{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R3IUFVBP2W2FMWSKQRXZ3GOSET","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":"756d893b752cde04f583b9287eb116fc87a634da62a90fe07fadba6a575d5893","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-05T21:08:31Z","title_canon_sha256":"e6ccf74afc87e4345582747074665b59b12267ff9dcd68306d1f7ce4d72420ef"},"schema_version":"1.0","source":{"id":"1705.02397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02397","created_at":"2026-05-18T00:44:56Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02397v1","created_at":"2026-05-18T00:44:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02397","created_at":"2026-05-18T00:44:56Z"},{"alias_kind":"pith_short_12","alias_value":"R3IUFVBP2W2F","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R3IUFVBP2W2FMWSK","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R3IUFVBP","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:5da3fe899e78c2990c74b00c375a6a2e2a1fdffea342db472b2ed7e5f9b5091a","target":"graph","created_at":"2026-05-18T00:44:56Z","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"},"paper":{"abstract_excerpt":"Proving super-polynomial lower bounds against depth-2 threshold circuits of the form THR of THR is a well-known open problem that represents a frontier of our understanding in boolean circuit complexity. By contrast, exponential lower bounds on the size of THR of MAJ circuits were shown by Razborov and Sherstov (SIAM J.Comput., 2010) even for computing functions in depth-3 AC^0. Yet, no separation among the two depth-2 threshold circuit classes were known. In fact, it is not clear a priori that they ought to be different. In particular, Goldmann, Hastad and Razborov (Computational Complexity, ","authors_text":"Arkadev Chattopadhyay, Nikhil S. Mande","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-05T21:08:31Z","title":"Weights at the Bottom Matter When the Top is Heavy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02397","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":"sha256:05a682df5cd7a1ab603dc2c4ee9e8983e66d470b65c2bf2c4f1931de3835adf8","target":"record","created_at":"2026-05-18T00:44:56Z","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":"756d893b752cde04f583b9287eb116fc87a634da62a90fe07fadba6a575d5893","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-05T21:08:31Z","title_canon_sha256":"e6ccf74afc87e4345582747074665b59b12267ff9dcd68306d1f7ce4d72420ef"},"schema_version":"1.0","source":{"id":"1705.02397","kind":"arxiv","version":1}},"canonical_sha256":"8ed142d42fd5b4565a4a846f9d99d224c3a42d1317c1bfe0a2f463f1934ac57b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ed142d42fd5b4565a4a846f9d99d224c3a42d1317c1bfe0a2f463f1934ac57b","first_computed_at":"2026-05-18T00:44:56.700885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:56.700885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3yxRFUuLntjCwF0jDz5JrSr+DsLGfDuHACSgbDD8BAZ5AZCBFUvXz5nXDW5YkEDWWWeHeT+pnTuTXb7VVcQ4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:56.701531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05a682df5cd7a1ab603dc2c4ee9e8983e66d470b65c2bf2c4f1931de3835adf8","sha256:5da3fe899e78c2990c74b00c375a6a2e2a1fdffea342db472b2ed7e5f9b5091a"],"state_sha256":"fc1c1b14d5afc326029b27362f2874d39022e2b161081fa9169f9b21c72244f1"}