{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DYRPQ4TJIOAXFMPDTHGHC5VIRD","short_pith_number":"pith:DYRPQ4TJ","canonical_record":{"source":{"id":"1803.07215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-20T01:54:33Z","cross_cats_sorted":[],"title_canon_sha256":"3e3e0436e44b07081319fd39c2c95fd5b6a1043573606e49f6873cf6faa4b371","abstract_canon_sha256":"341515bf22039125738e7da4332a2b40b2628ce10b9262ecf6a29e9ed2a318a5"},"schema_version":"1.0"},"canonical_sha256":"1e22f87269438172b1e399cc7176a888fca2cf7f45b08ac1b6b0e5c6c3f1b188","source":{"kind":"arxiv","id":"1803.07215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07215","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07215v1","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07215","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"pith_short_12","alias_value":"DYRPQ4TJIOAX","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DYRPQ4TJIOAXFMPD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DYRPQ4TJ","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DYRPQ4TJIOAXFMPDTHGHC5VIRD","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-20T01:54:33Z","cross_cats_sorted":[],"title_canon_sha256":"3e3e0436e44b07081319fd39c2c95fd5b6a1043573606e49f6873cf6faa4b371","abstract_canon_sha256":"341515bf22039125738e7da4332a2b40b2628ce10b9262ecf6a29e9ed2a318a5"},"schema_version":"1.0"},"canonical_sha256":"1e22f87269438172b1e399cc7176a888fca2cf7f45b08ac1b6b0e5c6c3f1b188","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:33.958208Z","signature_b64":"22mgQ5nNJKAsNIgL9KKHqjuxpizCVQ+Q87hG5Uq1AroxoQZNiCEVHMYkLED8ZsjA75xDKKhw9AbeLC07aDqJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e22f87269438172b1e399cc7176a888fca2cf7f45b08ac1b6b0e5c6c3f1b188","last_reissued_at":"2026-05-18T00:20:33.957555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:33.957555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07215","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":"2026-05-18T00:20:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2kwa9QGG2MTjCcqTuKLMjtNI1tWgFlckScguSUERJRFGEgHXug80kgGzmoLIIZJwuSo257lSQDzMGQ0aj5zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:44:49.638222Z"},"content_sha256":"96324a4db9d9a3eca976e8ab79d129f58737e2ba972ac2a0657533b5aafc9651","schema_version":"1.0","event_id":"sha256:96324a4db9d9a3eca976e8ab79d129f58737e2ba972ac2a0657533b5aafc9651"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DYRPQ4TJIOAXFMPDTHGHC5VIRD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supersimple structures with a dense independent subset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alexander Berenstein, Evgueni Vassiliev, Juan Felipe Carmona","submitted_at":"2018-03-20T01:54:33Z","abstract_excerpt":"Based on the work done in \\cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a partial type $\\mathcal{G}(x)$, which we call $H$-structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again $H$-structures. We prove that under these assumptions the expansion is supersimple and characterize forking and canonical bases of types in the expans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07215","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":"2026-05-18T00:20:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owc/fIg2Zzu/FbsAQBumEiNU5FuCZhp0xHF1umCbtr/oA5Heu9hjDVH+BZ5T7/9WH5nuDkNsvt3CJoZ0braLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:44:49.638879Z"},"content_sha256":"766c5f634c3d69c41e8f7d5839aad770fd05a0e45cacc58b6542d3310859749b","schema_version":"1.0","event_id":"sha256:766c5f634c3d69c41e8f7d5839aad770fd05a0e45cacc58b6542d3310859749b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/bundle.json","state_url":"https://pith.science/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/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":"2026-05-27T06:44:49Z","links":{"resolver":"https://pith.science/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD","bundle":"https://pith.science/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/bundle.json","state":"https://pith.science/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYRPQ4TJIOAXFMPDTHGHC5VIRD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DYRPQ4TJIOAXFMPDTHGHC5VIRD","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":"341515bf22039125738e7da4332a2b40b2628ce10b9262ecf6a29e9ed2a318a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-20T01:54:33Z","title_canon_sha256":"3e3e0436e44b07081319fd39c2c95fd5b6a1043573606e49f6873cf6faa4b371"},"schema_version":"1.0","source":{"id":"1803.07215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07215","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07215v1","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07215","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"pith_short_12","alias_value":"DYRPQ4TJIOAX","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DYRPQ4TJIOAXFMPD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DYRPQ4TJ","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:766c5f634c3d69c41e8f7d5839aad770fd05a0e45cacc58b6542d3310859749b","target":"graph","created_at":"2026-05-18T00:20:33Z","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":"Based on the work done in \\cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a partial type $\\mathcal{G}(x)$, which we call $H$-structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again $H$-structures. We prove that under these assumptions the expansion is supersimple and characterize forking and canonical bases of types in the expans","authors_text":"Alexander Berenstein, Evgueni Vassiliev, Juan Felipe Carmona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-20T01:54:33Z","title":"Supersimple structures with a dense independent subset"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07215","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":"sha256:96324a4db9d9a3eca976e8ab79d129f58737e2ba972ac2a0657533b5aafc9651","target":"record","created_at":"2026-05-18T00:20:33Z","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":"341515bf22039125738e7da4332a2b40b2628ce10b9262ecf6a29e9ed2a318a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-20T01:54:33Z","title_canon_sha256":"3e3e0436e44b07081319fd39c2c95fd5b6a1043573606e49f6873cf6faa4b371"},"schema_version":"1.0","source":{"id":"1803.07215","kind":"arxiv","version":1}},"canonical_sha256":"1e22f87269438172b1e399cc7176a888fca2cf7f45b08ac1b6b0e5c6c3f1b188","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e22f87269438172b1e399cc7176a888fca2cf7f45b08ac1b6b0e5c6c3f1b188","first_computed_at":"2026-05-18T00:20:33.957555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:33.957555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"22mgQ5nNJKAsNIgL9KKHqjuxpizCVQ+Q87hG5Uq1AroxoQZNiCEVHMYkLED8ZsjA75xDKKhw9AbeLC07aDqJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:33.958208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96324a4db9d9a3eca976e8ab79d129f58737e2ba972ac2a0657533b5aafc9651","sha256:766c5f634c3d69c41e8f7d5839aad770fd05a0e45cacc58b6542d3310859749b"],"state_sha256":"1e7c2a61c58d7ebd723e4725fbecbb1dc2545ce76fcd418f06c26f9fb95bb1ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOqSqLSY2pY0L2WQQYY58XKcG1rfJnXND4rCjrx1iFe2HCKZ7pklzOMGuEzASpxqLjek/M0/EX5HgvlsI/lqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:44:49.642461Z","bundle_sha256":"5f3df45645a81a10040102a6a34e70aa0c8e9f1dead0dfb8dcec683aed43f474"}}