{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KUHL6FNB7VCSSIJVKVB36CL54V","short_pith_number":"pith:KUHL6FNB","canonical_record":{"source":{"id":"1812.08531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-20T12:52:25Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"3851e3d439c08c97c3f63a16d0cb21949aafcaa275724571fad524c2cf0f3bba","abstract_canon_sha256":"e0a5cad4420447a7c7bfafb7549dcd193b74129c8247eb488040de9b681abd09"},"schema_version":"1.0"},"canonical_sha256":"550ebf15a1fd452921355543bf097de573f2094f932a46471eb9f3a5bea8ee26","source":{"kind":"arxiv","id":"1812.08531","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08531","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08531v2","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08531","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_12","alias_value":"KUHL6FNB7VCS","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_16","alias_value":"KUHL6FNB7VCSSIJV","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_8","alias_value":"KUHL6FNB","created_at":"2026-07-05T00:22:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KUHL6FNB7VCSSIJVKVB36CL54V","target":"record","payload":{"canonical_record":{"source":{"id":"1812.08531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-20T12:52:25Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"3851e3d439c08c97c3f63a16d0cb21949aafcaa275724571fad524c2cf0f3bba","abstract_canon_sha256":"e0a5cad4420447a7c7bfafb7549dcd193b74129c8247eb488040de9b681abd09"},"schema_version":"1.0"},"canonical_sha256":"550ebf15a1fd452921355543bf097de573f2094f932a46471eb9f3a5bea8ee26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:36.641196Z","signature_b64":"g25uep9r1NsQjItz7+C6mlcvptMXCf7tPuod7ZuClEQh5jdq7c51u9fYNYn9xwdQuJyfucAvw0y6ltIeAxdWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"550ebf15a1fd452921355543bf097de573f2094f932a46471eb9f3a5bea8ee26","last_reissued_at":"2026-07-05T00:22:36.640721Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:36.640721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.08531","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":"2026-07-05T00:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"io+kkJtit0/580Aehg9Nvo1EsMPd5NhtM8+3YS48EVBHY8ImFaqF65bxtcEVFcSR3GPv0WqpE1pbhAA/rtAKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T12:35:27.886859Z"},"content_sha256":"5f541d2cda1b122e2c33e696e56bd780a74877466efadc6c597f5125f3e2d22e","schema_version":"1.0","event_id":"sha256:5f541d2cda1b122e2c33e696e56bd780a74877466efadc6c597f5125f3e2d22e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KUHL6FNB7VCSSIJVKVB36CL54V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pathologies on the Hilbert scheme of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Joachim Jelisiejew","submitted_at":"2018-12-20T12:52:25Z","abstract_excerpt":"We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08531","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.08531/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOIKElzuqU6wQh5mhW1gQFa6p0FYmf0NixxVv7d/dRy8fHq63gnbtLO5BYumvlQ1IuS9sQLxpsUIXYRQNKK1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T12:35:27.887753Z"},"content_sha256":"41e160e4ee55fdfbdfeb883b071b4d813b511756a2c40da44e1ca1179d0f0d15","schema_version":"1.0","event_id":"sha256:41e160e4ee55fdfbdfeb883b071b4d813b511756a2c40da44e1ca1179d0f0d15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUHL6FNB7VCSSIJVKVB36CL54V/bundle.json","state_url":"https://pith.science/pith/KUHL6FNB7VCSSIJVKVB36CL54V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUHL6FNB7VCSSIJVKVB36CL54V/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":"2026-08-19T12:35:27Z","links":{"resolver":"https://pith.science/pith/KUHL6FNB7VCSSIJVKVB36CL54V","bundle":"https://pith.science/pith/KUHL6FNB7VCSSIJVKVB36CL54V/bundle.json","state":"https://pith.science/pith/KUHL6FNB7VCSSIJVKVB36CL54V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUHL6FNB7VCSSIJVKVB36CL54V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KUHL6FNB7VCSSIJVKVB36CL54V","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":"e0a5cad4420447a7c7bfafb7549dcd193b74129c8247eb488040de9b681abd09","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-20T12:52:25Z","title_canon_sha256":"3851e3d439c08c97c3f63a16d0cb21949aafcaa275724571fad524c2cf0f3bba"},"schema_version":"1.0","source":{"id":"1812.08531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08531","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08531v2","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08531","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_12","alias_value":"KUHL6FNB7VCS","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_16","alias_value":"KUHL6FNB7VCSSIJV","created_at":"2026-07-05T00:22:36Z"},{"alias_kind":"pith_short_8","alias_value":"KUHL6FNB","created_at":"2026-07-05T00:22:36Z"}],"graph_snapshots":[{"event_id":"sha256:41e160e4ee55fdfbdfeb883b071b4d813b511756a2c40da44e1ca1179d0f0d15","target":"graph","created_at":"2026-07-05T00:22:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1812.08531/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition.","authors_text":"Joachim Jelisiejew","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-20T12:52:25Z","title":"Pathologies on the Hilbert scheme of points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08531","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":"sha256:5f541d2cda1b122e2c33e696e56bd780a74877466efadc6c597f5125f3e2d22e","target":"record","created_at":"2026-07-05T00:22:36Z","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":"e0a5cad4420447a7c7bfafb7549dcd193b74129c8247eb488040de9b681abd09","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-20T12:52:25Z","title_canon_sha256":"3851e3d439c08c97c3f63a16d0cb21949aafcaa275724571fad524c2cf0f3bba"},"schema_version":"1.0","source":{"id":"1812.08531","kind":"arxiv","version":2}},"canonical_sha256":"550ebf15a1fd452921355543bf097de573f2094f932a46471eb9f3a5bea8ee26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"550ebf15a1fd452921355543bf097de573f2094f932a46471eb9f3a5bea8ee26","first_computed_at":"2026-07-05T00:22:36.640721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:36.640721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g25uep9r1NsQjItz7+C6mlcvptMXCf7tPuod7ZuClEQh5jdq7c51u9fYNYn9xwdQuJyfucAvw0y6ltIeAxdWAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:36.641196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f541d2cda1b122e2c33e696e56bd780a74877466efadc6c597f5125f3e2d22e","sha256:41e160e4ee55fdfbdfeb883b071b4d813b511756a2c40da44e1ca1179d0f0d15"],"state_sha256":"493604cbe3626cd9db8d691d9eb7aff852be11ea1814429f66d39efd0bf07791"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y1G77TQwkYAQjWE5B5aMfj/L5mTaCNFjHddO0uGpYRpnEx6+SRzmzTYZpezuU2ThN1MaFLfhGhnX14VkYImhAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T12:35:27.895694Z","bundle_sha256":"93ed9c49ff8d30f45aa09559f5b21dce98adb7bb6fcde705cd840fcfd973ce33"}}