{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QLJIYAIQ3VHFD5X775HBCJKVSX","short_pith_number":"pith:QLJIYAIQ","canonical_record":{"source":{"id":"0810.2840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-16T16:24:05Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"21159224c14cae2031695667c18d6eec6529e298883c2f09ad28ed25fe2dd6a1","abstract_canon_sha256":"e01969ee3c6ca2f9bad8172aad80a242c5be1ea3eb650294291cfe4b6e0217e1"},"schema_version":"1.0"},"canonical_sha256":"82d28c0110dd4e51f6ffff4e11255595ca39fc878ab183a87941e0c981d20e97","source":{"kind":"arxiv","id":"0810.2840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2840","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2840v1","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2840","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"QLJIYAIQ3VHF","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"QLJIYAIQ3VHFD5X7","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"QLJIYAIQ","created_at":"2026-07-04T15:15:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QLJIYAIQ3VHFD5X775HBCJKVSX","target":"record","payload":{"canonical_record":{"source":{"id":"0810.2840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-16T16:24:05Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"21159224c14cae2031695667c18d6eec6529e298883c2f09ad28ed25fe2dd6a1","abstract_canon_sha256":"e01969ee3c6ca2f9bad8172aad80a242c5be1ea3eb650294291cfe4b6e0217e1"},"schema_version":"1.0"},"canonical_sha256":"82d28c0110dd4e51f6ffff4e11255595ca39fc878ab183a87941e0c981d20e97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:15:10.641060Z","signature_b64":"W9YWF+VCq1YqLv6BaDXOWPd+6vIRoY/0e1CoEDDUl/yHZ9LrtSHdFD3Kew4u1fEHjt4ncunseUK3q+twdzkbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d28c0110dd4e51f6ffff4e11255595ca39fc878ab183a87941e0c981d20e97","last_reissued_at":"2026-07-04T15:15:10.640695Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:15:10.640695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.2840","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":"2026-07-04T15:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ts/LtUO68lL9w/xNxQlZjo82ju41LqVoQ0nTF5tpVnwOHrtIaKIJcetaNLI6i2+6fG47fYfZY1byBsTmfGVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T17:45:17.132544Z"},"content_sha256":"3676378218f6e20c36c24c577ebc97f428c37edc0e298d0cf34e2fd7b5b6bea4","schema_version":"1.0","event_id":"sha256:3676378218f6e20c36c24c577ebc97f428c37edc0e298d0cf34e2fd7b5b6bea4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QLJIYAIQ3VHFD5X775HBCJKVSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Cycles of a Fixed Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2008-10-16T16:24:05Z","abstract_excerpt":"In this paper, the homotopy groups of Chow variety $C_{p,d}(P^n)$ of effective $p$-cycles of degree $d$ is proved to be stable in the sense that $p$ or $n$ increases. We also obtain a negative answer to a question by Lawson and Michelsohn on homotopy groups for the space of degree two cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2840","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0810.2840/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":"2026-07-04T15:15:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5+qwM9d8wPmacDPpQvKyNnqlyiXdeV5nGop2vLKskT6bnHYGLRZGMayy9W+q3IEt6tf/WwtbDkQZ5AGmE05Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T17:45:17.133552Z"},"content_sha256":"63330bee4a35d8f095e3aa4e79181b366f7dbeb49e39a4e24c441ec32846ba06","schema_version":"1.0","event_id":"sha256:63330bee4a35d8f095e3aa4e79181b366f7dbeb49e39a4e24c441ec32846ba06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/bundle.json","state_url":"https://pith.science/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/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":"2026-08-19T17:45:17Z","links":{"resolver":"https://pith.science/pith/QLJIYAIQ3VHFD5X775HBCJKVSX","bundle":"https://pith.science/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/bundle.json","state":"https://pith.science/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QLJIYAIQ3VHFD5X775HBCJKVSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QLJIYAIQ3VHFD5X775HBCJKVSX","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":"e01969ee3c6ca2f9bad8172aad80a242c5be1ea3eb650294291cfe4b6e0217e1","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-16T16:24:05Z","title_canon_sha256":"21159224c14cae2031695667c18d6eec6529e298883c2f09ad28ed25fe2dd6a1"},"schema_version":"1.0","source":{"id":"0810.2840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2840","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2840v1","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2840","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"QLJIYAIQ3VHF","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"QLJIYAIQ3VHFD5X7","created_at":"2026-07-04T15:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"QLJIYAIQ","created_at":"2026-07-04T15:15:10Z"}],"graph_snapshots":[{"event_id":"sha256:63330bee4a35d8f095e3aa4e79181b366f7dbeb49e39a4e24c441ec32846ba06","target":"graph","created_at":"2026-07-04T15:15:10Z","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/0810.2840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, the homotopy groups of Chow variety $C_{p,d}(P^n)$ of effective $p$-cycles of degree $d$ is proved to be stable in the sense that $p$ or $n$ increases. We also obtain a negative answer to a question by Lawson and Michelsohn on homotopy groups for the space of degree two cycles.","authors_text":"Wenchuan Hu","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-16T16:24:05Z","title":"Algebraic Cycles of a Fixed Degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2840","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":"sha256:3676378218f6e20c36c24c577ebc97f428c37edc0e298d0cf34e2fd7b5b6bea4","target":"record","created_at":"2026-07-04T15:15:10Z","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":"e01969ee3c6ca2f9bad8172aad80a242c5be1ea3eb650294291cfe4b6e0217e1","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-16T16:24:05Z","title_canon_sha256":"21159224c14cae2031695667c18d6eec6529e298883c2f09ad28ed25fe2dd6a1"},"schema_version":"1.0","source":{"id":"0810.2840","kind":"arxiv","version":1}},"canonical_sha256":"82d28c0110dd4e51f6ffff4e11255595ca39fc878ab183a87941e0c981d20e97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82d28c0110dd4e51f6ffff4e11255595ca39fc878ab183a87941e0c981d20e97","first_computed_at":"2026-07-04T15:15:10.640695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:15:10.640695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W9YWF+VCq1YqLv6BaDXOWPd+6vIRoY/0e1CoEDDUl/yHZ9LrtSHdFD3Kew4u1fEHjt4ncunseUK3q+twdzkbDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:15:10.641060Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.2840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3676378218f6e20c36c24c577ebc97f428c37edc0e298d0cf34e2fd7b5b6bea4","sha256:63330bee4a35d8f095e3aa4e79181b366f7dbeb49e39a4e24c441ec32846ba06"],"state_sha256":"39ce473721e318207410e6b11293f6e8921e829758f11447b533fd4e1b5baab1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rk7MHrt6y+uXIyPEvpmd9pY3PewbOs9t7L08zJZugE39HMjmtTB7kDOxwpWHsB7cQO+E7TSLR8pVNoxcy1KdCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T17:45:17.139160Z","bundle_sha256":"a51ebd03555602918ab03e5a423d5c00581f2ee86b110246ed9ffe1c2ea2e6ad"}}