","submitted_at":"2012-10-29T21:02:28Z","abstract_excerpt":"This paper partially addresses the problem of characterizing the lengths of vectors in a family of Euclidean lattices that arise from any CM number field. We define a modified quadratic form on these lattices, the weighted norm, that contains the standard field trace as a special case. Using this modified quadratic form, we obtain a bound on the field norm of any vector that has a minimal length in any of these lattices, in terms of a basis for the group of units of the ring of integers of the field. For any CM number field F, we prove that there exists a finite set of elements of F which allo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7840","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":""},"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":"2026-05-18T03:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l6svmJ92aLVsE4n4d3qeHIKJcJTRpCBbOAkjJt91HjeuJnA2X/DpRMa3BOvicVrcE8o/Dk+F9rbDp8Ay5cabCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:16:18.458111Z"},"content_sha256":"bb1df63c58a0550b706f4674e9d313671185a54f7bacef1ea4628a31c29fe3ca","schema_version":"1.0","event_id":"sha256:bb1df63c58a0550b706f4674e9d313671185a54f7bacef1ea4628a31c29fe3ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/bundle.json","state_url":"https://pith.science/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/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":"2026-06-07T16:16:18Z","links":{"resolver":"https://pith.science/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV","bundle":"https://pith.science/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/bundle.json","state":"https://pith.science/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UOGPPKSRTCIJHVL4KGGG2IOFV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6UOGPPKSRTCIJHVL4KGGG2IOFV","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":"0e7da262ae0df54ed8d779f5d329e697ed7c42b50aa0e31ffac3339bfd2dcfe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:02:28Z","title_canon_sha256":"728dc3597c01212ce53f2f99272e1badc56425bf922ccccd356bb27e6557894c"},"schema_version":"1.0","source":{"id":"1210.7840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7840","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7840v1","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7840","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6UOGPPKSRTCI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6UOGPPKSRTCIJHVL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6UOGPPKS","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:bb1df63c58a0550b706f4674e9d313671185a54f7bacef1ea4628a31c29fe3ca","target":"graph","created_at":"2026-05-18T03:41:58Z","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":"This paper partially addresses the problem of characterizing the lengths of vectors in a family of Euclidean lattices that arise from any CM number field. We define a modified quadratic form on these lattices, the weighted norm, that contains the standard field trace as a special case. Using this modified quadratic form, we obtain a bound on the field norm of any vector that has a minimal length in any of these lattices, in terms of a basis for the group of units of the ring of integers of the field. For any CM number field F, we prove that there exists a finite set of elements of F which allo","authors_text":"Jacob McNamara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:02:28Z","title":"A Bound on the Norm of Shortest Vectors in Lattices Arising from CM Number Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7840","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:b944b9cb87f3c57443e9850e5b99ce0347edd1fb03131f15dbca09cb95cf3d53","target":"record","created_at":"2026-05-18T03:41:58Z","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":"0e7da262ae0df54ed8d779f5d329e697ed7c42b50aa0e31ffac3339bfd2dcfe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:02:28Z","title_canon_sha256":"728dc3597c01212ce53f2f99272e1badc56425bf922ccccd356bb27e6557894c"},"schema_version":"1.0","source":{"id":"1210.7840","kind":"arxiv","version":1}},"canonical_sha256":"f51c67bd528cc4849eabe28c63690e2d5ddb2139b56287dd0f18440d35030266","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f51c67bd528cc4849eabe28c63690e2d5ddb2139b56287dd0f18440d35030266","first_computed_at":"2026-05-18T03:41:58.019221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:58.019221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ejBFnHKKIA595leoRk7lXft6p6g3BRclYTezi4xMurEvyCpsvOSm9kHPf1D0MHEicr33edr6OcEq/9S4t7c5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:58.020078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b944b9cb87f3c57443e9850e5b99ce0347edd1fb03131f15dbca09cb95cf3d53","sha256:bb1df63c58a0550b706f4674e9d313671185a54f7bacef1ea4628a31c29fe3ca"],"state_sha256":"0fab84930a963276dbfda09bcfcd7021518753e0d15dbc1790af36ad535415de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZANMAHG8Ovp+kVow4mxZvSPXyVKMWvppssnkLNWGkrbRcLnNrcA7cVfLSLZmFbdmPo2HcKXa0ebUK+Rl8k9iDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:16:18.461327Z","bundle_sha256":"ee0cef06a6ca4ddbee475d80dde5a3108a407c068386811a56506e42de018ab0"}}