{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BLQTTRGXQOUMT7XHD5PT5KASIH","short_pith_number":"pith:BLQTTRGX","canonical_record":{"source":{"id":"1708.03724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-11T22:48:56Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"1705733bd5334a67d1297779d3703f02500429e5fa81d8855bff7c58e62b34a5","abstract_canon_sha256":"67c79af371742de0c0e4099f98a33d6b6566bc4f894854325a3f390f1bb39819"},"schema_version":"1.0"},"canonical_sha256":"0ae139c4d783a8c9fee71f5f3ea81241e8ac05a9185f8913b6006657d5075f54","source":{"kind":"arxiv","id":"1708.03724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03724","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03724v2","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03724","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"BLQTTRGXQOUM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BLQTTRGXQOUMT7XH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BLQTTRGX","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BLQTTRGXQOUMT7XHD5PT5KASIH","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-11T22:48:56Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"1705733bd5334a67d1297779d3703f02500429e5fa81d8855bff7c58e62b34a5","abstract_canon_sha256":"67c79af371742de0c0e4099f98a33d6b6566bc4f894854325a3f390f1bb39819"},"schema_version":"1.0"},"canonical_sha256":"0ae139c4d783a8c9fee71f5f3ea81241e8ac05a9185f8913b6006657d5075f54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:18.769217Z","signature_b64":"J0VHSCLdyXjXcDFYf0jMPfJu6iTJrCDgCVRkc8rdYB/X7gzIUtF0+/KqCYy7lQGjei56kgZ564IHNS9+lHQfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ae139c4d783a8c9fee71f5f3ea81241e8ac05a9185f8913b6006657d5075f54","last_reissued_at":"2026-05-18T00:11:18.768574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:18.768574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03724","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxVnW1frPlMT8rRdYfwUttgz6XXIshEidI/0f5ajjTomBEqzbWByxkY1BkMuz/bNdz4zKlWrVSRNlHt7eTkWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:45:37.062801Z"},"content_sha256":"c4a9838439a8b323ad35d8282dce0e7d9d7b0439ff90ebb2fb5de78b36b86bf1","schema_version":"1.0","event_id":"sha256:c4a9838439a8b323ad35d8282dce0e7d9d7b0439ff90ebb2fb5de78b36b86bf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BLQTTRGXQOUMT7XHD5PT5KASIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mekler's construction and generalized stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.LO","authors_text":"Artem Chernikov, Nadja Hempel","submitted_at":"2017-08-11T22:48:56Z","abstract_excerpt":"Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a bi-interpretation, it is known to preserve some model-theoretic tameness properties of the original structure including stability and simplicity. We demonstrate that $k$-dependence of the theory is preserved, for all $k \\in \\mathbb{N}$, and that NTP$_2$ is preserved. We apply this result to obtain first examples of strictly $k$-dependent groups (with no additional stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03724","kind":"arxiv","version":2},"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":"2026-05-18T00:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRPUxAvX2h2h/FuVYMm+TccbF/KjCSTzTX97zRydsW5AmPGwp4QKdLITkoGeqGXEYPa9hw4DxsNF60mC/kirAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:45:37.063151Z"},"content_sha256":"c2bb0ba46bc0354896b3f76a8def0fc532b5e7373fc1ff07ecf330e533ff1d05","schema_version":"1.0","event_id":"sha256:c2bb0ba46bc0354896b3f76a8def0fc532b5e7373fc1ff07ecf330e533ff1d05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/bundle.json","state_url":"https://pith.science/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/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":"2026-06-25T08:45:37Z","links":{"resolver":"https://pith.science/pith/BLQTTRGXQOUMT7XHD5PT5KASIH","bundle":"https://pith.science/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/bundle.json","state":"https://pith.science/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLQTTRGXQOUMT7XHD5PT5KASIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BLQTTRGXQOUMT7XHD5PT5KASIH","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":"67c79af371742de0c0e4099f98a33d6b6566bc4f894854325a3f390f1bb39819","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-11T22:48:56Z","title_canon_sha256":"1705733bd5334a67d1297779d3703f02500429e5fa81d8855bff7c58e62b34a5"},"schema_version":"1.0","source":{"id":"1708.03724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03724","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03724v2","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03724","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"BLQTTRGXQOUM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BLQTTRGXQOUMT7XH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BLQTTRGX","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:c2bb0ba46bc0354896b3f76a8def0fc532b5e7373fc1ff07ecf330e533ff1d05","target":"graph","created_at":"2026-05-18T00:11:18Z","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":"Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a bi-interpretation, it is known to preserve some model-theoretic tameness properties of the original structure including stability and simplicity. We demonstrate that $k$-dependence of the theory is preserved, for all $k \\in \\mathbb{N}$, and that NTP$_2$ is preserved. We apply this result to obtain first examples of strictly $k$-dependent groups (with no additional stru","authors_text":"Artem Chernikov, Nadja Hempel","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-11T22:48:56Z","title":"Mekler's construction and generalized stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03724","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:c4a9838439a8b323ad35d8282dce0e7d9d7b0439ff90ebb2fb5de78b36b86bf1","target":"record","created_at":"2026-05-18T00:11:18Z","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":"67c79af371742de0c0e4099f98a33d6b6566bc4f894854325a3f390f1bb39819","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-11T22:48:56Z","title_canon_sha256":"1705733bd5334a67d1297779d3703f02500429e5fa81d8855bff7c58e62b34a5"},"schema_version":"1.0","source":{"id":"1708.03724","kind":"arxiv","version":2}},"canonical_sha256":"0ae139c4d783a8c9fee71f5f3ea81241e8ac05a9185f8913b6006657d5075f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ae139c4d783a8c9fee71f5f3ea81241e8ac05a9185f8913b6006657d5075f54","first_computed_at":"2026-05-18T00:11:18.768574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:18.768574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J0VHSCLdyXjXcDFYf0jMPfJu6iTJrCDgCVRkc8rdYB/X7gzIUtF0+/KqCYy7lQGjei56kgZ564IHNS9+lHQfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:18.769217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4a9838439a8b323ad35d8282dce0e7d9d7b0439ff90ebb2fb5de78b36b86bf1","sha256:c2bb0ba46bc0354896b3f76a8def0fc532b5e7373fc1ff07ecf330e533ff1d05"],"state_sha256":"5512a8dee50d9c112fcf21eda6a75b9fdbc45f139eceead5e0be7907536ea43a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3L74IauPITnRNCnYETa6nEwuYzMK7tngFDu249kqYcCFrXlIsxk3WNLCkd6MPwQP6TFge7DuykoAuBK88LcMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:45:37.065047Z","bundle_sha256":"8d1f656727f38ee03dac1f09af5e0505aaad45140f83ff465689ce135201b5e2"}}