{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:LFFKNRXTLNRKV7CUZDPW3A6G6T","short_pith_number":"pith:LFFKNRXT","canonical_record":{"source":{"id":"2010.06563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-10-13T17:26:09Z","cross_cats_sorted":["cs.DS","math.PR","stat.ML"],"title_canon_sha256":"54fde087465d0d0a28fce9a72ffea1126a15ca60de9ed28c9559026d04f8d466","abstract_canon_sha256":"ce19d9871b682a3f79de7fbdcfa9bff793d2f3790a8197e5ccfaa1037137a2d2"},"schema_version":"1.0"},"canonical_sha256":"594aa6c6f35b62aafc54c8df6d83c6f4c7475aacc16afbb220082a6ea6f1ae2a","source":{"kind":"arxiv","id":"2010.06563","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06563","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06563v2","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06563","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_12","alias_value":"LFFKNRXTLNRK","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_16","alias_value":"LFFKNRXTLNRKV7CU","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_8","alias_value":"LFFKNRXT","created_at":"2026-07-05T01:51:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:LFFKNRXTLNRKV7CUZDPW3A6G6T","target":"record","payload":{"canonical_record":{"source":{"id":"2010.06563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-10-13T17:26:09Z","cross_cats_sorted":["cs.DS","math.PR","stat.ML"],"title_canon_sha256":"54fde087465d0d0a28fce9a72ffea1126a15ca60de9ed28c9559026d04f8d466","abstract_canon_sha256":"ce19d9871b682a3f79de7fbdcfa9bff793d2f3790a8197e5ccfaa1037137a2d2"},"schema_version":"1.0"},"canonical_sha256":"594aa6c6f35b62aafc54c8df6d83c6f4c7475aacc16afbb220082a6ea6f1ae2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:51:09.426717Z","signature_b64":"dUKL8NtcOlz/OzBWAziVrmgx3ZFqmCi8evbEjqoQT+S3YCMmPqFaTypUQjCWi/mHM/VCu4lrI2hFDQ2LKFSeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"594aa6c6f35b62aafc54c8df6d83c6f4c7475aacc16afbb220082a6ea6f1ae2a","last_reissued_at":"2026-07-05T01:51:09.426209Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:51:09.426209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.06563","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":"2026-07-05T01:51:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G99+K9LNTR8tZxhJhEBneQMNBK0iczP1PPvAR/f99HPaLRg6pih5DdhMeYsBOUQqiLhTcAhbe7v2PrSkIMXnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:13:20.268642Z"},"content_sha256":"4b25896a27c5429e1f78fde9e7b063da2c22e361c87f1fe8b54d5b8e6b51a0fc","schema_version":"1.0","event_id":"sha256:4b25896a27c5429e1f78fde9e7b063da2c22e361c87f1fe8b54d5b8e6b51a0fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:LFFKNRXTLNRKV7CUZDPW3A6G6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Low-Degree Hardness of Maximum Independent Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR","stat.ML"],"primary_cat":"cs.CC","authors_text":"Alexander S. Wein","submitted_at":"2020-10-13T17:26:09Z","abstract_excerpt":"We study the algorithmic task of finding a large independent set in a sparse Erd\\H{o}s-R\\'{e}nyi random graph with $n$ vertices and average degree $d$. The maximum independent set is known to have size $(2 \\log d / d)n$ in the double limit $n \\to \\infty$ followed by $d \\to \\infty$, but the best known polynomial-time algorithms can only find an independent set of half-optimal size $(\\log d / d)n$. We show that the class of low-degree polynomial algorithms can find independent sets of half-optimal size but no larger, improving upon a result of Gamarnik, Jagannath, and the author. This generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06563","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06563/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":"2026-07-05T01:51:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEwX0mRmyKtm96m+r78Vu3NvPkHLWg5AHVQougvsyfvbimLLGD97rpW50WgSP7EDUwqtUyI2grsPEPqAlZ38AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:13:20.269175Z"},"content_sha256":"d9033946f2ca38a395305ff75f3a7980fa7178468618228a7d4e2a31f8081c44","schema_version":"1.0","event_id":"sha256:d9033946f2ca38a395305ff75f3a7980fa7178468618228a7d4e2a31f8081c44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/bundle.json","state_url":"https://pith.science/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/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":"2026-08-07T05:13:20Z","links":{"resolver":"https://pith.science/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T","bundle":"https://pith.science/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/bundle.json","state":"https://pith.science/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFFKNRXTLNRKV7CUZDPW3A6G6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LFFKNRXTLNRKV7CUZDPW3A6G6T","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":"ce19d9871b682a3f79de7fbdcfa9bff793d2f3790a8197e5ccfaa1037137a2d2","cross_cats_sorted":["cs.DS","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-10-13T17:26:09Z","title_canon_sha256":"54fde087465d0d0a28fce9a72ffea1126a15ca60de9ed28c9559026d04f8d466"},"schema_version":"1.0","source":{"id":"2010.06563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06563","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06563v2","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06563","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_12","alias_value":"LFFKNRXTLNRK","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_16","alias_value":"LFFKNRXTLNRKV7CU","created_at":"2026-07-05T01:51:09Z"},{"alias_kind":"pith_short_8","alias_value":"LFFKNRXT","created_at":"2026-07-05T01:51:09Z"}],"graph_snapshots":[{"event_id":"sha256:d9033946f2ca38a395305ff75f3a7980fa7178468618228a7d4e2a31f8081c44","target":"graph","created_at":"2026-07-05T01:51:09Z","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/2010.06563/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the algorithmic task of finding a large independent set in a sparse Erd\\H{o}s-R\\'{e}nyi random graph with $n$ vertices and average degree $d$. The maximum independent set is known to have size $(2 \\log d / d)n$ in the double limit $n \\to \\infty$ followed by $d \\to \\infty$, but the best known polynomial-time algorithms can only find an independent set of half-optimal size $(\\log d / d)n$. We show that the class of low-degree polynomial algorithms can find independent sets of half-optimal size but no larger, improving upon a result of Gamarnik, Jagannath, and the author. This generalize","authors_text":"Alexander S. Wein","cross_cats":["cs.DS","math.PR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-10-13T17:26:09Z","title":"Optimal Low-Degree Hardness of Maximum Independent Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06563","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":"sha256:4b25896a27c5429e1f78fde9e7b063da2c22e361c87f1fe8b54d5b8e6b51a0fc","target":"record","created_at":"2026-07-05T01:51:09Z","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":"ce19d9871b682a3f79de7fbdcfa9bff793d2f3790a8197e5ccfaa1037137a2d2","cross_cats_sorted":["cs.DS","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-10-13T17:26:09Z","title_canon_sha256":"54fde087465d0d0a28fce9a72ffea1126a15ca60de9ed28c9559026d04f8d466"},"schema_version":"1.0","source":{"id":"2010.06563","kind":"arxiv","version":2}},"canonical_sha256":"594aa6c6f35b62aafc54c8df6d83c6f4c7475aacc16afbb220082a6ea6f1ae2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"594aa6c6f35b62aafc54c8df6d83c6f4c7475aacc16afbb220082a6ea6f1ae2a","first_computed_at":"2026-07-05T01:51:09.426209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:09.426209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dUKL8NtcOlz/OzBWAziVrmgx3ZFqmCi8evbEjqoQT+S3YCMmPqFaTypUQjCWi/mHM/VCu4lrI2hFDQ2LKFSeBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:09.426717Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.06563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b25896a27c5429e1f78fde9e7b063da2c22e361c87f1fe8b54d5b8e6b51a0fc","sha256:d9033946f2ca38a395305ff75f3a7980fa7178468618228a7d4e2a31f8081c44"],"state_sha256":"04eb06cc1afcb6ecc82144804cac11d0f76fae4f7e80bc7f30f90510ae929878"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mCRiSXi14OvZnCzCKHqkAjkq9zWc4i2qympIFDCJLK4PBeUOSQ/U0sUTElZnxbEJnzmxyBPDKLzyEaRA2tFcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T05:13:20.273923Z","bundle_sha256":"9c226d73bfd80c4668e2b65816f4653fa8c2ca18e3f63ae87562b53b21bb57f8"}}