{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KAZHFFRA6QWJAGK7ZQYIRH3RIS","short_pith_number":"pith:KAZHFFRA","canonical_record":{"source":{"id":"2406.03424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-05T16:20:52Z","cross_cats_sorted":["cs.CC","math.PR","stat.TH"],"title_canon_sha256":"01d6169dbf7cced7b5e889d67dd525d796a8cc8645fe9793696193e315e062e6","abstract_canon_sha256":"7e694b6041bec9b8c311bee539bbd184c2bb49e6d2bd3ee180688f542741699d"},"schema_version":"1.0"},"canonical_sha256":"5032729620f42c90195fcc30889f71449c8a49ad932fbd9dcc6392c6c5b4153b","source":{"kind":"arxiv","id":"2406.03424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03424","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03424v1","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03424","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"KAZHFFRA6QWJ","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"KAZHFFRA6QWJAGK7","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"KAZHFFRA","created_at":"2026-07-05T08:27:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KAZHFFRA6QWJAGK7ZQYIRH3RIS","target":"record","payload":{"canonical_record":{"source":{"id":"2406.03424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-05T16:20:52Z","cross_cats_sorted":["cs.CC","math.PR","stat.TH"],"title_canon_sha256":"01d6169dbf7cced7b5e889d67dd525d796a8cc8645fe9793696193e315e062e6","abstract_canon_sha256":"7e694b6041bec9b8c311bee539bbd184c2bb49e6d2bd3ee180688f542741699d"},"schema_version":"1.0"},"canonical_sha256":"5032729620f42c90195fcc30889f71449c8a49ad932fbd9dcc6392c6c5b4153b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:56.506852Z","signature_b64":"OWUAexzp6K2Wro0kO2cuS+HAETPysQhiDmSevP2A/6zHFM9dPkcxvJ09l5FCfmxAgEdVf5oBoc+c7tWFCQ/ZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5032729620f42c90195fcc30889f71449c8a49ad932fbd9dcc6392c6c5b4153b","last_reissued_at":"2026-07-05T08:27:56.506368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:56.506368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.03424","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":"2026-07-05T08:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcEUnsqRD9Q0fw4BO9OQIiIVnw1GOhklstzKeedV1GhKNIiYgw9n8a0+Fs0ynurqtVKnOs31Ggzk1f3vpB+JAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:30:25.336207Z"},"content_sha256":"e8fd19aeeb3bf1028c83302265243aba9acc064fed091f1ee9625b8672e211d4","schema_version":"1.0","event_id":"sha256:e8fd19aeeb3bf1028c83302265243aba9acc064fed091f1ee9625b8672e211d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KAZHFFRA6QWJAGK7ZQYIRH3RIS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational lower bounds for multi-frequency group synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Afonso S. Bandeira, Anastasia Kireeva, Dmitriy Kunisky","submitted_at":"2024-06-05T16:20:52Z","abstract_excerpt":"We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase transition in the problem of detecting whether a structured signal is present in such observations by analyzing low-degree polynomial algorithms. We show that, assuming the low-degree conjecture, in synchronization models over arbitrary finite groups as well as over the circle group $SO(2)$, a simple spectral algorithm is optimal among algorithms of runtime $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03424","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/2406.03424/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":"2026-07-05T08:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvqtFchundq6z7eBYFnjYPpoxtjnbH2mwvia5L3zv40XdWaem2Dl7dyN6NUzP+BbftClWhTI/Fh2kkE0IR7fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:30:25.336844Z"},"content_sha256":"cb7c3e57d27c9bdc3a28372afbc4cd4043d4aeaa5755fac209723d91dd938bbc","schema_version":"1.0","event_id":"sha256:cb7c3e57d27c9bdc3a28372afbc4cd4043d4aeaa5755fac209723d91dd938bbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/bundle.json","state_url":"https://pith.science/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/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":"2026-08-13T09:30:25Z","links":{"resolver":"https://pith.science/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS","bundle":"https://pith.science/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/bundle.json","state":"https://pith.science/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAZHFFRA6QWJAGK7ZQYIRH3RIS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KAZHFFRA6QWJAGK7ZQYIRH3RIS","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":"7e694b6041bec9b8c311bee539bbd184c2bb49e6d2bd3ee180688f542741699d","cross_cats_sorted":["cs.CC","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-05T16:20:52Z","title_canon_sha256":"01d6169dbf7cced7b5e889d67dd525d796a8cc8645fe9793696193e315e062e6"},"schema_version":"1.0","source":{"id":"2406.03424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03424","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03424v1","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03424","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"KAZHFFRA6QWJ","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"KAZHFFRA6QWJAGK7","created_at":"2026-07-05T08:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"KAZHFFRA","created_at":"2026-07-05T08:27:56Z"}],"graph_snapshots":[{"event_id":"sha256:cb7c3e57d27c9bdc3a28372afbc4cd4043d4aeaa5755fac209723d91dd938bbc","target":"graph","created_at":"2026-07-05T08:27:56Z","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/2406.03424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase transition in the problem of detecting whether a structured signal is present in such observations by analyzing low-degree polynomial algorithms. We show that, assuming the low-degree conjecture, in synchronization models over arbitrary finite groups as well as over the circle group $SO(2)$, a simple spectral algorithm is optimal among algorithms of runtime $\\","authors_text":"Afonso S. Bandeira, Anastasia Kireeva, Dmitriy Kunisky","cross_cats":["cs.CC","math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-05T16:20:52Z","title":"Computational lower bounds for multi-frequency group synchronization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03424","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:e8fd19aeeb3bf1028c83302265243aba9acc064fed091f1ee9625b8672e211d4","target":"record","created_at":"2026-07-05T08:27:56Z","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":"7e694b6041bec9b8c311bee539bbd184c2bb49e6d2bd3ee180688f542741699d","cross_cats_sorted":["cs.CC","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-06-05T16:20:52Z","title_canon_sha256":"01d6169dbf7cced7b5e889d67dd525d796a8cc8645fe9793696193e315e062e6"},"schema_version":"1.0","source":{"id":"2406.03424","kind":"arxiv","version":1}},"canonical_sha256":"5032729620f42c90195fcc30889f71449c8a49ad932fbd9dcc6392c6c5b4153b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5032729620f42c90195fcc30889f71449c8a49ad932fbd9dcc6392c6c5b4153b","first_computed_at":"2026-07-05T08:27:56.506368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:56.506368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OWUAexzp6K2Wro0kO2cuS+HAETPysQhiDmSevP2A/6zHFM9dPkcxvJ09l5FCfmxAgEdVf5oBoc+c7tWFCQ/ZBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:56.506852Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8fd19aeeb3bf1028c83302265243aba9acc064fed091f1ee9625b8672e211d4","sha256:cb7c3e57d27c9bdc3a28372afbc4cd4043d4aeaa5755fac209723d91dd938bbc"],"state_sha256":"1ecef4265d15e0293fbceecf96c182cc5b716dd269daecec0158b8384fbe6a65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fIplA91nk4kPwTD79FfvAHTfxX9/a9pA1CfGOV3t67CDlmR94O3XBaYFBYT8t6jKH8c/BXU2cO63mpeDFmV0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:30:25.392567Z","bundle_sha256":"a1395fe6746a37bfd9fc8f1f44ad7e7ec1dee47908f1d88b862d6fe2d160cf21"}}