{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7HMCRSL27ADRMBV34GJYXALKP7","short_pith_number":"pith:7HMCRSL2","canonical_record":{"source":{"id":"1103.1562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-08T15:38:54Z","cross_cats_sorted":[],"title_canon_sha256":"106cbfa638eb7d87b2b5a6d228532e9b62b34c002cadb11f8126316f8772d79c","abstract_canon_sha256":"06db10dd0b58a2e90420bbb85344ed5e1e45f5c9d794e6fe735dbbe641ec4645"},"schema_version":"1.0"},"canonical_sha256":"f9d828c97af8071606bbe1938b816a7fdc597837988f028a8c501f313e4f1769","source":{"kind":"arxiv","id":"1103.1562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1562","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1562v2","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1562","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"7HMCRSL27ADR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7HMCRSL27ADRMBV3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7HMCRSL2","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7HMCRSL27ADRMBV34GJYXALKP7","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-08T15:38:54Z","cross_cats_sorted":[],"title_canon_sha256":"106cbfa638eb7d87b2b5a6d228532e9b62b34c002cadb11f8126316f8772d79c","abstract_canon_sha256":"06db10dd0b58a2e90420bbb85344ed5e1e45f5c9d794e6fe735dbbe641ec4645"},"schema_version":"1.0"},"canonical_sha256":"f9d828c97af8071606bbe1938b816a7fdc597837988f028a8c501f313e4f1769","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:06.091985Z","signature_b64":"cN3GmRvXMKTXPmdk6PefOYpHgVos83pxHyvoOo+tXs6dUqN13kWcknY6axsIsDn1YgGyujONhY9C+hnLRVMYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9d828c97af8071606bbe1938b816a7fdc597837988f028a8c501f313e4f1769","last_reissued_at":"2026-05-18T04:27:06.091367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:06.091367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1562","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":"2026-05-18T04:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixj+E2o/PfpwHO+RHGPuRyyR7Pkk5PtI0zcVIejP8fZsO3WLbQpTnDpIRKMI3RDszGPoTlNZr6EAszydaahnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:15:08.817756Z"},"content_sha256":"678e4ef9d04ddf1cd8ebb1cc0f72f9d4c13c10ac5bbf0a602a93414937219eb2","schema_version":"1.0","event_id":"sha256:678e4ef9d04ddf1cd8ebb1cc0f72f9d4c13c10ac5bbf0a602a93414937219eb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7HMCRSL27ADRMBV34GJYXALKP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On piecewise isomorphism of some varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Melle-Hernandez, I. Luengo, S.M. Gusein-Zade","submitted_at":"2011-03-08T15:38:54Z","abstract_excerpt":"Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power $S^m(C^n)$ of the complex affine space $C^n$ is piecewise isomorphic to $C^{mn}$ and the m-th symmetric power $S^m(CP^\\infty)$ of the infinite dimensional complex projective space is piecewise isomorphic to the infinite dimensional Grassmannian $Gr(m,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1562","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":"2026-05-18T04:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8Gq1WijjP0bkap5B47GWjRNfpq0sOvMd/mYXao5evkXw10ttriC0g99Po3sBnPMe0PFxdt6p2SC0xJrN6bDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:15:08.818557Z"},"content_sha256":"2893d54550e19df3197662e1ed6e80d40c73324bc3956cfc539af18c2d3172ee","schema_version":"1.0","event_id":"sha256:2893d54550e19df3197662e1ed6e80d40c73324bc3956cfc539af18c2d3172ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HMCRSL27ADRMBV34GJYXALKP7/bundle.json","state_url":"https://pith.science/pith/7HMCRSL27ADRMBV34GJYXALKP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HMCRSL27ADRMBV34GJYXALKP7/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":"2026-06-08T00:15:08Z","links":{"resolver":"https://pith.science/pith/7HMCRSL27ADRMBV34GJYXALKP7","bundle":"https://pith.science/pith/7HMCRSL27ADRMBV34GJYXALKP7/bundle.json","state":"https://pith.science/pith/7HMCRSL27ADRMBV34GJYXALKP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HMCRSL27ADRMBV34GJYXALKP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7HMCRSL27ADRMBV34GJYXALKP7","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":"06db10dd0b58a2e90420bbb85344ed5e1e45f5c9d794e6fe735dbbe641ec4645","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-08T15:38:54Z","title_canon_sha256":"106cbfa638eb7d87b2b5a6d228532e9b62b34c002cadb11f8126316f8772d79c"},"schema_version":"1.0","source":{"id":"1103.1562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1562","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1562v2","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1562","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"7HMCRSL27ADR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7HMCRSL27ADRMBV3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7HMCRSL2","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:2893d54550e19df3197662e1ed6e80d40c73324bc3956cfc539af18c2d3172ee","target":"graph","created_at":"2026-05-18T04:27:06Z","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":"Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power $S^m(C^n)$ of the complex affine space $C^n$ is piecewise isomorphic to $C^{mn}$ and the m-th symmetric power $S^m(CP^\\infty)$ of the infinite dimensional complex projective space is piecewise isomorphic to the infinite dimensional Grassmannian $Gr(m,\\infty)$.","authors_text":"A. Melle-Hernandez, I. Luengo, S.M. Gusein-Zade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-08T15:38:54Z","title":"On piecewise isomorphism of some varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1562","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":"sha256:678e4ef9d04ddf1cd8ebb1cc0f72f9d4c13c10ac5bbf0a602a93414937219eb2","target":"record","created_at":"2026-05-18T04:27:06Z","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":"06db10dd0b58a2e90420bbb85344ed5e1e45f5c9d794e6fe735dbbe641ec4645","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-08T15:38:54Z","title_canon_sha256":"106cbfa638eb7d87b2b5a6d228532e9b62b34c002cadb11f8126316f8772d79c"},"schema_version":"1.0","source":{"id":"1103.1562","kind":"arxiv","version":2}},"canonical_sha256":"f9d828c97af8071606bbe1938b816a7fdc597837988f028a8c501f313e4f1769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d828c97af8071606bbe1938b816a7fdc597837988f028a8c501f313e4f1769","first_computed_at":"2026-05-18T04:27:06.091367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:06.091367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cN3GmRvXMKTXPmdk6PefOYpHgVos83pxHyvoOo+tXs6dUqN13kWcknY6axsIsDn1YgGyujONhY9C+hnLRVMYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:06.091985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:678e4ef9d04ddf1cd8ebb1cc0f72f9d4c13c10ac5bbf0a602a93414937219eb2","sha256:2893d54550e19df3197662e1ed6e80d40c73324bc3956cfc539af18c2d3172ee"],"state_sha256":"e96784fbbe4bbf110ab4bb636791194b46affd4af1362e229a8d5bebb8ea7daa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X79WLixYmuOyEOSUmrSoCccQ7TL1tpbQEk9okKzxp7RLo1k323lB0gRgJlfUxF3/dV92WWps9p2dtijBtGJpAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:15:08.825209Z","bundle_sha256":"5a00ac6de39a26033edada5e2929c7cdff615a4bcfeb5b2d4d5d927b63b99d67"}}