{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DQRFXEWKOTZQDVIQICUGMH2UDG","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":"79cb976d060d9c3e6ed13aa48952efa78ce2ca404f3d1b7c6bd8c029e1a7c9bd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-14T16:59:23Z","title_canon_sha256":"596542320d8c531ae321dacce676e2f85397e8d6939156e7875669659e559411"},"schema_version":"1.0","source":{"id":"0808.2027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2027","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2027v2","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2027","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"DQRFXEWKOTZQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DQRFXEWKOTZQDVIQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DQRFXEWK","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:bed67e1eda4ee6f19bf3c840259670263a05d9918ca5d1209d3e5d79c7d7cb98","target":"graph","created_at":"2026-05-18T04:03:44Z","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":"Associated to the cohomology ring A of the complement X(A) of a hyperplane arrangement A in complex m-space are the resonance varieties R^k(A). The most studied of these is R^1(A), which is the union of the tangent cones at the origin to the characteristic varieties of the fundamental group of X. R^1(A) may be described in terms of Fitting ideals, or as the locus where a certain Ext module is supported. Both these descriptions give obvious algorithms for computation. In this note, we show that interpreting R^1(A) as the locus of decomposable two-tensors in the Orlik-Solomon ideal leads to a de","authors_text":"H. Schenck, P. Lima-Filho","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-14T16:59:23Z","title":"Efficient computation of resonance varieties via Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2027","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:c4337ca6bd6d775ea21388383af18b9c2e826aea89c263519eeef42bae3acba6","target":"record","created_at":"2026-05-18T04:03:44Z","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":"79cb976d060d9c3e6ed13aa48952efa78ce2ca404f3d1b7c6bd8c029e1a7c9bd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-14T16:59:23Z","title_canon_sha256":"596542320d8c531ae321dacce676e2f85397e8d6939156e7875669659e559411"},"schema_version":"1.0","source":{"id":"0808.2027","kind":"arxiv","version":2}},"canonical_sha256":"1c225b92ca74f301d51040a8661f5419be0ae109b322cafd092235bd348125f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c225b92ca74f301d51040a8661f5419be0ae109b322cafd092235bd348125f7","first_computed_at":"2026-05-18T04:03:44.074023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.074023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wijt0BhkPjx7Wlb3lOWELEmnlY4a0AuyTDCvqT2AERQsReTqudMoIx3YCjkVvPcghwINZ405yNPVUhtLQKUTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.074883Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4337ca6bd6d775ea21388383af18b9c2e826aea89c263519eeef42bae3acba6","sha256:bed67e1eda4ee6f19bf3c840259670263a05d9918ca5d1209d3e5d79c7d7cb98"],"state_sha256":"343f58bbe35240aa1571b8fdc2ed0dfe00b706b30f51ad17632bc79c26f9086b"}