{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3FK43AL5YPBPKGSCZSZLFIH227","short_pith_number":"pith:3FK43AL5","canonical_record":{"source":{"id":"1704.03892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-12T18:31:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"144cb2b1191a2de041a817217255d0c660c5fff7ea86ebb7338735d07cfcd7be","abstract_canon_sha256":"73efe1582f19280f23881160debc82e3f553a60fa9ee7bf27e005e1685e7e6e5"},"schema_version":"1.0"},"canonical_sha256":"d955cd817dc3c2f51a42ccb2b2a0fad7c506636f88171553080d99eef219715a","source":{"kind":"arxiv","id":"1704.03892","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03892","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03892v1","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03892","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"3FK43AL5YPBP","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3FK43AL5YPBPKGSC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3FK43AL5","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3FK43AL5YPBPKGSCZSZLFIH227","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-12T18:31:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"144cb2b1191a2de041a817217255d0c660c5fff7ea86ebb7338735d07cfcd7be","abstract_canon_sha256":"73efe1582f19280f23881160debc82e3f553a60fa9ee7bf27e005e1685e7e6e5"},"schema_version":"1.0"},"canonical_sha256":"d955cd817dc3c2f51a42ccb2b2a0fad7c506636f88171553080d99eef219715a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:25.924030Z","signature_b64":"HbtaNDSlTAN5VdsaTPvoxYsnY5Oru2+2ZWbvIQ0nIGT5JJjaE/5IUXIIXIypYPv6DnzUzGZqlJ0WZG/PI1iqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d955cd817dc3c2f51a42ccb2b2a0fad7c506636f88171553080d99eef219715a","last_reissued_at":"2026-05-18T00:46:25.923502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:25.923502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03892","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":"2026-05-18T00:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JzYAsh6Y+IWmzKTqnnHEgc5qGP2W1nl1ano9GvB/VtYBn1k6Fize2HcFGpxtI/5VdmldEwFmSXK8MW8qtfqZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:40:16.208949Z"},"content_sha256":"74a0f7daa8c28b4749745e6f981f99b03ad5008a4361cfe48ebd681a55050f8e","schema_version":"1.0","event_id":"sha256:74a0f7daa8c28b4749745e6f981f99b03ad5008a4361cfe48ebd681a55050f8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3FK43AL5YPBPKGSCZSZLFIH227","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating the Largest Root and Applications to Interlacing Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Amin Saberi, Nikhil Srivastava, Nima Anari, Shayan Oveis Gharan","submitted_at":"2017-04-12T18:31:52Z","abstract_excerpt":"We study the problem of approximating the largest root of a real-rooted polynomial of degree $n$ using its top $k$ coefficients and give nearly matching upper and lower bounds. We present algorithms with running time polynomial in $k$ that use the top $k$ coefficients to approximate the maximum root within a factor of $n^{1/k}$ and $1+O(\\tfrac{\\log n}{k})^2$ when $k\\leq \\log n$ and $k>\\log n$ respectively. We also prove corresponding information-theoretic lower bounds of $n^{\\Omega(1/k)}$ and $1+\\Omega\\left(\\frac{\\log \\frac{2n}{k}}{k}\\right)^2$, and show strong lower bounds for noisy version o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03892","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":"2026-05-18T00:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ivuHpG9jwSBCwbTZknD05ezGyMiKTtdjo0AGcQ18NXx879lIU1rdn5hw+yRVtsZHE28w6QEpaff+Fp82R71DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T04:40:16.209702Z"},"content_sha256":"acbfca96de291cf42336f44e42e77386b03ba7a6f3ac627cfe588d401d689767","schema_version":"1.0","event_id":"sha256:acbfca96de291cf42336f44e42e77386b03ba7a6f3ac627cfe588d401d689767"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FK43AL5YPBPKGSCZSZLFIH227/bundle.json","state_url":"https://pith.science/pith/3FK43AL5YPBPKGSCZSZLFIH227/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FK43AL5YPBPKGSCZSZLFIH227/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":"2026-05-20T04:40:16Z","links":{"resolver":"https://pith.science/pith/3FK43AL5YPBPKGSCZSZLFIH227","bundle":"https://pith.science/pith/3FK43AL5YPBPKGSCZSZLFIH227/bundle.json","state":"https://pith.science/pith/3FK43AL5YPBPKGSCZSZLFIH227/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FK43AL5YPBPKGSCZSZLFIH227/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3FK43AL5YPBPKGSCZSZLFIH227","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":"73efe1582f19280f23881160debc82e3f553a60fa9ee7bf27e005e1685e7e6e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-12T18:31:52Z","title_canon_sha256":"144cb2b1191a2de041a817217255d0c660c5fff7ea86ebb7338735d07cfcd7be"},"schema_version":"1.0","source":{"id":"1704.03892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03892","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03892v1","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03892","created_at":"2026-05-18T00:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"3FK43AL5YPBP","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3FK43AL5YPBPKGSC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3FK43AL5","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:acbfca96de291cf42336f44e42e77386b03ba7a6f3ac627cfe588d401d689767","target":"graph","created_at":"2026-05-18T00:46:25Z","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 study the problem of approximating the largest root of a real-rooted polynomial of degree $n$ using its top $k$ coefficients and give nearly matching upper and lower bounds. We present algorithms with running time polynomial in $k$ that use the top $k$ coefficients to approximate the maximum root within a factor of $n^{1/k}$ and $1+O(\\tfrac{\\log n}{k})^2$ when $k\\leq \\log n$ and $k>\\log n$ respectively. We also prove corresponding information-theoretic lower bounds of $n^{\\Omega(1/k)}$ and $1+\\Omega\\left(\\frac{\\log \\frac{2n}{k}}{k}\\right)^2$, and show strong lower bounds for noisy version o","authors_text":"Amin Saberi, Nikhil Srivastava, Nima Anari, Shayan Oveis Gharan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-12T18:31:52Z","title":"Approximating the Largest Root and Applications to Interlacing Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03892","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":"sha256:74a0f7daa8c28b4749745e6f981f99b03ad5008a4361cfe48ebd681a55050f8e","target":"record","created_at":"2026-05-18T00:46:25Z","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":"73efe1582f19280f23881160debc82e3f553a60fa9ee7bf27e005e1685e7e6e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-12T18:31:52Z","title_canon_sha256":"144cb2b1191a2de041a817217255d0c660c5fff7ea86ebb7338735d07cfcd7be"},"schema_version":"1.0","source":{"id":"1704.03892","kind":"arxiv","version":1}},"canonical_sha256":"d955cd817dc3c2f51a42ccb2b2a0fad7c506636f88171553080d99eef219715a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d955cd817dc3c2f51a42ccb2b2a0fad7c506636f88171553080d99eef219715a","first_computed_at":"2026-05-18T00:46:25.923502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:25.923502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HbtaNDSlTAN5VdsaTPvoxYsnY5Oru2+2ZWbvIQ0nIGT5JJjaE/5IUXIIXIypYPv6DnzUzGZqlJ0WZG/PI1iqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:25.924030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74a0f7daa8c28b4749745e6f981f99b03ad5008a4361cfe48ebd681a55050f8e","sha256:acbfca96de291cf42336f44e42e77386b03ba7a6f3ac627cfe588d401d689767"],"state_sha256":"f861fb5e0e8dfa3b7c8c5e7bcffa4e9f38346f39d103bf0b4b43f2795c0bb914"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xWWw8jF1ry1fxj2agVJRqiS4qtGwDdh+fRHFnVXx4u6Bs+XLaRtwyiwTfthg2FbMC9nMbzldGsOBCa1tvbHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T04:40:16.213828Z","bundle_sha256":"714e5fd62fae229a470279ef34198ac403993eb7eb7b99d7ef274e46080a73a1"}}