{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VSGJ6YEWSWIZBIIFGQ377XOZON","short_pith_number":"pith:VSGJ6YEW","canonical_record":{"source":{"id":"1902.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-05T16:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"cce578a50e89f7c681c077ac1daebaffb0610a64fdad06d92bc7c561886bcc8f","abstract_canon_sha256":"81d42c67b32412ca1aa6b6f5602d9a0b0892d8895832c7de197aedc4bbaaea71"},"schema_version":"1.0"},"canonical_sha256":"ac8c9f6096959190a1053437ffddd97373e10b189cd5225f0b2b8c04f30e3789","source":{"kind":"arxiv","id":"1902.01773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01773","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01773v1","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01773","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"VSGJ6YEWSWIZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VSGJ6YEWSWIZBIIF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VSGJ6YEW","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VSGJ6YEWSWIZBIIFGQ377XOZON","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-05T16:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"cce578a50e89f7c681c077ac1daebaffb0610a64fdad06d92bc7c561886bcc8f","abstract_canon_sha256":"81d42c67b32412ca1aa6b6f5602d9a0b0892d8895832c7de197aedc4bbaaea71"},"schema_version":"1.0"},"canonical_sha256":"ac8c9f6096959190a1053437ffddd97373e10b189cd5225f0b2b8c04f30e3789","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:46.771362Z","signature_b64":"zbN2aBoSOvDXRktKw1CA1tSv6TRl/qiVzoEgntRqNrrEBOBqwRK/BmI2Of8SU2X9DzZ9rN09d04oMpuKTtN5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8c9f6096959190a1053437ffddd97373e10b189cd5225f0b2b8c04f30e3789","last_reissued_at":"2026-05-17T23:54:46.770801Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:46.770801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01773","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":"2026-05-17T23:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOtJHR6PDKmIsiDQKpJgk7yFYkLTuUCr7cw+U3nXNLibUNonJ7IB1efDlgt4nShfDaY72W55ObPQ4JBPJFJOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:22:13.531714Z"},"content_sha256":"9cef3f56d8346bdc08de838959f00274c5282ec5bfbac5186354adcc437cf6bb","schema_version":"1.0","event_id":"sha256:9cef3f56d8346bdc08de838959f00274c5282ec5bfbac5186354adcc437cf6bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VSGJ6YEWSWIZBIIFGQ377XOZON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A complete classification of well-rounded real quadratic ideal lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anitha Srinivasan","submitted_at":"2019-02-05T16:32:19Z","abstract_excerpt":"We provide a complete classification of well-rounded ideal lattices arising from real quadratic fields. We show that the ideals that give rise to such lattices are precisely the ones that correspond to divisors $a$ of the discriminant $d$ that satisfy $\\sqrt{\\frac{d}{3}}<a<\\sqrt{3d}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01773","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":"2026-05-17T23:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7BIUVBHjuNm3EL8NBFL+q/VGuosiAXatql9NziuGZGdlNUxbTa6roqtSPh5Q49GtUSI7jgyOfNxn09bxlG5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:22:13.532072Z"},"content_sha256":"7edfbd58dbeccb5677c78da29bca77afa812623ae5d91e354bc2c62cbd6d765c","schema_version":"1.0","event_id":"sha256:7edfbd58dbeccb5677c78da29bca77afa812623ae5d91e354bc2c62cbd6d765c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/bundle.json","state_url":"https://pith.science/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/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":"2026-06-07T10:22:13Z","links":{"resolver":"https://pith.science/pith/VSGJ6YEWSWIZBIIFGQ377XOZON","bundle":"https://pith.science/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/bundle.json","state":"https://pith.science/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSGJ6YEWSWIZBIIFGQ377XOZON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VSGJ6YEWSWIZBIIFGQ377XOZON","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":"81d42c67b32412ca1aa6b6f5602d9a0b0892d8895832c7de197aedc4bbaaea71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-05T16:32:19Z","title_canon_sha256":"cce578a50e89f7c681c077ac1daebaffb0610a64fdad06d92bc7c561886bcc8f"},"schema_version":"1.0","source":{"id":"1902.01773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01773","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01773v1","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01773","created_at":"2026-05-17T23:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"VSGJ6YEWSWIZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VSGJ6YEWSWIZBIIF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VSGJ6YEW","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:7edfbd58dbeccb5677c78da29bca77afa812623ae5d91e354bc2c62cbd6d765c","target":"graph","created_at":"2026-05-17T23:54:46Z","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"},"paper":{"abstract_excerpt":"We provide a complete classification of well-rounded ideal lattices arising from real quadratic fields. We show that the ideals that give rise to such lattices are precisely the ones that correspond to divisors $a$ of the discriminant $d$ that satisfy $\\sqrt{\\frac{d}{3}}<a<\\sqrt{3d}.$","authors_text":"Anitha Srinivasan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-05T16:32:19Z","title":"A complete classification of well-rounded real quadratic ideal lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01773","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":"sha256:9cef3f56d8346bdc08de838959f00274c5282ec5bfbac5186354adcc437cf6bb","target":"record","created_at":"2026-05-17T23:54:46Z","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":"81d42c67b32412ca1aa6b6f5602d9a0b0892d8895832c7de197aedc4bbaaea71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-05T16:32:19Z","title_canon_sha256":"cce578a50e89f7c681c077ac1daebaffb0610a64fdad06d92bc7c561886bcc8f"},"schema_version":"1.0","source":{"id":"1902.01773","kind":"arxiv","version":1}},"canonical_sha256":"ac8c9f6096959190a1053437ffddd97373e10b189cd5225f0b2b8c04f30e3789","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac8c9f6096959190a1053437ffddd97373e10b189cd5225f0b2b8c04f30e3789","first_computed_at":"2026-05-17T23:54:46.770801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:46.770801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zbN2aBoSOvDXRktKw1CA1tSv6TRl/qiVzoEgntRqNrrEBOBqwRK/BmI2Of8SU2X9DzZ9rN09d04oMpuKTtN5Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:46.771362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cef3f56d8346bdc08de838959f00274c5282ec5bfbac5186354adcc437cf6bb","sha256:7edfbd58dbeccb5677c78da29bca77afa812623ae5d91e354bc2c62cbd6d765c"],"state_sha256":"5f7836c11fac724e7b16beda0d3222b342dd50ee5e1bd0df1c00894f905d5039"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGF/5LNd8L5S2EJOK7DLqZQBsbIvZuhMNSl+OtHwaT3RRIfnS2BtJ6kOxIg8Ry3vk/GzKCgHEBfcGfwbkw1MDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:22:13.534153Z","bundle_sha256":"9f35113958f5e4c94fa4eeff2d9184464a4893c4d9e148aaacbfd0239af8835f"}}