{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O35TNP7JRY3TSXS5X3EJDE32XX","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":"dca6943e3ade9ee6d329a2a28b141b5b6cc2e6689a9486df11ecfd9aeb8222ca","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-26T23:14:47Z","title_canon_sha256":"d13b30701d91a98647cd8899da25d6ecfcabaeb8061315fabe6a23ec3d2c1da3"},"schema_version":"1.0","source":{"id":"1801.09001","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09001","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09001v5","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09001","created_at":"2026-05-17T23:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"O35TNP7JRY3T","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O35TNP7JRY3TSXS5","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O35TNP7J","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:eced573ab003820d86595d781bb3d3a22ca82bb44e0f70d61288336b9f671ca1","target":"graph","created_at":"2026-05-17T23:53:51Z","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":"Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we require a characterization suitable for work in $\\mu$-abstract elementary classes, i.e. accessible categories with all morphisms monomorphisms) and expository (we hope, with this account, to make forking accessible - and useful - to a broader mathematical audience). In particular, we present an axiomatic definition of what we call a stable independence notion on","authors_text":"Ji\\v{r}\\'i Rosick\\'y, Michael Lieberman, Sebastien Vasey","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-26T23:14:47Z","title":"Forking independence from the categorical point of view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09001","kind":"arxiv","version":5},"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:fbea149f6de33e7eae398f627779bc1c1d9b6af7571ba5362be83b84271e0544","target":"record","created_at":"2026-05-17T23:53:51Z","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":"dca6943e3ade9ee6d329a2a28b141b5b6cc2e6689a9486df11ecfd9aeb8222ca","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-01-26T23:14:47Z","title_canon_sha256":"d13b30701d91a98647cd8899da25d6ecfcabaeb8061315fabe6a23ec3d2c1da3"},"schema_version":"1.0","source":{"id":"1801.09001","kind":"arxiv","version":5}},"canonical_sha256":"76fb36bfe98e37395e5dbec891937abdca6be094dab66b7129bcc262d5ab353b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76fb36bfe98e37395e5dbec891937abdca6be094dab66b7129bcc262d5ab353b","first_computed_at":"2026-05-17T23:53:51.739554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:51.739554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KDHPzA1DoV1/cb1zqlQ+5kU7Q/bj8Ty7U2jwHvQHqrtL8qoT4E+6gmoQfhBCYrZcMtuyXlSuC9aSrUIGhBCKDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:51.740250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09001","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbea149f6de33e7eae398f627779bc1c1d9b6af7571ba5362be83b84271e0544","sha256:eced573ab003820d86595d781bb3d3a22ca82bb44e0f70d61288336b9f671ca1"],"state_sha256":"82f69c7cea3b62679d3808bc77285bde9e18d4e679abc138f7e6b6af92a2740d"}