{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PYCLHRLUDCNUYNWLDN5C3EFR2D","short_pith_number":"pith:PYCLHRLU","canonical_record":{"source":{"id":"1305.1681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-07T23:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"a76eda5623aad5910fa63a7ff77853d8328e66fffec2e9dad4cbbd511f4ce5e9","abstract_canon_sha256":"9ae035e3f2b414aace0e952d98e6f0a0aefb78d319208caa484461c37338ea9d"},"schema_version":"1.0"},"canonical_sha256":"7e04b3c574189b4c36cb1b7a2d90b1d0ce3a19b56be88731bb3261ed03cac031","source":{"kind":"arxiv","id":"1305.1681","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1681","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1681v3","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1681","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"PYCLHRLUDCNU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PYCLHRLUDCNUYNWL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PYCLHRLU","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PYCLHRLUDCNUYNWLDN5C3EFR2D","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-07T23:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"a76eda5623aad5910fa63a7ff77853d8328e66fffec2e9dad4cbbd511f4ce5e9","abstract_canon_sha256":"9ae035e3f2b414aace0e952d98e6f0a0aefb78d319208caa484461c37338ea9d"},"schema_version":"1.0"},"canonical_sha256":"7e04b3c574189b4c36cb1b7a2d90b1d0ce3a19b56be88731bb3261ed03cac031","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:23.385649Z","signature_b64":"EYuGYQIeKR+IW/z+ECDcjGsQ2jdK7gOpxUCoOYTGF2WLiXpmypCibclL88685vcKzGXANh6jo1pSyvxMpzXNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e04b3c574189b4c36cb1b7a2d90b1d0ce3a19b56be88731bb3261ed03cac031","last_reissued_at":"2026-05-18T03:07:23.385101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:23.385101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1681","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBYZ4C6JQaVj0XgDnLqt2e/fzSS5hBzzckvynHmUSsYVHddetANvBH9WkyYfX1T2Swy0gz0sX3LZ/VpmOs+xDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:41.299912Z"},"content_sha256":"662c3677fd261de783496a76ec1dc2a480ffeccc10f307e92ed0c8c38720b5f3","schema_version":"1.0","event_id":"sha256:662c3677fd261de783496a76ec1dc2a480ffeccc10f307e92ed0c8c38720b5f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PYCLHRLUDCNUYNWLDN5C3EFR2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bilu-Linial Stable Instances of Max Cut and Minimum Multiway Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aravindan Vijayaraghavan, Konstantin Makarychev, Yury Makarychev","submitted_at":"2013-05-07T23:54:03Z","abstract_excerpt":"We investigate the notion of stability proposed by Bilu and Linial. We obtain an exact polynomial-time algorithm for $\\gamma$-stable Max Cut instances with $\\gamma \\geq c\\sqrt{\\log n}\\log\\log n$ for some absolute constant $c > 0$. Our algorithm is robust: it never returns an incorrect answer; if the instance is $\\gamma$-stable, it finds the maximum cut, otherwise, it either finds the maximum cut or certifies that the instance is not $\\gamma$-stable. We prove that there is no robust polynomial-time algorithm for $\\gamma$-stable instances of Max Cut when $\\gamma < \\alpha_{SC}(n/2)$, where $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1681","kind":"arxiv","version":3},"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":"2026-05-18T03:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"La5CF3Du4eQ87YrjTEDRdeErolUZjin9K+lqRwQbYJ//RI9UEz9b/+URcid+I1QDUAMzMr/z3V+ATVno9bb3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:48:41.300252Z"},"content_sha256":"26f1c7f2f276f7c52b933ef4c762836852e11466199d7c9da2031de18579452c","schema_version":"1.0","event_id":"sha256:26f1c7f2f276f7c52b933ef4c762836852e11466199d7c9da2031de18579452c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/bundle.json","state_url":"https://pith.science/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/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":"2026-06-02T19:48:41Z","links":{"resolver":"https://pith.science/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D","bundle":"https://pith.science/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/bundle.json","state":"https://pith.science/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYCLHRLUDCNUYNWLDN5C3EFR2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PYCLHRLUDCNUYNWLDN5C3EFR2D","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":"9ae035e3f2b414aace0e952d98e6f0a0aefb78d319208caa484461c37338ea9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-07T23:54:03Z","title_canon_sha256":"a76eda5623aad5910fa63a7ff77853d8328e66fffec2e9dad4cbbd511f4ce5e9"},"schema_version":"1.0","source":{"id":"1305.1681","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1681","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1681v3","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1681","created_at":"2026-05-18T03:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"PYCLHRLUDCNU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PYCLHRLUDCNUYNWL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PYCLHRLU","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:26f1c7f2f276f7c52b933ef4c762836852e11466199d7c9da2031de18579452c","target":"graph","created_at":"2026-05-18T03:07:23Z","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 investigate the notion of stability proposed by Bilu and Linial. We obtain an exact polynomial-time algorithm for $\\gamma$-stable Max Cut instances with $\\gamma \\geq c\\sqrt{\\log n}\\log\\log n$ for some absolute constant $c > 0$. Our algorithm is robust: it never returns an incorrect answer; if the instance is $\\gamma$-stable, it finds the maximum cut, otherwise, it either finds the maximum cut or certifies that the instance is not $\\gamma$-stable. We prove that there is no robust polynomial-time algorithm for $\\gamma$-stable instances of Max Cut when $\\gamma < \\alpha_{SC}(n/2)$, where $\\alph","authors_text":"Aravindan Vijayaraghavan, Konstantin Makarychev, Yury Makarychev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-07T23:54:03Z","title":"Bilu-Linial Stable Instances of Max Cut and Minimum Multiway Cut"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1681","kind":"arxiv","version":3},"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":"sha256:662c3677fd261de783496a76ec1dc2a480ffeccc10f307e92ed0c8c38720b5f3","target":"record","created_at":"2026-05-18T03:07:23Z","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":"9ae035e3f2b414aace0e952d98e6f0a0aefb78d319208caa484461c37338ea9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-07T23:54:03Z","title_canon_sha256":"a76eda5623aad5910fa63a7ff77853d8328e66fffec2e9dad4cbbd511f4ce5e9"},"schema_version":"1.0","source":{"id":"1305.1681","kind":"arxiv","version":3}},"canonical_sha256":"7e04b3c574189b4c36cb1b7a2d90b1d0ce3a19b56be88731bb3261ed03cac031","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e04b3c574189b4c36cb1b7a2d90b1d0ce3a19b56be88731bb3261ed03cac031","first_computed_at":"2026-05-18T03:07:23.385101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:23.385101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EYuGYQIeKR+IW/z+ECDcjGsQ2jdK7gOpxUCoOYTGF2WLiXpmypCibclL88685vcKzGXANh6jo1pSyvxMpzXNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:23.385649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1681","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:662c3677fd261de783496a76ec1dc2a480ffeccc10f307e92ed0c8c38720b5f3","sha256:26f1c7f2f276f7c52b933ef4c762836852e11466199d7c9da2031de18579452c"],"state_sha256":"a6bc71cb2e26655e70d39ddcd4047bc7266df3577e567311ec86ba94da68d438"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vX43TaVugalKuNTkSSQ+ppJfs79+JJ6LPJHQqjy6aCd1/cldrVZ1TIf/L99E5eSNY3ZGGhu524h0xu/Pcl0FBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:48:41.302123Z","bundle_sha256":"a51ef2d48c6c09c97db3c469f7cd6db13b6741816b1b4df677aec3fee90d2c3d"}}