{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZS4UAVNSDUJXTDDYINADUBHZGJ","short_pith_number":"pith:ZS4UAVNS","canonical_record":{"source":{"id":"1608.01504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-04T11:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"98cc5e0305c5059d7672e72ebbf2331d318b5ec8c82d5425eb505cb4076afcb7","abstract_canon_sha256":"684fa09ab4fcaf14b7a9e04823f342b97aad4d34dd9ddad63aec44f7f18d2ac5"},"schema_version":"1.0"},"canonical_sha256":"ccb94055b21d13798c7843403a04f93257350d565d7d5e86994b20a47b860107","source":{"kind":"arxiv","id":"1608.01504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01504","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01504v3","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01504","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZS4UAVNSDUJX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZS4UAVNSDUJXTDDY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZS4UAVNS","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZS4UAVNSDUJXTDDYINADUBHZGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-04T11:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"98cc5e0305c5059d7672e72ebbf2331d318b5ec8c82d5425eb505cb4076afcb7","abstract_canon_sha256":"684fa09ab4fcaf14b7a9e04823f342b97aad4d34dd9ddad63aec44f7f18d2ac5"},"schema_version":"1.0"},"canonical_sha256":"ccb94055b21d13798c7843403a04f93257350d565d7d5e86994b20a47b860107","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:17.579997Z","signature_b64":"ymVYtnHI+txWfI1k+m2wuQIcfhs6+TwTgcwfs3A4gfQ3Uft5YPBaKYPkBWXWI8cKko27HWlL9I/jfTKVOn2nDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccb94055b21d13798c7843403a04f93257350d565d7d5e86994b20a47b860107","last_reissued_at":"2026-05-18T00:30:17.579352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:17.579352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01504","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5EdPQw7ZCYQP8qI031qjfXntZ9N+nXgVOYePhbmw9w4i2MwiZ2FzITjE6T4uRAYqwHXl6G/hvZ/uypZtjKfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:26:38.442401Z"},"content_sha256":"57d114d78da4d0b560d5f9ae6d7b92147a8382f86532ac0f8d1c75c8968802a2","schema_version":"1.0","event_id":"sha256:57d114d78da4d0b560d5f9ae6d7b92147a8382f86532ac0f8d1c75c8968802a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZS4UAVNSDUJXTDDYINADUBHZGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stratifications of flag spaces and functoriality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jean-Stefan Koskivirta, Wushi Goldring","submitted_at":"2016-08-04T11:50:40Z","abstract_excerpt":"We define quotient stacks of \"zip flags\". They form towers above the stack of $G$-zips introduced by Moonen, Pink, Wedhorn and Ziegler. We define a stratification on the stack of zip flags, and prove that it is principally pure, under a certain assumption on $p$. The fiber product with a Shimura variety of Hodge-type is a generalization of flag spaces considered by Ekedahl-Van der Geer. For large $p$, we prove that all strata are affine. We prove a theorem on discreteness of fibers for finite morphisms between stacks of $G$-zips. This allows us to prove that the zip stratification is principal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01504","kind":"arxiv","version":3},"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":"2026-05-18T00:30:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJ3j9qwg4tRFMqR+9r8zprgdUN/C2Uch4K/93Ca46m7gYZA8fSMaQlYOGedFdDnfhgvePPTIntH0Q6QCHSSGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:26:38.443130Z"},"content_sha256":"8dd33139cc0ba96e07cdc720b2c9729bc999ccccc86d83da03a56b744e486653","schema_version":"1.0","event_id":"sha256:8dd33139cc0ba96e07cdc720b2c9729bc999ccccc86d83da03a56b744e486653"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/bundle.json","state_url":"https://pith.science/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/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":"2026-06-10T06:26:38Z","links":{"resolver":"https://pith.science/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ","bundle":"https://pith.science/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/bundle.json","state":"https://pith.science/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZS4UAVNSDUJXTDDYINADUBHZGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZS4UAVNSDUJXTDDYINADUBHZGJ","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":"684fa09ab4fcaf14b7a9e04823f342b97aad4d34dd9ddad63aec44f7f18d2ac5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-04T11:50:40Z","title_canon_sha256":"98cc5e0305c5059d7672e72ebbf2331d318b5ec8c82d5425eb505cb4076afcb7"},"schema_version":"1.0","source":{"id":"1608.01504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01504","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01504v3","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01504","created_at":"2026-05-18T00:30:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZS4UAVNSDUJX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZS4UAVNSDUJXTDDY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZS4UAVNS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:8dd33139cc0ba96e07cdc720b2c9729bc999ccccc86d83da03a56b744e486653","target":"graph","created_at":"2026-05-18T00:30:17Z","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 define quotient stacks of \"zip flags\". They form towers above the stack of $G$-zips introduced by Moonen, Pink, Wedhorn and Ziegler. We define a stratification on the stack of zip flags, and prove that it is principally pure, under a certain assumption on $p$. The fiber product with a Shimura variety of Hodge-type is a generalization of flag spaces considered by Ekedahl-Van der Geer. For large $p$, we prove that all strata are affine. We prove a theorem on discreteness of fibers for finite morphisms between stacks of $G$-zips. This allows us to prove that the zip stratification is principal","authors_text":"Jean-Stefan Koskivirta, Wushi Goldring","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-04T11:50:40Z","title":"Stratifications of flag spaces and functoriality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01504","kind":"arxiv","version":3},"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":"sha256:57d114d78da4d0b560d5f9ae6d7b92147a8382f86532ac0f8d1c75c8968802a2","target":"record","created_at":"2026-05-18T00:30:17Z","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":"684fa09ab4fcaf14b7a9e04823f342b97aad4d34dd9ddad63aec44f7f18d2ac5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-04T11:50:40Z","title_canon_sha256":"98cc5e0305c5059d7672e72ebbf2331d318b5ec8c82d5425eb505cb4076afcb7"},"schema_version":"1.0","source":{"id":"1608.01504","kind":"arxiv","version":3}},"canonical_sha256":"ccb94055b21d13798c7843403a04f93257350d565d7d5e86994b20a47b860107","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccb94055b21d13798c7843403a04f93257350d565d7d5e86994b20a47b860107","first_computed_at":"2026-05-18T00:30:17.579352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:17.579352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ymVYtnHI+txWfI1k+m2wuQIcfhs6+TwTgcwfs3A4gfQ3Uft5YPBaKYPkBWXWI8cKko27HWlL9I/jfTKVOn2nDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:17.579997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57d114d78da4d0b560d5f9ae6d7b92147a8382f86532ac0f8d1c75c8968802a2","sha256:8dd33139cc0ba96e07cdc720b2c9729bc999ccccc86d83da03a56b744e486653"],"state_sha256":"e1f36596ade300ad320e1683f96147ed41c098a686ca0ac05a844913a8b15001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qg/kJknlX3RUr/pZWI9lqmk/z3xiM1lMrMOzt+NadN66Cf48D5EmUZj59t/bzx0jPIvrOIWddN/LWU2U/dCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T06:26:38.447413Z","bundle_sha256":"66f60ad7e29092d0bf7cf139caf712c073945e8cf9b4f34dc15b2bd2f80c1c30"}}