{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L6W2VDTUD5DRWFIM27XD66WB2F","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":"52f7aab1e80fd8752118e238b0b8a5939b6179ad103ecdeb2aa4aaae692cde8e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-07T12:37:19Z","title_canon_sha256":"6f20a21df4cfba0e82e11c9b10127c34d55e6f1faab9b49deb3f2d8738a0d469"},"schema_version":"1.0","source":{"id":"1706.02156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02156","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02156v2","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02156","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"L6W2VDTUD5DR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L6W2VDTUD5DRWFIM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L6W2VDTU","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:6b43256d772c9ee56be9ae6ff3354d3329dabe26474fc2d5fb453b8fbc542113","target":"graph","created_at":"2026-05-18T00:16:19Z","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":"This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying free modules, or the total length of their homology, is less than predicted by various conjectures in the theory of transformation groups and in local algebra.","authors_text":"Mark E. Walker, Srikanth B. Iyengar","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-07T12:37:19Z","title":"Examples of finite free complexes of small rank and small homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02156","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":"sha256:96832064f67960d7fea1de70f9e21adf8441856511bc47ed50aad848d4ca07a9","target":"record","created_at":"2026-05-18T00:16:19Z","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":"52f7aab1e80fd8752118e238b0b8a5939b6179ad103ecdeb2aa4aaae692cde8e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-07T12:37:19Z","title_canon_sha256":"6f20a21df4cfba0e82e11c9b10127c34d55e6f1faab9b49deb3f2d8738a0d469"},"schema_version":"1.0","source":{"id":"1706.02156","kind":"arxiv","version":2}},"canonical_sha256":"5fadaa8e741f471b150cd7ee3f7ac1d17eb88600bb134169d69058e6a34a3dce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fadaa8e741f471b150cd7ee3f7ac1d17eb88600bb134169d69058e6a34a3dce","first_computed_at":"2026-05-18T00:16:19.507166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:19.507166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k1aEWCaYf9URbJt3fWu9Q1fmiI5clnWoLIoE+lgsjyDpjmECUl+nL5DZlJNzB39v92x9lfMscy0J1SwzeMmdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:19.507706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96832064f67960d7fea1de70f9e21adf8441856511bc47ed50aad848d4ca07a9","sha256:6b43256d772c9ee56be9ae6ff3354d3329dabe26474fc2d5fb453b8fbc542113"],"state_sha256":"356e006f5ad14d9c2fc647f1b30fd9ae8db4293ecea38cc363901ebf22b963f6"}