{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6DHDYIVZNMW5TUT2GIE5IAJCMQ","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":"5a47e4bc770329e3c8d38c9ec5a32f11fe5633452d34e30a7320f501f314703c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-15T08:56:33Z","title_canon_sha256":"d8de3e9395485fc7513d2f615d39c929c1b11fe6b5316a916ed034ca1f2cfe7e"},"schema_version":"1.0","source":{"id":"1803.05643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05643","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05643v1","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05643","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"6DHDYIVZNMW5","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6DHDYIVZNMW5TUT2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6DHDYIVZ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:dfede30363ac51107f9fab05258c6c93b5c3c79ae6075e511c9ca01d32d19ec6","target":"graph","created_at":"2026-05-18T00:20:55Z","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":"It is shown that the good expander codes introduced by Sipser and Spielman, can be realized as the first homology of a graph with respect to a certain twisted coefficient system.","authors_text":"Roy Meshulam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-15T08:56:33Z","title":"Graph codes and local systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05643","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":"sha256:003fae1a1b113380665a2db39c31e15b8c8b643abf7b463de390a0bf52009624","target":"record","created_at":"2026-05-18T00:20:55Z","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":"5a47e4bc770329e3c8d38c9ec5a32f11fe5633452d34e30a7320f501f314703c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-15T08:56:33Z","title_canon_sha256":"d8de3e9395485fc7513d2f615d39c929c1b11fe6b5316a916ed034ca1f2cfe7e"},"schema_version":"1.0","source":{"id":"1803.05643","kind":"arxiv","version":1}},"canonical_sha256":"f0ce3c22b96b2dd9d27a3209d401226412db1895c21757c60a9e5743d99336ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0ce3c22b96b2dd9d27a3209d401226412db1895c21757c60a9e5743d99336ab","first_computed_at":"2026-05-18T00:20:55.006641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:55.006641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cj7uYJ4rB2dAxtp2QFlvCZu+6GPxvT0W/uRwuHEGKhoyhWyqwTrKxT8Jy4XFVw72/SiTjs2pKJbaElKEPG0UAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:55.007049Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:003fae1a1b113380665a2db39c31e15b8c8b643abf7b463de390a0bf52009624","sha256:dfede30363ac51107f9fab05258c6c93b5c3c79ae6075e511c9ca01d32d19ec6"],"state_sha256":"ea06d7ab64248fb7a95cb1f32e7e4b71fb59bb8219d1a5b63e92b031fad78388"}