{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:L526JERBCWOGGVSWYM6H4P3TS4","short_pith_number":"pith:L526JERB","canonical_record":{"source":{"id":"1107.1434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-07T15:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"5cf6420d43a029b1bd51ff5c53d6e3d5fcb2ea80233d709db4db525ac18b01f6","abstract_canon_sha256":"5bc76858af274b5da8567ff9a00baa0fdd6289da22b578372f64af2dba8bee43"},"schema_version":"1.0"},"canonical_sha256":"5f75e49221159c635656c33c7e3f73970aebea87f975e12a656876e79c4fab6f","source":{"kind":"arxiv","id":"1107.1434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1434","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1434v1","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1434","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"L526JERBCWOG","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L526JERBCWOGGVSW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L526JERB","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:L526JERBCWOGGVSWYM6H4P3TS4","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-07T15:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"5cf6420d43a029b1bd51ff5c53d6e3d5fcb2ea80233d709db4db525ac18b01f6","abstract_canon_sha256":"5bc76858af274b5da8567ff9a00baa0fdd6289da22b578372f64af2dba8bee43"},"schema_version":"1.0"},"canonical_sha256":"5f75e49221159c635656c33c7e3f73970aebea87f975e12a656876e79c4fab6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:13.536765Z","signature_b64":"gIBA50auXMrl6j88keLqbuaWdCYX1o8cHNbWD421tqjUSdah1kn3h0uD25k/sUwY8vCgT67TG7el/DKLOWYdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f75e49221159c635656c33c7e3f73970aebea87f975e12a656876e79c4fab6f","last_reissued_at":"2026-05-18T04:02:13.536083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:13.536083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1434","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":"2026-05-18T04:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"is8Ziwc/PhsDQeg5xF7rE2to3Yq/dD4Hxzt6my4N72SNmopZhZ/NBQTwcS5BOzCtnxlAvfwAKGi5YVFcMa+xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:15:50.598789Z"},"content_sha256":"e1e0adbe6f02ca4717025d06d2f7af1c0429511f23e949e23d61d11b345f1215","schema_version":"1.0","event_id":"sha256:e1e0adbe6f02ca4717025d06d2f7af1c0429511f23e949e23d61d11b345f1215"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:L526JERBCWOGGVSWYM6H4P3TS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Limited Power of Powering: Polynomial Identity Testing and a Depth-four Lower Bound for the Permanent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bruno Grenet, Natacha Portier, Pascal Koiran, Yann Strozecki","submitted_at":"2011-07-07T15:48:17Z","abstract_excerpt":"Polynomial identity testing and arithmetic circuit lower bounds are two central questions in algebraic complexity theory. It is an intriguing fact that these questions are actually related. One of the authors of the present paper has recently proposed a \"real {\\tau}-conjecture\" which is inspired by this connection. The real {\\tau}-conjecture states that the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded. It implies a superpolynomial lower bound on the size of arithmetic circuits computing the permanent polynomial. In this paper we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1434","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":"2026-05-18T04:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4BMjh3I9nypbuskpIv5xpCOwQPq3e1jV7T4Ruf2FWxFtmGfXjYmHxl0KSYCDWmGVTi8IhEU10nlqOpCs1YMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:15:50.599122Z"},"content_sha256":"d2cb1fd69a7240abe8ca6f13809e84f866b079693a1340f686d99c79af6914c7","schema_version":"1.0","event_id":"sha256:d2cb1fd69a7240abe8ca6f13809e84f866b079693a1340f686d99c79af6914c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L526JERBCWOGGVSWYM6H4P3TS4/bundle.json","state_url":"https://pith.science/pith/L526JERBCWOGGVSWYM6H4P3TS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L526JERBCWOGGVSWYM6H4P3TS4/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":"2026-06-23T03:15:50Z","links":{"resolver":"https://pith.science/pith/L526JERBCWOGGVSWYM6H4P3TS4","bundle":"https://pith.science/pith/L526JERBCWOGGVSWYM6H4P3TS4/bundle.json","state":"https://pith.science/pith/L526JERBCWOGGVSWYM6H4P3TS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L526JERBCWOGGVSWYM6H4P3TS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L526JERBCWOGGVSWYM6H4P3TS4","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":"5bc76858af274b5da8567ff9a00baa0fdd6289da22b578372f64af2dba8bee43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-07T15:48:17Z","title_canon_sha256":"5cf6420d43a029b1bd51ff5c53d6e3d5fcb2ea80233d709db4db525ac18b01f6"},"schema_version":"1.0","source":{"id":"1107.1434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1434","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1434v1","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1434","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"L526JERBCWOG","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L526JERBCWOGGVSW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L526JERB","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:d2cb1fd69a7240abe8ca6f13809e84f866b079693a1340f686d99c79af6914c7","target":"graph","created_at":"2026-05-18T04:02:13Z","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":"Polynomial identity testing and arithmetic circuit lower bounds are two central questions in algebraic complexity theory. It is an intriguing fact that these questions are actually related. One of the authors of the present paper has recently proposed a \"real {\\tau}-conjecture\" which is inspired by this connection. The real {\\tau}-conjecture states that the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded. It implies a superpolynomial lower bound on the size of arithmetic circuits computing the permanent polynomial. In this paper we show","authors_text":"Bruno Grenet, Natacha Portier, Pascal Koiran, Yann Strozecki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-07T15:48:17Z","title":"The Limited Power of Powering: Polynomial Identity Testing and a Depth-four Lower Bound for the Permanent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1434","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:e1e0adbe6f02ca4717025d06d2f7af1c0429511f23e949e23d61d11b345f1215","target":"record","created_at":"2026-05-18T04:02:13Z","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":"5bc76858af274b5da8567ff9a00baa0fdd6289da22b578372f64af2dba8bee43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-07-07T15:48:17Z","title_canon_sha256":"5cf6420d43a029b1bd51ff5c53d6e3d5fcb2ea80233d709db4db525ac18b01f6"},"schema_version":"1.0","source":{"id":"1107.1434","kind":"arxiv","version":1}},"canonical_sha256":"5f75e49221159c635656c33c7e3f73970aebea87f975e12a656876e79c4fab6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f75e49221159c635656c33c7e3f73970aebea87f975e12a656876e79c4fab6f","first_computed_at":"2026-05-18T04:02:13.536083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:13.536083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gIBA50auXMrl6j88keLqbuaWdCYX1o8cHNbWD421tqjUSdah1kn3h0uD25k/sUwY8vCgT67TG7el/DKLOWYdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:13.536765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1e0adbe6f02ca4717025d06d2f7af1c0429511f23e949e23d61d11b345f1215","sha256:d2cb1fd69a7240abe8ca6f13809e84f866b079693a1340f686d99c79af6914c7"],"state_sha256":"c2be011b4c83fddb47ba4b12bc0b12ad21a005ec672e9372a629035fb7651637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TU48S5u3PVO0qNVIFoz2gBdcQ+zPg8Tw+OnQhQWbd5y04f1bTbJCJX91T+ry+SuXV9uiu6rzuzm2+xHevNJfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:15:50.601021Z","bundle_sha256":"39a15aa0631882bc3711332a56a2ba68f5fe591e7e3ea609d7e49560680ffaa9"}}