{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:L5FBWCYXEWY6NXOMVD75BTH3KU","short_pith_number":"pith:L5FBWCYX","canonical_record":{"source":{"id":"math/0412057","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-12-02T17:02:33Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"cab3dcb525d10c7fe94a9215ea22fbb4bfd97f1d403e5d552e11e4f472e4445d","abstract_canon_sha256":"cdc2f03f0457ff028c44d14f40155758177e9527a878548117efe725c3ce3baa"},"schema_version":"1.0"},"canonical_sha256":"5f4a1b0b1725b1e6ddcca8ffd0ccfb553d0f8af1bd40ce2b81de49fd04b0b6fd","source":{"kind":"arxiv","id":"math/0412057","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412057","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412057v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412057","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"L5FBWCYXEWY6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"L5FBWCYXEWY6NXOM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"L5FBWCYX","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:L5FBWCYXEWY6NXOMVD75BTH3KU","target":"record","payload":{"canonical_record":{"source":{"id":"math/0412057","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-12-02T17:02:33Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"cab3dcb525d10c7fe94a9215ea22fbb4bfd97f1d403e5d552e11e4f472e4445d","abstract_canon_sha256":"cdc2f03f0457ff028c44d14f40155758177e9527a878548117efe725c3ce3baa"},"schema_version":"1.0"},"canonical_sha256":"5f4a1b0b1725b1e6ddcca8ffd0ccfb553d0f8af1bd40ce2b81de49fd04b0b6fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.171153Z","signature_b64":"+krtC3+u2jfyCR+bLxTCJB4cGe5auXj3Ipqmfxt8dLD2lklTNV9ixoEstZqXdgQD8AKLtgKehi0IysMcUTH4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f4a1b0b1725b1e6ddcca8ffd0ccfb553d0f8af1bd40ce2b81de49fd04b0b6fd","last_reissued_at":"2026-05-18T02:41:32.170712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.170712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0412057","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":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vf3/X4i+u4z7I29tkoXbvvLvr9l/F52kUjIWsHfWcMmmPF7OHJ4xMPJPwZHah5t7+LfsEATTaCT9qSPY+DArAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:33:56.611461Z"},"content_sha256":"02a234b00ce972c76cf4cf005ec58b30b4de300c6cf413b8e05ad41a2431b8d7","schema_version":"1.0","event_id":"sha256:02a234b00ce972c76cf4cf005ec58b30b4de300c6cf413b8e05ad41a2431b8d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:L5FBWCYXEWY6NXOMVD75BTH3KU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugation spaces","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AT","authors_text":"Jean-Claude Hausmann, Tara Holm, Volker Puppe","submitted_at":"2004-12-02T17:02:33Z","abstract_excerpt":"There are classical examples of spaces X with an involution tau whose mod 2-comhomology ring resembles that of their fixed point set X^tau: there is a ring isomorphism kappa: H^2*(X) --> H^*(X^tau). Such examples include complex Grassmannians, toric manifolds, polygon spaces. In this paper, we show that the ring isomorphism kappa is part of an interesting structure in equivariant cohomology called an H^*-frame. An H^*-frame, if it exists, is natural and unique. A space with involution admitting an H^*-frame is called a conjugation space. Many examples of conjugation spaces are constructed, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412057","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":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L6ChHz8+9O5A0+t7xH2TmmXONgDQyP7AH72GQmYEjSQMGHr9AB95h+9J+wyh1b5BPUbIKavPeZEX7MooBRCtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:33:56.612196Z"},"content_sha256":"f33afc9025a5e63aae31c848527a1ff6f77ccff8d4ff816827739d4d9f25eafe","schema_version":"1.0","event_id":"sha256:f33afc9025a5e63aae31c848527a1ff6f77ccff8d4ff816827739d4d9f25eafe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/bundle.json","state_url":"https://pith.science/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/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":"2026-06-10T11:33:56Z","links":{"resolver":"https://pith.science/pith/L5FBWCYXEWY6NXOMVD75BTH3KU","bundle":"https://pith.science/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/bundle.json","state":"https://pith.science/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5FBWCYXEWY6NXOMVD75BTH3KU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:L5FBWCYXEWY6NXOMVD75BTH3KU","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":"cdc2f03f0457ff028c44d14f40155758177e9527a878548117efe725c3ce3baa","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AT","submitted_at":"2004-12-02T17:02:33Z","title_canon_sha256":"cab3dcb525d10c7fe94a9215ea22fbb4bfd97f1d403e5d552e11e4f472e4445d"},"schema_version":"1.0","source":{"id":"math/0412057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412057","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412057v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412057","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"L5FBWCYXEWY6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"L5FBWCYXEWY6NXOM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"L5FBWCYX","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f33afc9025a5e63aae31c848527a1ff6f77ccff8d4ff816827739d4d9f25eafe","target":"graph","created_at":"2026-05-18T02:41:32Z","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":"There are classical examples of spaces X with an involution tau whose mod 2-comhomology ring resembles that of their fixed point set X^tau: there is a ring isomorphism kappa: H^2*(X) --> H^*(X^tau). Such examples include complex Grassmannians, toric manifolds, polygon spaces. In this paper, we show that the ring isomorphism kappa is part of an interesting structure in equivariant cohomology called an H^*-frame. An H^*-frame, if it exists, is natural and unique. A space with involution admitting an H^*-frame is called a conjugation space. Many examples of conjugation spaces are constructed, for","authors_text":"Jean-Claude Hausmann, Tara Holm, Volker Puppe","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2004-12-02T17:02:33Z","title":"Conjugation spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412057","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":"sha256:02a234b00ce972c76cf4cf005ec58b30b4de300c6cf413b8e05ad41a2431b8d7","target":"record","created_at":"2026-05-18T02:41:32Z","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":"cdc2f03f0457ff028c44d14f40155758177e9527a878548117efe725c3ce3baa","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AT","submitted_at":"2004-12-02T17:02:33Z","title_canon_sha256":"cab3dcb525d10c7fe94a9215ea22fbb4bfd97f1d403e5d552e11e4f472e4445d"},"schema_version":"1.0","source":{"id":"math/0412057","kind":"arxiv","version":2}},"canonical_sha256":"5f4a1b0b1725b1e6ddcca8ffd0ccfb553d0f8af1bd40ce2b81de49fd04b0b6fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f4a1b0b1725b1e6ddcca8ffd0ccfb553d0f8af1bd40ce2b81de49fd04b0b6fd","first_computed_at":"2026-05-18T02:41:32.170712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.170712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+krtC3+u2jfyCR+bLxTCJB4cGe5auXj3Ipqmfxt8dLD2lklTNV9ixoEstZqXdgQD8AKLtgKehi0IysMcUTH4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.171153Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02a234b00ce972c76cf4cf005ec58b30b4de300c6cf413b8e05ad41a2431b8d7","sha256:f33afc9025a5e63aae31c848527a1ff6f77ccff8d4ff816827739d4d9f25eafe"],"state_sha256":"c1e64c1e97c9fc579550010e2e1afcbe296ebeeb464702a2ff6c05225672e8e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTy21wXeaAddAxyvZB9M+68vhfe3vLrk12PBTY82IJz5nTj6ZmUaohGiMcX5TLRbPu0y9bbm9WQIjE+EVWBpDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:33:56.616489Z","bundle_sha256":"5c147f11c1960833ef2e125bb9737f2a843b78eeb42a75059d33f88bda818d1d"}}