{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EPODYQ76RC5QGFPB2KT65FWQTU","short_pith_number":"pith:EPODYQ76","canonical_record":{"source":{"id":"1304.5320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T06:38:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4577f2296d3239b77d2ed5262dec4d2f94686631df4c3ef26517ecedc64d9901","abstract_canon_sha256":"5cbcf270f080f339f77b5421d185f674e2ed620ef5e671dbbb4553484c456e63"},"schema_version":"1.0"},"canonical_sha256":"23dc3c43fe88bb0315e1d2a7ee96d09d1d47a8973d1556b72211523317db789c","source":{"kind":"arxiv","id":"1304.5320","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5320","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5320v2","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5320","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"EPODYQ76RC5Q","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EPODYQ76RC5QGFPB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EPODYQ76","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EPODYQ76RC5QGFPB2KT65FWQTU","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T06:38:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4577f2296d3239b77d2ed5262dec4d2f94686631df4c3ef26517ecedc64d9901","abstract_canon_sha256":"5cbcf270f080f339f77b5421d185f674e2ed620ef5e671dbbb4553484c456e63"},"schema_version":"1.0"},"canonical_sha256":"23dc3c43fe88bb0315e1d2a7ee96d09d1d47a8973d1556b72211523317db789c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.678278Z","signature_b64":"wIkkxvv2BcsJHOBx2ZNl5Rgicq37pUaq9C5UEbK6WAQXs31D8Co/wiSIPrrfkaSa+1n4Uu7CUGFAR7YFXMDRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23dc3c43fe88bb0315e1d2a7ee96d09d1d47a8973d1556b72211523317db789c","last_reissued_at":"2026-05-18T02:46:04.677666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.677666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5320","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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Yxoa6qHWR/5js71BG6MXCefpkm8MLLqa01zOhLyEbo5Ivav9AYPVpb4E+6b9NxGoj/359l6j9aVFoqGYk73AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:33:03.755049Z"},"content_sha256":"c7e34c4bc95aaa5c2add0d246dfa0b46189830cbfa83b31149dc157c49a2007a","schema_version":"1.0","event_id":"sha256:c7e34c4bc95aaa5c2add0d246dfa0b46189830cbfa83b31149dc157c49a2007a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EPODYQ76RC5QGFPB2KT65FWQTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Growth in product replacement graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Anton Malyshev, Igor Pak","submitted_at":"2013-04-19T06:38:40Z","abstract_excerpt":"We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5320","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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k6mQ08EoAnNq4Vdphi0nWoCINxEiMHkcUJ6DGDGi+Owx0Z1yi20WpPuuyaeGEN2JvauByssl+YPgnRaqKL0RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:33:03.755702Z"},"content_sha256":"789a771f239b23902b40b76cb3b49bcd6b0c7fbc35adebcce1621a92b34c519f","schema_version":"1.0","event_id":"sha256:789a771f239b23902b40b76cb3b49bcd6b0c7fbc35adebcce1621a92b34c519f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPODYQ76RC5QGFPB2KT65FWQTU/bundle.json","state_url":"https://pith.science/pith/EPODYQ76RC5QGFPB2KT65FWQTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPODYQ76RC5QGFPB2KT65FWQTU/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":"2026-05-31T10:33:03Z","links":{"resolver":"https://pith.science/pith/EPODYQ76RC5QGFPB2KT65FWQTU","bundle":"https://pith.science/pith/EPODYQ76RC5QGFPB2KT65FWQTU/bundle.json","state":"https://pith.science/pith/EPODYQ76RC5QGFPB2KT65FWQTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPODYQ76RC5QGFPB2KT65FWQTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EPODYQ76RC5QGFPB2KT65FWQTU","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":"5cbcf270f080f339f77b5421d185f674e2ed620ef5e671dbbb4553484c456e63","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T06:38:40Z","title_canon_sha256":"4577f2296d3239b77d2ed5262dec4d2f94686631df4c3ef26517ecedc64d9901"},"schema_version":"1.0","source":{"id":"1304.5320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5320","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5320v2","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5320","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"EPODYQ76RC5Q","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EPODYQ76RC5QGFPB","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EPODYQ76","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:789a771f239b23902b40b76cb3b49bcd6b0c7fbc35adebcce1621a92b34c519f","target":"graph","created_at":"2026-05-18T02:46:04Z","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 prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.","authors_text":"Anton Malyshev, Igor Pak","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T06:38:40Z","title":"Growth in product replacement graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5320","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:c7e34c4bc95aaa5c2add0d246dfa0b46189830cbfa83b31149dc157c49a2007a","target":"record","created_at":"2026-05-18T02:46:04Z","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":"5cbcf270f080f339f77b5421d185f674e2ed620ef5e671dbbb4553484c456e63","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T06:38:40Z","title_canon_sha256":"4577f2296d3239b77d2ed5262dec4d2f94686631df4c3ef26517ecedc64d9901"},"schema_version":"1.0","source":{"id":"1304.5320","kind":"arxiv","version":2}},"canonical_sha256":"23dc3c43fe88bb0315e1d2a7ee96d09d1d47a8973d1556b72211523317db789c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23dc3c43fe88bb0315e1d2a7ee96d09d1d47a8973d1556b72211523317db789c","first_computed_at":"2026-05-18T02:46:04.677666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:04.677666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wIkkxvv2BcsJHOBx2ZNl5Rgicq37pUaq9C5UEbK6WAQXs31D8Co/wiSIPrrfkaSa+1n4Uu7CUGFAR7YFXMDRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:04.678278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7e34c4bc95aaa5c2add0d246dfa0b46189830cbfa83b31149dc157c49a2007a","sha256:789a771f239b23902b40b76cb3b49bcd6b0c7fbc35adebcce1621a92b34c519f"],"state_sha256":"59cbb00305505a806471b06d8962ffe0eeac8ce159d4fe2c938ae1a133311dbd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUPavysoqehcYFwyCDndGVmld6pRaZ4GMO01bV0bJ5GsEtYxT+x3fE6CjExVybS/6Nd9NP2RhDhRiE0O25UuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:33:03.758849Z","bundle_sha256":"88e567a0778f8de9d1b19c3fca2d02934f98e2d637d7da966db325fa8c7faeff"}}