{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XGCZ34OOFX4AXU2VRQDUMZSK2J","short_pith_number":"pith:XGCZ34OO","canonical_record":{"source":{"id":"1801.04366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-13T02:29:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e9292f12da51ebd88596a8d9182cc2cb280af7d9e4d19b7264fa19d2a5a4fb55","abstract_canon_sha256":"a04a95ec25a90521da9dd3e8bfcdac76209e28fef20c76c5c68f3f0e79be8993"},"schema_version":"1.0"},"canonical_sha256":"b9859df1ce2df80bd3558c0746664ad24ad95a58feda0a0b8160ff69477b7cd0","source":{"kind":"arxiv","id":"1801.04366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04366","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04366v1","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04366","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"XGCZ34OOFX4A","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XGCZ34OOFX4AXU2V","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XGCZ34OO","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XGCZ34OOFX4AXU2VRQDUMZSK2J","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-13T02:29:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e9292f12da51ebd88596a8d9182cc2cb280af7d9e4d19b7264fa19d2a5a4fb55","abstract_canon_sha256":"a04a95ec25a90521da9dd3e8bfcdac76209e28fef20c76c5c68f3f0e79be8993"},"schema_version":"1.0"},"canonical_sha256":"b9859df1ce2df80bd3558c0746664ad24ad95a58feda0a0b8160ff69477b7cd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:06.667840Z","signature_b64":"v34ziaEPg/ISf4ENLf18POVACcbJN/S+K3rqJJrqZ3De7nWaa8NL1rj7JafBiRJiWQYjdBhSwP10sEIOf1oMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9859df1ce2df80bd3558c0746664ad24ad95a58feda0a0b8160ff69477b7cd0","last_reissued_at":"2026-05-18T00:26:06.666966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:06.666966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04366","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":"2026-05-18T00:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kiX3y/mwxC5Y2sagFtSozCiM8wq2dEhhywhd7IhfHNXoO0IM6jze4VjARhEadfuDBeCE58+KUOiVr1499jMWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:32:21.813941Z"},"content_sha256":"8d693ce200b4b607ed9060538f7b65edbc5da77630444c89c47370244860aa39","schema_version":"1.0","event_id":"sha256:8d693ce200b4b607ed9060538f7b65edbc5da77630444c89c47370244860aa39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XGCZ34OOFX4AXU2VRQDUMZSK2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation in the group action channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amit Singer, Emmanuel Abbe, Jo\\~ao M. Pereira","submitted_at":"2018-01-13T02:29:11Z","abstract_excerpt":"We analyze the problem of estimating a signal from multiple measurements on a $\\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryo-electron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04366","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":""},"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":"2026-05-18T00:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRf+/MLBNWUxSC+yTDeOPj5K1H5iFoCTX/aD1UkTbIMNDv7Bul8AbdcHTNDM3hBPVnjhKWttA+HQ4dvXbp9GAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:32:21.814376Z"},"content_sha256":"a9527386a94524866b5574ae22188cb205a5e6f8925b3af3d84857b48c639261","schema_version":"1.0","event_id":"sha256:a9527386a94524866b5574ae22188cb205a5e6f8925b3af3d84857b48c639261"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/bundle.json","state_url":"https://pith.science/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/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":"2026-05-27T03:32:21Z","links":{"resolver":"https://pith.science/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J","bundle":"https://pith.science/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/bundle.json","state":"https://pith.science/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGCZ34OOFX4AXU2VRQDUMZSK2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XGCZ34OOFX4AXU2VRQDUMZSK2J","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":"a04a95ec25a90521da9dd3e8bfcdac76209e28fef20c76c5c68f3f0e79be8993","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-13T02:29:11Z","title_canon_sha256":"e9292f12da51ebd88596a8d9182cc2cb280af7d9e4d19b7264fa19d2a5a4fb55"},"schema_version":"1.0","source":{"id":"1801.04366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04366","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04366v1","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04366","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"XGCZ34OOFX4A","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XGCZ34OOFX4AXU2V","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XGCZ34OO","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:a9527386a94524866b5574ae22188cb205a5e6f8925b3af3d84857b48c639261","target":"graph","created_at":"2026-05-18T00:26:06Z","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":"We analyze the problem of estimating a signal from multiple measurements on a $\\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryo-electron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away","authors_text":"Amit Singer, Emmanuel Abbe, Jo\\~ao M. Pereira","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-13T02:29:11Z","title":"Estimation in the group action channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04366","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":"sha256:8d693ce200b4b607ed9060538f7b65edbc5da77630444c89c47370244860aa39","target":"record","created_at":"2026-05-18T00:26:06Z","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":"a04a95ec25a90521da9dd3e8bfcdac76209e28fef20c76c5c68f3f0e79be8993","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-13T02:29:11Z","title_canon_sha256":"e9292f12da51ebd88596a8d9182cc2cb280af7d9e4d19b7264fa19d2a5a4fb55"},"schema_version":"1.0","source":{"id":"1801.04366","kind":"arxiv","version":1}},"canonical_sha256":"b9859df1ce2df80bd3558c0746664ad24ad95a58feda0a0b8160ff69477b7cd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9859df1ce2df80bd3558c0746664ad24ad95a58feda0a0b8160ff69477b7cd0","first_computed_at":"2026-05-18T00:26:06.666966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:06.666966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v34ziaEPg/ISf4ENLf18POVACcbJN/S+K3rqJJrqZ3De7nWaa8NL1rj7JafBiRJiWQYjdBhSwP10sEIOf1oMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:06.667840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d693ce200b4b607ed9060538f7b65edbc5da77630444c89c47370244860aa39","sha256:a9527386a94524866b5574ae22188cb205a5e6f8925b3af3d84857b48c639261"],"state_sha256":"24fcd927a6162e24959bec36c70535d58d2f4e4d0353ca6e022e8c6f95c70e65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2pV0VyAqBZX5x6tlFZX2QhxfxZill3Y91ZS8AZO1Ni///9zlO1kwiPc/WCCwk5l8dAfz8gn2enkJbeXgmkaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:32:21.817383Z","bundle_sha256":"433566dee70826e746a4a489edc7bf08827736b46c41d14fbe56949d1795c369"}}