{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BMXEZQSYYLCL4NL2SX2AS4IZ7G","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":"fce95bebf1e386b0d49c2fd055dfc6588052b9e071370167de557ef84f2cbc57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-15T18:34:29Z","title_canon_sha256":"92c9d251c09e72904a4da18fd7762f9f2ec41dc3c013896e8098bbefa629127e"},"schema_version":"1.0","source":{"id":"1204.3303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3303","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3303v1","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3303","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"BMXEZQSYYLCL","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BMXEZQSYYLCL4NL2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BMXEZQSY","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:3be9ed6a0eb4a38ba7c6b1e240f72d0038ad6ebe710b2ac13f7134ecced73675","target":"graph","created_at":"2026-05-18T03:57:51Z","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":"In this this paper we introduce entanglement among the points in a non-commutative scheme, in addition to the tangent directions. A diagram of $A$-modules is a pair $\\uc=(|\\uc|,\\Gamma)$ where $|\\uc|={V_1,...,V_r}$ is a set of $A$-modules, and $\\Gamma=\\{\\gamma_{ij}(l)\\}$ is a set of $A$-module homomorphisms $\\gamma_{ij}(l):V_i\\rightarrow V_j$, seen as the 0'th order tangent directions. This concludes the discussion on non-commutative schemes by defining the deformation theory for diagrams, making these the fundamental points of the non-commutative algebraic geometry, which means that the constr","authors_text":"Arvid Siqveland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-15T18:34:29Z","title":"Deformation of diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3303","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":"sha256:4626caafba0ef04f23cf28b57320d4878cd83e1609a8f2fcd8d39fafe4c278ae","target":"record","created_at":"2026-05-18T03:57:51Z","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":"fce95bebf1e386b0d49c2fd055dfc6588052b9e071370167de557ef84f2cbc57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-15T18:34:29Z","title_canon_sha256":"92c9d251c09e72904a4da18fd7762f9f2ec41dc3c013896e8098bbefa629127e"},"schema_version":"1.0","source":{"id":"1204.3303","kind":"arxiv","version":1}},"canonical_sha256":"0b2e4cc258c2c4be357a95f4097119f9b3ba8fb1c83daf4b6162a30334743c84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b2e4cc258c2c4be357a95f4097119f9b3ba8fb1c83daf4b6162a30334743c84","first_computed_at":"2026-05-18T03:57:51.890372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:51.890372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0+0f6T2ymAOoB0p1PgV3SP97Kq8Nm/v9ObvbzRf6efTBVE7kCT+y1qFJlsacSHNdHok91LCnbzTk4dLhYA5DCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:51.890918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4626caafba0ef04f23cf28b57320d4878cd83e1609a8f2fcd8d39fafe4c278ae","sha256:3be9ed6a0eb4a38ba7c6b1e240f72d0038ad6ebe710b2ac13f7134ecced73675"],"state_sha256":"4229af853749bff312e5aaff11a74562873773ac3d158dcb4c92bdbf8f08061d"}