{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U7EWNGLH4Y2XO3ZMRTBT6WMP3V","short_pith_number":"pith:U7EWNGLH","canonical_record":{"source":{"id":"1802.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-23T04:56:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"aeaad8c9355cf5bab21c5852b75768965a94b65f6ef1b68892b36996fbe93307","abstract_canon_sha256":"36aa9fcaa6e40d2da0af690464e87fc0ff402470d79467dc27af04c12593412e"},"schema_version":"1.0"},"canonical_sha256":"a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210","source":{"kind":"arxiv","id":"1802.08387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08387","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08387v1","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08387","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"pith_short_12","alias_value":"U7EWNGLH4Y2X","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U7EWNGLH4Y2XO3ZM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U7EWNGLH","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U7EWNGLH4Y2XO3ZMRTBT6WMP3V","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-23T04:56:55Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"aeaad8c9355cf5bab21c5852b75768965a94b65f6ef1b68892b36996fbe93307","abstract_canon_sha256":"36aa9fcaa6e40d2da0af690464e87fc0ff402470d79467dc27af04c12593412e"},"schema_version":"1.0"},"canonical_sha256":"a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:43.848626Z","signature_b64":"Uv3JU9ZNUZLY9IAziZUFGMtofrdPKIblbC8BkDGFjrEhU6858jYBFIb/qRKAfuP5TyN7WS8Wa+6g6l1ydxbBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210","last_reissued_at":"2026-05-18T00:22:43.848227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:43.848227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08387","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":"2026-05-18T00:22:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9FECdOOUz45b06vZ7l2Hep1HkOX39jNqb3KezhRXFCIM0hrwjjGCTSUfT20vdYA1hsV7Wj5lkay8cq4eGyZMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:47:56.383056Z"},"content_sha256":"82d21262413fe9b1499a4a86483002efd6d78980113116a7e50b4e03b5e1bf73","schema_version":"1.0","event_id":"sha256:82d21262413fe9b1499a4a86483002efd6d78980113116a7e50b4e03b5e1bf73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U7EWNGLH4Y2XO3ZMRTBT6WMP3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rigidity of rank gradient in a group of intermediate growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Rostislav Grigorchuk, Rostyslav Kravchenko","submitted_at":"2018-02-23T04:56:55Z","abstract_excerpt":"We introduce and investigate the rigidity property of rank gradient in the case of the group $\\mathcal G$ of intermediate growth constructed by the first author. We show that $\\mathcal G$ is normally $(f,g)$-RG rigid where $f(n)=\\log(n)$ and $g(n) =\\log(\\log(n)).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08387","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":"2026-05-18T00:22:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3qY7nKfKxKkWSgypZBto9oPeWYoNvNwx4aiIfjMHu82Kz70B7Mht+bcZu/Ltlz+yCJ/bI3qOtDNEZOT9SEIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:47:56.383698Z"},"content_sha256":"ab37b5bc204c6cee2a3f56cc6048b5fe8702f698287e00d751856ecb9d59da6b","schema_version":"1.0","event_id":"sha256:ab37b5bc204c6cee2a3f56cc6048b5fe8702f698287e00d751856ecb9d59da6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/bundle.json","state_url":"https://pith.science/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/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":"2026-06-09T03:47:56Z","links":{"resolver":"https://pith.science/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V","bundle":"https://pith.science/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/bundle.json","state":"https://pith.science/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7EWNGLH4Y2XO3ZMRTBT6WMP3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U7EWNGLH4Y2XO3ZMRTBT6WMP3V","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":"36aa9fcaa6e40d2da0af690464e87fc0ff402470d79467dc27af04c12593412e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-23T04:56:55Z","title_canon_sha256":"aeaad8c9355cf5bab21c5852b75768965a94b65f6ef1b68892b36996fbe93307"},"schema_version":"1.0","source":{"id":"1802.08387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08387","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08387v1","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08387","created_at":"2026-05-18T00:22:43Z"},{"alias_kind":"pith_short_12","alias_value":"U7EWNGLH4Y2X","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U7EWNGLH4Y2XO3ZM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U7EWNGLH","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:ab37b5bc204c6cee2a3f56cc6048b5fe8702f698287e00d751856ecb9d59da6b","target":"graph","created_at":"2026-05-18T00:22:43Z","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 introduce and investigate the rigidity property of rank gradient in the case of the group $\\mathcal G$ of intermediate growth constructed by the first author. We show that $\\mathcal G$ is normally $(f,g)$-RG rigid where $f(n)=\\log(n)$ and $g(n) =\\log(\\log(n)).$","authors_text":"Rostislav Grigorchuk, Rostyslav Kravchenko","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-23T04:56:55Z","title":"On the rigidity of rank gradient in a group of intermediate growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08387","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":"sha256:82d21262413fe9b1499a4a86483002efd6d78980113116a7e50b4e03b5e1bf73","target":"record","created_at":"2026-05-18T00:22:43Z","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":"36aa9fcaa6e40d2da0af690464e87fc0ff402470d79467dc27af04c12593412e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-23T04:56:55Z","title_canon_sha256":"aeaad8c9355cf5bab21c5852b75768965a94b65f6ef1b68892b36996fbe93307"},"schema_version":"1.0","source":{"id":"1802.08387","kind":"arxiv","version":1}},"canonical_sha256":"a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210","first_computed_at":"2026-05-18T00:22:43.848227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:43.848227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uv3JU9ZNUZLY9IAziZUFGMtofrdPKIblbC8BkDGFjrEhU6858jYBFIb/qRKAfuP5TyN7WS8Wa+6g6l1ydxbBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:43.848626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82d21262413fe9b1499a4a86483002efd6d78980113116a7e50b4e03b5e1bf73","sha256:ab37b5bc204c6cee2a3f56cc6048b5fe8702f698287e00d751856ecb9d59da6b"],"state_sha256":"7e024fb31bbeb7471d0691cf8e4026db4074652395ae67f895c42539f865a6c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8K5fFZGrSqk/57EVNpNWKpMk/r/egyj71mFKMkIasMuWgK/4FONBOsIpEPyQvHbCBPhFW9Gmymq36TC6Q5RoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:47:56.386902Z","bundle_sha256":"bc37ae4c61a89ab481c7e3c17bb7eb85403d5f7a6e7629a75d5f514569f3d483"}}