{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4T6DAYIZYNTC447MCK5MOAJUEI","short_pith_number":"pith:4T6DAYIZ","canonical_record":{"source":{"id":"1508.05599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-23T12:13:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8ca43cc9ff047efaffce1ff6dba212f39393c69bb5dd9508cd2fa306a8238aac","abstract_canon_sha256":"499517534b692367f22ea95d3fede43415ec5ed344e63a22366075c9c8f0c11f"},"schema_version":"1.0"},"canonical_sha256":"e4fc306119c3662e73ec12bac701342219b5e0bfe542ebc5fe60c30167ffb8f7","source":{"kind":"arxiv","id":"1508.05599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05599","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05599v2","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05599","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"pith_short_12","alias_value":"4T6DAYIZYNTC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4T6DAYIZYNTC447M","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4T6DAYIZ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4T6DAYIZYNTC447MCK5MOAJUEI","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-23T12:13:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8ca43cc9ff047efaffce1ff6dba212f39393c69bb5dd9508cd2fa306a8238aac","abstract_canon_sha256":"499517534b692367f22ea95d3fede43415ec5ed344e63a22366075c9c8f0c11f"},"schema_version":"1.0"},"canonical_sha256":"e4fc306119c3662e73ec12bac701342219b5e0bfe542ebc5fe60c30167ffb8f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:45.677543Z","signature_b64":"sTsqYt7iTZ2AK829aNY6jsj9zflnqliy5XLCFmdspfUNxdIZ417Z3jA1O98LilaeYQjRCJZW5xjlM70Jcs2VCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4fc306119c3662e73ec12bac701342219b5e0bfe542ebc5fe60c30167ffb8f7","last_reissued_at":"2026-05-18T01:27:45.677027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:45.677027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05599","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caMIEAjN5w0Uv14MCoRmvCBaMtYb4sZNONGPnvIp7NtkjHgN/tk8HQ1oauZNhqsj0ZuPNL0iqNv519cWtB2/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:05:39.201136Z"},"content_sha256":"4cb74947b6e00365a6dd8b109898ded4972ed8b3bcbc8f8a867fc6ddc8a8f9fe","schema_version":"1.0","event_id":"sha256:4cb74947b6e00365a6dd8b109898ded4972ed8b3bcbc8f8a867fc6ddc8a8f9fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4T6DAYIZYNTC447MCK5MOAJUEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The homotopy type of the Baily-Borel and allied compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Eduard Looijenga, Jiaming Chen","submitted_at":"2015-08-23T12:13:11Z","abstract_excerpt":"A number of compactifications familiar in complex-analytic geometry, in particular, the Baily-Borel compactification and its toroidal variants, as well as the Deligne-Mumford compactifications, can be covered by open subsets whose nonempty intersections are Eilenberg-MacLane spaces. We exploit this fact to describe the (rational) homotopy type of these spaces and the natural maps between them in terms of the simplicial sets attached to certain categories. We thus generalize an old result of Charney-Lee on the Baily-Borel compactification of A_g and recover (and rephrase) a more recent one of E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05599","kind":"arxiv","version":2},"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":"2026-05-18T01:27:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqCL4pH/vZP3c9LigOIRvJxGY5VCHI0wnutAiVElCXf8+xNMN3A+L0rznhafh4nJYN+sPgOLkcyz0CTwibG9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:05:39.201799Z"},"content_sha256":"24d8add15c7ec702849934f3519345d41592249c49e8a4dda1ad91ef252b0d77","schema_version":"1.0","event_id":"sha256:24d8add15c7ec702849934f3519345d41592249c49e8a4dda1ad91ef252b0d77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4T6DAYIZYNTC447MCK5MOAJUEI/bundle.json","state_url":"https://pith.science/pith/4T6DAYIZYNTC447MCK5MOAJUEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4T6DAYIZYNTC447MCK5MOAJUEI/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":"2026-05-30T05:05:39Z","links":{"resolver":"https://pith.science/pith/4T6DAYIZYNTC447MCK5MOAJUEI","bundle":"https://pith.science/pith/4T6DAYIZYNTC447MCK5MOAJUEI/bundle.json","state":"https://pith.science/pith/4T6DAYIZYNTC447MCK5MOAJUEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4T6DAYIZYNTC447MCK5MOAJUEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4T6DAYIZYNTC447MCK5MOAJUEI","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":"499517534b692367f22ea95d3fede43415ec5ed344e63a22366075c9c8f0c11f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-23T12:13:11Z","title_canon_sha256":"8ca43cc9ff047efaffce1ff6dba212f39393c69bb5dd9508cd2fa306a8238aac"},"schema_version":"1.0","source":{"id":"1508.05599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05599","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05599v2","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05599","created_at":"2026-05-18T01:27:45Z"},{"alias_kind":"pith_short_12","alias_value":"4T6DAYIZYNTC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4T6DAYIZYNTC447M","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4T6DAYIZ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:24d8add15c7ec702849934f3519345d41592249c49e8a4dda1ad91ef252b0d77","target":"graph","created_at":"2026-05-18T01:27:45Z","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":"A number of compactifications familiar in complex-analytic geometry, in particular, the Baily-Borel compactification and its toroidal variants, as well as the Deligne-Mumford compactifications, can be covered by open subsets whose nonempty intersections are Eilenberg-MacLane spaces. We exploit this fact to describe the (rational) homotopy type of these spaces and the natural maps between them in terms of the simplicial sets attached to certain categories. We thus generalize an old result of Charney-Lee on the Baily-Borel compactification of A_g and recover (and rephrase) a more recent one of E","authors_text":"Eduard Looijenga, Jiaming Chen","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-23T12:13:11Z","title":"The homotopy type of the Baily-Borel and allied compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05599","kind":"arxiv","version":2},"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":"sha256:4cb74947b6e00365a6dd8b109898ded4972ed8b3bcbc8f8a867fc6ddc8a8f9fe","target":"record","created_at":"2026-05-18T01:27:45Z","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":"499517534b692367f22ea95d3fede43415ec5ed344e63a22366075c9c8f0c11f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-23T12:13:11Z","title_canon_sha256":"8ca43cc9ff047efaffce1ff6dba212f39393c69bb5dd9508cd2fa306a8238aac"},"schema_version":"1.0","source":{"id":"1508.05599","kind":"arxiv","version":2}},"canonical_sha256":"e4fc306119c3662e73ec12bac701342219b5e0bfe542ebc5fe60c30167ffb8f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4fc306119c3662e73ec12bac701342219b5e0bfe542ebc5fe60c30167ffb8f7","first_computed_at":"2026-05-18T01:27:45.677027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:45.677027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTsqYt7iTZ2AK829aNY6jsj9zflnqliy5XLCFmdspfUNxdIZ417Z3jA1O98LilaeYQjRCJZW5xjlM70Jcs2VCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:45.677543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb74947b6e00365a6dd8b109898ded4972ed8b3bcbc8f8a867fc6ddc8a8f9fe","sha256:24d8add15c7ec702849934f3519345d41592249c49e8a4dda1ad91ef252b0d77"],"state_sha256":"7fa2656e0c79f0c6369bee532db1d127bab263296e7cee3dd077b951d3e39821"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Y/WDQNW8Oifqmn3ujC2RiTjjiznlMmZHSMCU78qE3SAblhi7hXnGlJEVXyDCxZgAymfEw83WaVQOdrDJIr+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:05:39.204933Z","bundle_sha256":"591c99fc3bd3e28ac50f883eccad58c026d6d31affb935c4ad3acb55db1c9b69"}}