{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M5HVLV65WFNL7YYY5CPOX2J75C","short_pith_number":"pith:M5HVLV65","canonical_record":{"source":{"id":"1206.3341","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-14T22:50:40Z","cross_cats_sorted":["math.AG","math.DG","math.KT"],"title_canon_sha256":"3430cbcd649f7926898dfe62afadc3d29725aabe85e016432bd21c91dfe0ad69","abstract_canon_sha256":"8fb3b459604b714da2e9e4cd5c0c9ffe2f5575b3588a4e9ff9fecab602085af0"},"schema_version":"1.0"},"canonical_sha256":"674f55d7ddb15abfe318e89eebe93fe88868a6b1bba99aaeac28243bae8ebf84","source":{"kind":"arxiv","id":"1206.3341","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3341","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3341v4","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3341","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"M5HVLV65WFNL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M5HVLV65WFNL7YYY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M5HVLV65","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M5HVLV65WFNL7YYY5CPOX2J75C","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3341","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-14T22:50:40Z","cross_cats_sorted":["math.AG","math.DG","math.KT"],"title_canon_sha256":"3430cbcd649f7926898dfe62afadc3d29725aabe85e016432bd21c91dfe0ad69","abstract_canon_sha256":"8fb3b459604b714da2e9e4cd5c0c9ffe2f5575b3588a4e9ff9fecab602085af0"},"schema_version":"1.0"},"canonical_sha256":"674f55d7ddb15abfe318e89eebe93fe88868a6b1bba99aaeac28243bae8ebf84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:18.937002Z","signature_b64":"Vaf3uYtjVrmWW6J2FVxPnfs0mYOJaMdlQHaz7bw4bCdct6wOdOcz5G/F7/hnhd0i4ACI+6S+Eez+7oRR+LsFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"674f55d7ddb15abfe318e89eebe93fe88868a6b1bba99aaeac28243bae8ebf84","last_reissued_at":"2026-05-18T02:40:18.936553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:18.936553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3341","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+wyHolJWYmTIEFIDZ/EnNMsuElU6rJ0IKXfBUVQpzG2zvkgDcAHqVC9euVEVGInLvA1rZbF0I3jqbDXUDk1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:10:54.427988Z"},"content_sha256":"6ad7061ad1be6b297dcf4d15e1e186ad8ee5f7f0f2d0468a26a75543cdab4d13","schema_version":"1.0","event_id":"sha256:6ad7061ad1be6b297dcf4d15e1e186ad8ee5f7f0f2d0468a26a75543cdab4d13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M5HVLV65WFNL7YYY5CPOX2J75C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothing maps into algebraic sets and spaces of flat connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.KT"],"primary_cat":"math.AT","authors_text":"Daniel A. Ramras, Thomas Baird","submitted_at":"2012-06-14T22:50:40Z","abstract_excerpt":"Let X be a real algebraic subset of R^n and M a smooth, closed manifold. We show that all continuous maps from M to X are homotopic (in X) to C^\\infty maps. We apply this result to study characteristic classes of vector bundles associated to continuous families of complex group representations, and we establish lower bounds on the ranks of the homotopy groups of spaces of flat connections over aspherical manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3341","kind":"arxiv","version":4},"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":"2026-05-18T02:40:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSfLqo4JP+7i4U/6z0IfQwyTh+bpAeabGbRZXwEa44A65B+gSZV/HnEjETUE/p/REcQe8pTN96CpvufiKdupBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:10:54.428704Z"},"content_sha256":"83e1960522d24d44c494e89eadb222b2a60ffb0224ff3fa39196f4fc39715b5c","schema_version":"1.0","event_id":"sha256:83e1960522d24d44c494e89eadb222b2a60ffb0224ff3fa39196f4fc39715b5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5HVLV65WFNL7YYY5CPOX2J75C/bundle.json","state_url":"https://pith.science/pith/M5HVLV65WFNL7YYY5CPOX2J75C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5HVLV65WFNL7YYY5CPOX2J75C/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":"2026-06-07T22:10:54Z","links":{"resolver":"https://pith.science/pith/M5HVLV65WFNL7YYY5CPOX2J75C","bundle":"https://pith.science/pith/M5HVLV65WFNL7YYY5CPOX2J75C/bundle.json","state":"https://pith.science/pith/M5HVLV65WFNL7YYY5CPOX2J75C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5HVLV65WFNL7YYY5CPOX2J75C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M5HVLV65WFNL7YYY5CPOX2J75C","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":"8fb3b459604b714da2e9e4cd5c0c9ffe2f5575b3588a4e9ff9fecab602085af0","cross_cats_sorted":["math.AG","math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-14T22:50:40Z","title_canon_sha256":"3430cbcd649f7926898dfe62afadc3d29725aabe85e016432bd21c91dfe0ad69"},"schema_version":"1.0","source":{"id":"1206.3341","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3341","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3341v4","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3341","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"M5HVLV65WFNL","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M5HVLV65WFNL7YYY","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M5HVLV65","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:83e1960522d24d44c494e89eadb222b2a60ffb0224ff3fa39196f4fc39715b5c","target":"graph","created_at":"2026-05-18T02:40:18Z","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":"Let X be a real algebraic subset of R^n and M a smooth, closed manifold. We show that all continuous maps from M to X are homotopic (in X) to C^\\infty maps. We apply this result to study characteristic classes of vector bundles associated to continuous families of complex group representations, and we establish lower bounds on the ranks of the homotopy groups of spaces of flat connections over aspherical manifolds.","authors_text":"Daniel A. Ramras, Thomas Baird","cross_cats":["math.AG","math.DG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-14T22:50:40Z","title":"Smoothing maps into algebraic sets and spaces of flat connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3341","kind":"arxiv","version":4},"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":"sha256:6ad7061ad1be6b297dcf4d15e1e186ad8ee5f7f0f2d0468a26a75543cdab4d13","target":"record","created_at":"2026-05-18T02:40:18Z","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":"8fb3b459604b714da2e9e4cd5c0c9ffe2f5575b3588a4e9ff9fecab602085af0","cross_cats_sorted":["math.AG","math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-06-14T22:50:40Z","title_canon_sha256":"3430cbcd649f7926898dfe62afadc3d29725aabe85e016432bd21c91dfe0ad69"},"schema_version":"1.0","source":{"id":"1206.3341","kind":"arxiv","version":4}},"canonical_sha256":"674f55d7ddb15abfe318e89eebe93fe88868a6b1bba99aaeac28243bae8ebf84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"674f55d7ddb15abfe318e89eebe93fe88868a6b1bba99aaeac28243bae8ebf84","first_computed_at":"2026-05-18T02:40:18.936553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:18.936553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vaf3uYtjVrmWW6J2FVxPnfs0mYOJaMdlQHaz7bw4bCdct6wOdOcz5G/F7/hnhd0i4ACI+6S+Eez+7oRR+LsFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:18.937002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3341","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ad7061ad1be6b297dcf4d15e1e186ad8ee5f7f0f2d0468a26a75543cdab4d13","sha256:83e1960522d24d44c494e89eadb222b2a60ffb0224ff3fa39196f4fc39715b5c"],"state_sha256":"0672cf56814299f6d128d330f591a299c13341a4ed7b80105e788d8dca14f216"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1RAK3W00/omOCBMpUdPuSxWT0b/xPrP6BLrMeM4ejKTZtpFUiCN86d6l8EGMEJK/eAsbrPKcZAuD5dEe0iW6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:10:54.432365Z","bundle_sha256":"bb9e2bca77d771038940da6bc21106045ac771e1dabbc70f6017309a06b3ed00"}}