{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CP6S3KIVALY6YDUFOAXQBKRV2W","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":"2042591e31d1d7134cca9f6f4f8eca1cdfefb45906c3738276ba57307ac1d211","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-22T18:55:54Z","title_canon_sha256":"6a7a48941acaefd8bde955f913671550f834b72442e81e2b6f65fbed41463118"},"schema_version":"1.0","source":{"id":"1109.4914","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4914","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4914v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4914","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"CP6S3KIVALY6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CP6S3KIVALY6YDUF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CP6S3KIV","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:fff4a78195090dc352c9c7793aafaa92c0693cc59a049437bcd3c34c016ea288","target":"graph","created_at":"2026-05-18T04:05:27Z","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 prove that the independence complexes of some grids have exponential Betti numbers. This corresponds to the number of ground states in the hard-core model in statistical physics with fermions in the vertices of the grid.","authors_text":"Michal Adamaszek","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-22T18:55:54Z","title":"Special cycles in independence complexes and superfrustration in some lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4914","kind":"arxiv","version":2},"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":"sha256:8a0003628691de2550f6fdd77d31f7862781c04d74fb44f5421ce1ed23214832","target":"record","created_at":"2026-05-18T04:05:27Z","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":"2042591e31d1d7134cca9f6f4f8eca1cdfefb45906c3738276ba57307ac1d211","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-22T18:55:54Z","title_canon_sha256":"6a7a48941acaefd8bde955f913671550f834b72442e81e2b6f65fbed41463118"},"schema_version":"1.0","source":{"id":"1109.4914","kind":"arxiv","version":2}},"canonical_sha256":"13fd2da91502f1ec0e85702f00aa35d5b920a8a28b5418bf42bad0455e307baa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13fd2da91502f1ec0e85702f00aa35d5b920a8a28b5418bf42bad0455e307baa","first_computed_at":"2026-05-18T04:05:27.017470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:27.017470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGnF/6kLt0xvv2/Rx+XzDNrWDUsw+hdRApBPiBusl3YLWBVggf5ogtbtve1kzvL1n1MIDPH5UUpbQoIID3v/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:27.018302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4914","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a0003628691de2550f6fdd77d31f7862781c04d74fb44f5421ce1ed23214832","sha256:fff4a78195090dc352c9c7793aafaa92c0693cc59a049437bcd3c34c016ea288"],"state_sha256":"8a1ab4f49ee20d40f6e1f000962d4026031943ce8b89f8b67b2346ba4fbdf752"}