{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HOY4TOWAJ4VWV4X4PPVAQPN4BL","short_pith_number":"pith:HOY4TOWA","canonical_record":{"source":{"id":"2209.04069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-09T00:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"271a78438c5b46fabebd0ddfcf2c0249e0f48172f7de65cbb6342800c1df68f1","abstract_canon_sha256":"9ac8206f304002dc0f7fcaff271b784d0890c050be98c4b9c37a0fb0df0290b5"},"schema_version":"1.0"},"canonical_sha256":"3bb1c9bac04f2b6af2fc7bea083dbc0ac212dbd463777aaa1177e0d293b6dd23","source":{"kind":"arxiv","id":"2209.04069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.04069","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"2209.04069v1","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04069","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"HOY4TOWAJ4VW","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_16","alias_value":"HOY4TOWAJ4VWV4X4","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_8","alias_value":"HOY4TOWA","created_at":"2026-07-05T04:55:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HOY4TOWAJ4VWV4X4PPVAQPN4BL","target":"record","payload":{"canonical_record":{"source":{"id":"2209.04069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-09T00:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"271a78438c5b46fabebd0ddfcf2c0249e0f48172f7de65cbb6342800c1df68f1","abstract_canon_sha256":"9ac8206f304002dc0f7fcaff271b784d0890c050be98c4b9c37a0fb0df0290b5"},"schema_version":"1.0"},"canonical_sha256":"3bb1c9bac04f2b6af2fc7bea083dbc0ac212dbd463777aaa1177e0d293b6dd23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:55:55.514030Z","signature_b64":"OzX/j7SoJZZRPUP+bsU+hF8IoY9Iz8if//74jHWEJ2lJDErIumd9U3QQoTueMH7ZY1r1eAbqhPz1Zm10zWk1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bb1c9bac04f2b6af2fc7bea083dbc0ac212dbd463777aaa1177e0d293b6dd23","last_reissued_at":"2026-07-05T04:55:55.513677Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:55:55.513677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.04069","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":"2026-07-05T04:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBE23urB5Lp4v2CQnd1OqHpZ35k9r36R06kSwQaIFcQm9LdUHSOHSjbOefXeJzpVUoH5I5/fRFeoBehg0JXuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:26:51.095305Z"},"content_sha256":"1f7677cefb17d2342d16d91815a40748fdb6b754e3aa770b8cc0c3c6b5f75571","schema_version":"1.0","event_id":"sha256:1f7677cefb17d2342d16d91815a40748fdb6b754e3aa770b8cc0c3c6b5f75571"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HOY4TOWAJ4VWV4X4PPVAQPN4BL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free structures and limiting density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Johanna N. Y. Franklin, Julia Knight, Meng-Che \"Turbo\" Ho","submitted_at":"2022-09-09T00:46:27Z","abstract_excerpt":"Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the non-abelian free groups. We ask Gromov's question more generally, for structures in an arbitrary algebraic variety (in the sense of universal algebra), with presentations of a specific form. We focus on elementary properties. We give examples illustrating different behaviors of the limiting density. Based on the examples, we identify sufficient conditions for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.04069","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.04069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:55:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7mNTOpgYxk18QLG/0EPk282t/dg3qzYDzMUkqMcJ+RQ08Q0tKepYmwBKxkKmn4JJ/TTh/nTd8tpYGi1OXk4uDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:26:51.095831Z"},"content_sha256":"a3e26f8212695cd257aab314d50952fca6e37d598ee6194623274f018d6487d5","schema_version":"1.0","event_id":"sha256:a3e26f8212695cd257aab314d50952fca6e37d598ee6194623274f018d6487d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/bundle.json","state_url":"https://pith.science/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/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":"2026-08-05T01:26:51Z","links":{"resolver":"https://pith.science/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL","bundle":"https://pith.science/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/bundle.json","state":"https://pith.science/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOY4TOWAJ4VWV4X4PPVAQPN4BL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HOY4TOWAJ4VWV4X4PPVAQPN4BL","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":"9ac8206f304002dc0f7fcaff271b784d0890c050be98c4b9c37a0fb0df0290b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-09T00:46:27Z","title_canon_sha256":"271a78438c5b46fabebd0ddfcf2c0249e0f48172f7de65cbb6342800c1df68f1"},"schema_version":"1.0","source":{"id":"2209.04069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.04069","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"arxiv_version","alias_value":"2209.04069v1","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.04069","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_12","alias_value":"HOY4TOWAJ4VW","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_16","alias_value":"HOY4TOWAJ4VWV4X4","created_at":"2026-07-05T04:55:55Z"},{"alias_kind":"pith_short_8","alias_value":"HOY4TOWA","created_at":"2026-07-05T04:55:55Z"}],"graph_snapshots":[{"event_id":"sha256:a3e26f8212695cd257aab314d50952fca6e37d598ee6194623274f018d6487d5","target":"graph","created_at":"2026-07-05T04:55:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.04069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the non-abelian free groups. We ask Gromov's question more generally, for structures in an arbitrary algebraic variety (in the sense of universal algebra), with presentations of a specific form. We focus on elementary properties. We give examples illustrating different behaviors of the limiting density. Based on the examples, we identify sufficient conditions for","authors_text":"Johanna N. Y. Franklin, Julia Knight, Meng-Che \"Turbo\" Ho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-09T00:46:27Z","title":"Free structures and limiting density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.04069","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":"sha256:1f7677cefb17d2342d16d91815a40748fdb6b754e3aa770b8cc0c3c6b5f75571","target":"record","created_at":"2026-07-05T04:55:55Z","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":"9ac8206f304002dc0f7fcaff271b784d0890c050be98c4b9c37a0fb0df0290b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-09T00:46:27Z","title_canon_sha256":"271a78438c5b46fabebd0ddfcf2c0249e0f48172f7de65cbb6342800c1df68f1"},"schema_version":"1.0","source":{"id":"2209.04069","kind":"arxiv","version":1}},"canonical_sha256":"3bb1c9bac04f2b6af2fc7bea083dbc0ac212dbd463777aaa1177e0d293b6dd23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bb1c9bac04f2b6af2fc7bea083dbc0ac212dbd463777aaa1177e0d293b6dd23","first_computed_at":"2026-07-05T04:55:55.513677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:55.513677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OzX/j7SoJZZRPUP+bsU+hF8IoY9Iz8if//74jHWEJ2lJDErIumd9U3QQoTueMH7ZY1r1eAbqhPz1Zm10zWk1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:55.514030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.04069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f7677cefb17d2342d16d91815a40748fdb6b754e3aa770b8cc0c3c6b5f75571","sha256:a3e26f8212695cd257aab314d50952fca6e37d598ee6194623274f018d6487d5"],"state_sha256":"e362b4fd62b80abffa099f240bca05f4db1171ad121e30aec7d9835161057c24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMQja0BAp9Z7EAolWpLyDR309p5B8SRVU8dIGq1O4WUHsnm5hkbu2oZasS//WmcIk6njr77MCOUaPnAIRoiHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T01:26:51.099574Z","bundle_sha256":"ccf88609a432ccada1ee741a003790a56aca0763b9079495af2cf5df6f94b0d9"}}