{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HWRYBNMJWWL4K33A7D3WTNEINM","short_pith_number":"pith:HWRYBNMJ","canonical_record":{"source":{"id":"1210.7883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-30T01:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"965536e6a5bd5619caa0be6eb247a3bd43bf2ef530da367a09a8b4250209a680","abstract_canon_sha256":"960dc174d94463ae471eafb2853019d3e1120b128f78521845fe5fbf4d89a012"},"schema_version":"1.0"},"canonical_sha256":"3da380b589b597c56f60f8f769b4886b326c475cc2d576d30e94dcced30510bd","source":{"kind":"arxiv","id":"1210.7883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7883","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7883v1","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7883","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"HWRYBNMJWWL4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HWRYBNMJWWL4K33A","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HWRYBNMJ","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HWRYBNMJWWL4K33A7D3WTNEINM","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-30T01:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"965536e6a5bd5619caa0be6eb247a3bd43bf2ef530da367a09a8b4250209a680","abstract_canon_sha256":"960dc174d94463ae471eafb2853019d3e1120b128f78521845fe5fbf4d89a012"},"schema_version":"1.0"},"canonical_sha256":"3da380b589b597c56f60f8f769b4886b326c475cc2d576d30e94dcced30510bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:57.841152Z","signature_b64":"CIZinB3/h4kjlsooEu2qKI09Dz4M32xszmtiMD2/vMuYXaqbuq3Gh+LIaFVA4PYBzwh82DFwVWMHnwzyNiPvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3da380b589b597c56f60f8f769b4886b326c475cc2d576d30e94dcced30510bd","last_reissued_at":"2026-05-18T03:41:57.840233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:57.840233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7883","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WVgVG/hOwwgawTXwDc9g04esw4fmQOQlNn4G922WTK7wQ4TmB/77WPvx1YudyadUrSXhHd+iYDKjqUffBjcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:26:07.592363Z"},"content_sha256":"f09e20960979ed50f32ad90f99f566374752e04761928b106dc4900cb18231c6","schema_version":"1.0","event_id":"sha256:f09e20960979ed50f32ad90f99f566374752e04761928b106dc4900cb18231c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HWRYBNMJWWL4K33A7D3WTNEINM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Weak Elimination of Hyperimaginaries and its Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Cameron Donnay Hill, Donald Brower","submitted_at":"2012-10-30T01:48:48Z","abstract_excerpt":"We analyze the notion of weak elimination of hyperimaginaries (WEHI) in simple theories. A key observation in the analysis is a characterization of WEHI in terms of forking dependence -- a condition we dub dependence-witnessed-by-imaginaries (DWIP). Generalizing results of [1] and [3], we show that in a simple theory with WEHI, forking and thorn-forking coincide. We also show that, conversely, the equivalence of independence and thorn-independence is (almost) sufficient for WEHI. Thus, the WEHI and the statement independence = thorn-independence are morally equivalent. As a further application"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7883","kind":"arxiv","version":1},"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":"2026-05-18T03:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNauQZUxQbQ+xdaeTLYDi9x80D5LF4pmZr+zvDDBs+Qf+Z6RA3Fd4qYZ4FaWruz3i9F6XIuataKDRo05Pt0CAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:26:07.592718Z"},"content_sha256":"82f07ac5bcb024999073a8f766d6497200319871017faa4e7cbb5f7405edb740","schema_version":"1.0","event_id":"sha256:82f07ac5bcb024999073a8f766d6497200319871017faa4e7cbb5f7405edb740"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWRYBNMJWWL4K33A7D3WTNEINM/bundle.json","state_url":"https://pith.science/pith/HWRYBNMJWWL4K33A7D3WTNEINM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWRYBNMJWWL4K33A7D3WTNEINM/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":"2026-06-23T03:26:07Z","links":{"resolver":"https://pith.science/pith/HWRYBNMJWWL4K33A7D3WTNEINM","bundle":"https://pith.science/pith/HWRYBNMJWWL4K33A7D3WTNEINM/bundle.json","state":"https://pith.science/pith/HWRYBNMJWWL4K33A7D3WTNEINM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWRYBNMJWWL4K33A7D3WTNEINM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HWRYBNMJWWL4K33A7D3WTNEINM","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":"960dc174d94463ae471eafb2853019d3e1120b128f78521845fe5fbf4d89a012","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-30T01:48:48Z","title_canon_sha256":"965536e6a5bd5619caa0be6eb247a3bd43bf2ef530da367a09a8b4250209a680"},"schema_version":"1.0","source":{"id":"1210.7883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7883","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7883v1","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7883","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"HWRYBNMJWWL4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HWRYBNMJWWL4K33A","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HWRYBNMJ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:82f07ac5bcb024999073a8f766d6497200319871017faa4e7cbb5f7405edb740","target":"graph","created_at":"2026-05-18T03:41:57Z","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 analyze the notion of weak elimination of hyperimaginaries (WEHI) in simple theories. A key observation in the analysis is a characterization of WEHI in terms of forking dependence -- a condition we dub dependence-witnessed-by-imaginaries (DWIP). Generalizing results of [1] and [3], we show that in a simple theory with WEHI, forking and thorn-forking coincide. We also show that, conversely, the equivalence of independence and thorn-independence is (almost) sufficient for WEHI. Thus, the WEHI and the statement independence = thorn-independence are morally equivalent. As a further application","authors_text":"Cameron Donnay Hill, Donald Brower","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-30T01:48:48Z","title":"On Weak Elimination of Hyperimaginaries and its Consequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7883","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:f09e20960979ed50f32ad90f99f566374752e04761928b106dc4900cb18231c6","target":"record","created_at":"2026-05-18T03:41:57Z","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":"960dc174d94463ae471eafb2853019d3e1120b128f78521845fe5fbf4d89a012","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-30T01:48:48Z","title_canon_sha256":"965536e6a5bd5619caa0be6eb247a3bd43bf2ef530da367a09a8b4250209a680"},"schema_version":"1.0","source":{"id":"1210.7883","kind":"arxiv","version":1}},"canonical_sha256":"3da380b589b597c56f60f8f769b4886b326c475cc2d576d30e94dcced30510bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3da380b589b597c56f60f8f769b4886b326c475cc2d576d30e94dcced30510bd","first_computed_at":"2026-05-18T03:41:57.840233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:57.840233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIZinB3/h4kjlsooEu2qKI09Dz4M32xszmtiMD2/vMuYXaqbuq3Gh+LIaFVA4PYBzwh82DFwVWMHnwzyNiPvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:57.841152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f09e20960979ed50f32ad90f99f566374752e04761928b106dc4900cb18231c6","sha256:82f07ac5bcb024999073a8f766d6497200319871017faa4e7cbb5f7405edb740"],"state_sha256":"35ddf73826e99ae106904ab89ff0c55826317da04e368b29ca03eec810dc87dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETzY7ewmuYzhb911ZLeExOWQBsee6iL2nvbCZIFCXouSYaOlGp+T1wGn+5HJGK+H/fq6YIyy0L5fH81uybKiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:26:07.594668Z","bundle_sha256":"60df98e1f10716810c1ae70bebfad0d74aabd6055d304ba26957c95e95cb5714"}}