{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:32SITMRNPNEQJC23FICQ4SPAOH","short_pith_number":"pith:32SITMRN","canonical_record":{"source":{"id":"2107.09699","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-07-20T18:07:10Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"89b0dc14ae585a0c9257d506ebba99c44ac82e85aa7fa458fba4e0b658960bf5","abstract_canon_sha256":"e2aff1d171f927c01f724b6c8809aadc011f6b78bd77c888f4812f4176e4243d"},"schema_version":"1.0"},"canonical_sha256":"dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be","source":{"kind":"arxiv","id":"2107.09699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.09699","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"2107.09699v1","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.09699","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"32SITMRNPNEQ","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_16","alias_value":"32SITMRNPNEQJC23","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_8","alias_value":"32SITMRN","created_at":"2026-07-05T02:59:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:32SITMRNPNEQJC23FICQ4SPAOH","target":"record","payload":{"canonical_record":{"source":{"id":"2107.09699","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-07-20T18:07:10Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"89b0dc14ae585a0c9257d506ebba99c44ac82e85aa7fa458fba4e0b658960bf5","abstract_canon_sha256":"e2aff1d171f927c01f724b6c8809aadc011f6b78bd77c888f4812f4176e4243d"},"schema_version":"1.0"},"canonical_sha256":"dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:59:38.748311Z","signature_b64":"RJ9/Gng43f4EPNk1zhIUUhiry1l1B2/eI1r1o241G3f/uALJeERvY/D/GVsMTy/rMc1OkMv1u/uRG2pFLIi8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be","last_reissued_at":"2026-07-05T02:59:38.747817Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:59:38.747817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.09699","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":"2026-07-05T02:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itBVFvfj7uytoEBRKLLegJMjsr36E2mek711nT56QUnveYDtjnZqbRd7iyT60YzJ3HevLo2eeeH9E7/AUQ+9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T20:42:31.408080Z"},"content_sha256":"374c16807e3f6e37a674842f79bf3c2fc908b3f599a9382ebc0d7918a737ef4a","schema_version":"1.0","event_id":"sha256:374c16807e3f6e37a674842f79bf3c2fc908b3f599a9382ebc0d7918a737ef4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:32SITMRNPNEQJC23FICQ4SPAOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Permutations -- A geometric point of view","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Jacopo Borga","submitted_at":"2021-07-20T18:07:10Z","abstract_excerpt":"We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling limits for permutations; and Benjamini-Schramm limits, introduced by the author to define a notion of local limits for permutations. The models of random permutations that we consider are mainly constrained models, that is, uniform permutations belonging to a given subset of the set of all permutations. We often identify this subset using pattern-avoidance, fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.09699","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/2107.09699/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":"2026-07-05T02:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Iyd67ZJi5oNwtCkMKxxBjw8i59M0n0cahvpx1ELQSUriHuRthLoLEk6cpoNCBPiJs0fA4dhSWsTs6Pj8f5pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T20:42:31.408647Z"},"content_sha256":"85f6e7bc5ce08db1499a33e40b93ad4198ca62b505283e3662258062ad34b9c7","schema_version":"1.0","event_id":"sha256:85f6e7bc5ce08db1499a33e40b93ad4198ca62b505283e3662258062ad34b9c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32SITMRNPNEQJC23FICQ4SPAOH/bundle.json","state_url":"https://pith.science/pith/32SITMRNPNEQJC23FICQ4SPAOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32SITMRNPNEQJC23FICQ4SPAOH/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":"2026-08-22T20:42:31Z","links":{"resolver":"https://pith.science/pith/32SITMRNPNEQJC23FICQ4SPAOH","bundle":"https://pith.science/pith/32SITMRNPNEQJC23FICQ4SPAOH/bundle.json","state":"https://pith.science/pith/32SITMRNPNEQJC23FICQ4SPAOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32SITMRNPNEQJC23FICQ4SPAOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:32SITMRNPNEQJC23FICQ4SPAOH","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":"e2aff1d171f927c01f724b6c8809aadc011f6b78bd77c888f4812f4176e4243d","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-07-20T18:07:10Z","title_canon_sha256":"89b0dc14ae585a0c9257d506ebba99c44ac82e85aa7fa458fba4e0b658960bf5"},"schema_version":"1.0","source":{"id":"2107.09699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.09699","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"2107.09699v1","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.09699","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"32SITMRNPNEQ","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_16","alias_value":"32SITMRNPNEQJC23","created_at":"2026-07-05T02:59:38Z"},{"alias_kind":"pith_short_8","alias_value":"32SITMRN","created_at":"2026-07-05T02:59:38Z"}],"graph_snapshots":[{"event_id":"sha256:85f6e7bc5ce08db1499a33e40b93ad4198ca62b505283e3662258062ad34b9c7","target":"graph","created_at":"2026-07-05T02:59:38Z","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/2107.09699/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling limits for permutations; and Benjamini-Schramm limits, introduced by the author to define a notion of local limits for permutations. The models of random permutations that we consider are mainly constrained models, that is, uniform permutations belonging to a given subset of the set of all permutations. We often identify this subset using pattern-avoidance, fo","authors_text":"Jacopo Borga","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-07-20T18:07:10Z","title":"Random Permutations -- A geometric point of view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.09699","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":"sha256:374c16807e3f6e37a674842f79bf3c2fc908b3f599a9382ebc0d7918a737ef4a","target":"record","created_at":"2026-07-05T02:59:38Z","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":"e2aff1d171f927c01f724b6c8809aadc011f6b78bd77c888f4812f4176e4243d","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-07-20T18:07:10Z","title_canon_sha256":"89b0dc14ae585a0c9257d506ebba99c44ac82e85aa7fa458fba4e0b658960bf5"},"schema_version":"1.0","source":{"id":"2107.09699","kind":"arxiv","version":1}},"canonical_sha256":"dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be","first_computed_at":"2026-07-05T02:59:38.747817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:59:38.747817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RJ9/Gng43f4EPNk1zhIUUhiry1l1B2/eI1r1o241G3f/uALJeERvY/D/GVsMTy/rMc1OkMv1u/uRG2pFLIi8CA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:59:38.748311Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.09699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:374c16807e3f6e37a674842f79bf3c2fc908b3f599a9382ebc0d7918a737ef4a","sha256:85f6e7bc5ce08db1499a33e40b93ad4198ca62b505283e3662258062ad34b9c7"],"state_sha256":"e3021f3ecbd1fbb8d011b0af8da7cb7df9f7e9e0734300853621e1fd0f88fc97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+uFRv44x5smASH4JlloEf4NDVPZyMcWDfJK7EvRyXXr6TISdEkdqyuv6iUQRA8ISVj+qw5ZE94fdZRzXF2VDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T20:42:31.413483Z","bundle_sha256":"9c9c470da9bc0653638a9ed47fa7da2d3781838382dc89fb4a022a4508c8aba8"}}