{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AWSHZTER2MFHYV47CWLKEHOKQ7","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":"54df61e7cca0a69b32b1fa5a0a7d636e21da24db3fdad374f951f67dc46658f2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T20:45:37Z","title_canon_sha256":"1c8be08a5903e30e0cfa18b182501b85f68c8b43f0ce0da3773bf614e010d570"},"schema_version":"1.0","source":{"id":"1211.1368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1368","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1368v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1368","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"AWSHZTER2MFH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AWSHZTER2MFHYV47","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AWSHZTER","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:8804e6c74d72d995ffbad0eca5a07618c9e426a01250f8a1416700cd6e2f9ae2","target":"graph","created_at":"2026-05-18T03:41:21Z","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 disprove Holtz and Ron's conjecture that the power ideal C_{A,-2} of a hyperplane arrangement A (also called the \"internal zonotopal space\") is generated by A-monomials. We also show that, in contrast with the case k \\geq -2, the Hilbert series of C_{A,k} is not determined by the matroid of A for k \\leq -6.","authors_text":"Alex Postnikov, Federico Ardila","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T20:45:37Z","title":"Two counterexamples for power ideals of arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1368","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:cb6662697e450794a054c33c8bfcec6ed7734ea428314b341800c77792549128","target":"record","created_at":"2026-05-18T03:41:21Z","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":"54df61e7cca0a69b32b1fa5a0a7d636e21da24db3fdad374f951f67dc46658f2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T20:45:37Z","title_canon_sha256":"1c8be08a5903e30e0cfa18b182501b85f68c8b43f0ce0da3773bf614e010d570"},"schema_version":"1.0","source":{"id":"1211.1368","kind":"arxiv","version":1}},"canonical_sha256":"05a47ccc91d30a7c579f1596a21dca87ecc0f4fb30f2ca60a8b504e186c1a800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05a47ccc91d30a7c579f1596a21dca87ecc0f4fb30f2ca60a8b504e186c1a800","first_computed_at":"2026-05-18T03:41:21.731186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:21.731186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9YJIo0qW2M1U6Dvq2HLuXgOodYcd0qHoUd/lIJKk1X/N9WErToFl/stA3ojvL8qrzg+Xlo/JvKjoRMY6919Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:21.731781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb6662697e450794a054c33c8bfcec6ed7734ea428314b341800c77792549128","sha256:8804e6c74d72d995ffbad0eca5a07618c9e426a01250f8a1416700cd6e2f9ae2"],"state_sha256":"6c6ede06f554d8dde14222e6b107cd81cdc65b90fcdb8dcd1af8d7b56f75d756"}