{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:I5QQ7M2ZPRARW3H3RDBDY33BC7","short_pith_number":"pith:I5QQ7M2Z","canonical_record":{"source":{"id":"1504.05171","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-20T19:44:41Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"a3455de75b98362e186751de8da44b9485644eb8cf9c9ae98cc550b6669150a2","abstract_canon_sha256":"ba7aecb095a20245142c2c311f68bba6b40b575c35150a8918d5f1547735b13e"},"schema_version":"1.0"},"canonical_sha256":"47610fb3597c411b6cfb88c23c6f6117c54bb6179bcf955899e5b2c82e9695de","source":{"kind":"arxiv","id":"1504.05171","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05171","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05171v3","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05171","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"I5QQ7M2ZPRAR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I5QQ7M2ZPRARW3H3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I5QQ7M2Z","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:I5QQ7M2ZPRARW3H3RDBDY33BC7","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05171","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-20T19:44:41Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"a3455de75b98362e186751de8da44b9485644eb8cf9c9ae98cc550b6669150a2","abstract_canon_sha256":"ba7aecb095a20245142c2c311f68bba6b40b575c35150a8918d5f1547735b13e"},"schema_version":"1.0"},"canonical_sha256":"47610fb3597c411b6cfb88c23c6f6117c54bb6179bcf955899e5b2c82e9695de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:02.081198Z","signature_b64":"vz9b5aIutRJyxiNdY4JojY+qoD+GnQgpMhgKik9k/IjZcKC/9Q/DiknCTgULEqsB0La+XRBkvAp9HF49ZjsOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47610fb3597c411b6cfb88c23c6f6117c54bb6179bcf955899e5b2c82e9695de","last_reissued_at":"2026-05-18T00:29:02.080726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:02.080726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05171","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEzox53hcxWTEYrMfDqXBiNppBGjxUU6WnY716v2QJpJoPm7iOy1Sq/Gikrj4al4r8pbGiSWxee5bbfr8lS+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:32:34.529746Z"},"content_sha256":"5c1840bb443de78ad51fffa553431b821c3275488c49fc5ba71e7f863a3a2333","schema_version":"1.0","event_id":"sha256:5c1840bb443de78ad51fffa553431b821c3275488c49fc5ba71e7f863a3a2333"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:I5QQ7M2ZPRARW3H3RDBDY33BC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On minimal free resolutions of sub-permanents and other ideals arising in complexity theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"cs.CC","authors_text":"Hal Schenck, Jerzy Weyman, J.M. Landsberg, Klim Efremenko","submitted_at":"2015-04-20T19:44:41Z","abstract_excerpt":"We compute the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x n generic matrix and of the ideal generated by square-free monomials of degree k. The latter calculation gives the full minimal free resolution by work of Biagioli-Faridi-Rosas. Our motivation is to lay groundwork for the use of commutative algebra in algebraic complexity theory. We also compute several Hilbert functions relevant for complexity theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05171","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9jIp75KnmPVaTt28Bb2gtHfdRSSPb8Ilip7MSVLemElOfiVUSpdwVCPr3KH8r78O/HHfr/RgK4QpghPxM8RAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:32:34.530528Z"},"content_sha256":"8266370e5aa4aeefe6007222ccd1412ee01bc98a0dfc4e02a23885a648c706b2","schema_version":"1.0","event_id":"sha256:8266370e5aa4aeefe6007222ccd1412ee01bc98a0dfc4e02a23885a648c706b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/bundle.json","state_url":"https://pith.science/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T06:32:34Z","links":{"resolver":"https://pith.science/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7","bundle":"https://pith.science/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/bundle.json","state":"https://pith.science/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5QQ7M2ZPRARW3H3RDBDY33BC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I5QQ7M2ZPRARW3H3RDBDY33BC7","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":"ba7aecb095a20245142c2c311f68bba6b40b575c35150a8918d5f1547735b13e","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-20T19:44:41Z","title_canon_sha256":"a3455de75b98362e186751de8da44b9485644eb8cf9c9ae98cc550b6669150a2"},"schema_version":"1.0","source":{"id":"1504.05171","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05171","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05171v3","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05171","created_at":"2026-05-18T00:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"I5QQ7M2ZPRAR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I5QQ7M2ZPRARW3H3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I5QQ7M2Z","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:8266370e5aa4aeefe6007222ccd1412ee01bc98a0dfc4e02a23885a648c706b2","target":"graph","created_at":"2026-05-18T00:29:02Z","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 compute the linear strand of the minimal free resolution of the ideal generated by k x k sub-permanents of an n x n generic matrix and of the ideal generated by square-free monomials of degree k. The latter calculation gives the full minimal free resolution by work of Biagioli-Faridi-Rosas. Our motivation is to lay groundwork for the use of commutative algebra in algebraic complexity theory. We also compute several Hilbert functions relevant for complexity theory.","authors_text":"Hal Schenck, Jerzy Weyman, J.M. Landsberg, Klim Efremenko","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-20T19:44:41Z","title":"On minimal free resolutions of sub-permanents and other ideals arising in complexity theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05171","kind":"arxiv","version":3},"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":"sha256:5c1840bb443de78ad51fffa553431b821c3275488c49fc5ba71e7f863a3a2333","target":"record","created_at":"2026-05-18T00:29:02Z","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":"ba7aecb095a20245142c2c311f68bba6b40b575c35150a8918d5f1547735b13e","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-20T19:44:41Z","title_canon_sha256":"a3455de75b98362e186751de8da44b9485644eb8cf9c9ae98cc550b6669150a2"},"schema_version":"1.0","source":{"id":"1504.05171","kind":"arxiv","version":3}},"canonical_sha256":"47610fb3597c411b6cfb88c23c6f6117c54bb6179bcf955899e5b2c82e9695de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47610fb3597c411b6cfb88c23c6f6117c54bb6179bcf955899e5b2c82e9695de","first_computed_at":"2026-05-18T00:29:02.080726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:02.080726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vz9b5aIutRJyxiNdY4JojY+qoD+GnQgpMhgKik9k/IjZcKC/9Q/DiknCTgULEqsB0La+XRBkvAp9HF49ZjsOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:02.081198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05171","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c1840bb443de78ad51fffa553431b821c3275488c49fc5ba71e7f863a3a2333","sha256:8266370e5aa4aeefe6007222ccd1412ee01bc98a0dfc4e02a23885a648c706b2"],"state_sha256":"44610787456492a2d4ce6dc184a3ca872e851ce11338fbbbcd2d97df9975594e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgfLc/eJ5xZSpAoI8DZaH/QxzzuZ4MzMy+rOw21d+aw9JSswmfavdHuZ9AhBYyEp2na1ejaQfisEUqN0VCNWAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:32:34.534206Z","bundle_sha256":"980bbc1e801d86e108f85d5df4d35edf52d302c3f433bc2e5c67d13d7fda4fee"}}