{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:6AIOCO2NAL5YQKBE3PVA5ZWM67","short_pith_number":"pith:6AIOCO2N","canonical_record":{"source":{"id":"0706.3580","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-06-25T16:21:33Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"172249c3a0be3d474a1bc12af9f6f93b47d3c1afb1e99d96b6c9210f843e72b2","abstract_canon_sha256":"a39a2366684647165b752c4baff78f99686edc7362dca29cfef68433a321fc98"},"schema_version":"1.0"},"canonical_sha256":"f010e13b4d02fb882824dbea0ee6ccf7c167ad2fb7ab21981853805f82296b7d","source":{"kind":"arxiv","id":"0706.3580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3580","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3580v1","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3580","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"6AIOCO2NAL5Y","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6AIOCO2NAL5YQKBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6AIOCO2N","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:6AIOCO2NAL5YQKBE3PVA5ZWM67","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3580","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-06-25T16:21:33Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"172249c3a0be3d474a1bc12af9f6f93b47d3c1afb1e99d96b6c9210f843e72b2","abstract_canon_sha256":"a39a2366684647165b752c4baff78f99686edc7362dca29cfef68433a321fc98"},"schema_version":"1.0"},"canonical_sha256":"f010e13b4d02fb882824dbea0ee6ccf7c167ad2fb7ab21981853805f82296b7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:29.903760Z","signature_b64":"vWTxxx0bj6Vu8aZKLGdogGJbNaTDVwRsljN8LYGgETPF+OvVh4OSgEDeybRgJnP7VFAPsbh4g/Q9zB/V78oLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f010e13b4d02fb882824dbea0ee6ccf7c167ad2fb7ab21981853805f82296b7d","last_reissued_at":"2026-05-18T02:16:29.903177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:29.903177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3580","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":"2026-05-18T02:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exsPHD7u+MgJpxuDG0Rm0DcHSWl8C1SG7M0tG0cVHgv1/Ddxj8hEZRt4Lu648uFc2xSfajsTDYM7Iaqyw8kaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:36:30.542460Z"},"content_sha256":"fc7fba34714748acc26769a681407950cbe24a4403ac35189b6cd8893f6cd1dc","schema_version":"1.0","event_id":"sha256:fc7fba34714748acc26769a681407950cbe24a4403ac35189b6cd8893f6cd1dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:6AIOCO2NAL5YQKBE3PVA5ZWM67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cusps of Hilbert modular varieties","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"D. B. McReynolds","submitted_at":"2007-06-25T16:21:33Z","abstract_excerpt":"Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3580","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":"2026-05-18T02:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwCsJQ+JjfrGXHqV9nVdoZW7EzLl9SRT3h3OPSDIALiH5YEdQrBHkbJptfDbuvboVmlMevhbwrwWqpjTRjk+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:36:30.543181Z"},"content_sha256":"93c7a9da9fe0e05eb6e59d871fe7bc7502b6a45f08dbe1e64bafc13ec0ec825a","schema_version":"1.0","event_id":"sha256:93c7a9da9fe0e05eb6e59d871fe7bc7502b6a45f08dbe1e64bafc13ec0ec825a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/bundle.json","state_url":"https://pith.science/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/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":"2026-05-31T18:36:30Z","links":{"resolver":"https://pith.science/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67","bundle":"https://pith.science/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/bundle.json","state":"https://pith.science/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6AIOCO2NAL5YQKBE3PVA5ZWM67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6AIOCO2NAL5YQKBE3PVA5ZWM67","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":"a39a2366684647165b752c4baff78f99686edc7362dca29cfef68433a321fc98","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-06-25T16:21:33Z","title_canon_sha256":"172249c3a0be3d474a1bc12af9f6f93b47d3c1afb1e99d96b6c9210f843e72b2"},"schema_version":"1.0","source":{"id":"0706.3580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3580","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3580v1","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3580","created_at":"2026-05-18T02:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"6AIOCO2NAL5Y","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6AIOCO2NAL5YQKBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6AIOCO2N","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:93c7a9da9fe0e05eb6e59d871fe7bc7502b6a45f08dbe1e64bafc13ec0ec825a","target":"graph","created_at":"2026-05-18T02:16:29Z","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":"Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped nonsingu","authors_text":"D. B. McReynolds","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-06-25T16:21:33Z","title":"Cusps of Hilbert modular varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3580","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:fc7fba34714748acc26769a681407950cbe24a4403ac35189b6cd8893f6cd1dc","target":"record","created_at":"2026-05-18T02:16:29Z","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":"a39a2366684647165b752c4baff78f99686edc7362dca29cfef68433a321fc98","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-06-25T16:21:33Z","title_canon_sha256":"172249c3a0be3d474a1bc12af9f6f93b47d3c1afb1e99d96b6c9210f843e72b2"},"schema_version":"1.0","source":{"id":"0706.3580","kind":"arxiv","version":1}},"canonical_sha256":"f010e13b4d02fb882824dbea0ee6ccf7c167ad2fb7ab21981853805f82296b7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f010e13b4d02fb882824dbea0ee6ccf7c167ad2fb7ab21981853805f82296b7d","first_computed_at":"2026-05-18T02:16:29.903177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:29.903177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vWTxxx0bj6Vu8aZKLGdogGJbNaTDVwRsljN8LYGgETPF+OvVh4OSgEDeybRgJnP7VFAPsbh4g/Q9zB/V78oLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:29.903760Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc7fba34714748acc26769a681407950cbe24a4403ac35189b6cd8893f6cd1dc","sha256:93c7a9da9fe0e05eb6e59d871fe7bc7502b6a45f08dbe1e64bafc13ec0ec825a"],"state_sha256":"580825bc0078a0189342d389870776c90ed15684cc02fdef34f0fa32d08ec34d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6DySHoS+boQNKhfHTDYo2AujAlcxgIaHsR0BC7Uxv0olDuWp8eXaKBcTstmVFi5BpgKcWYMw+WbcEMHRXP3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:36:30.547039Z","bundle_sha256":"d74b77c7131563f66a0255a783479f87c392d078bcc7ea28cdc715910c9d14f6"}}