{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6FXAWAGXELOQWS3EBXRRDUT73L","short_pith_number":"pith:6FXAWAGX","canonical_record":{"source":{"id":"1108.4267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-22T10:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"7b1aa0e42098e1a4dcbe6874f992cb5ac3e03a221cb852c149036035ad168224","abstract_canon_sha256":"a7d1d724a9fe12e26023d67449786c456b490f2c5311e3feaa5ecb61876e7594"},"schema_version":"1.0"},"canonical_sha256":"f16e0b00d722dd0b4b640de311d27fdafc6955f3cbdfab136dd1cd6a92c89d6b","source":{"kind":"arxiv","id":"1108.4267","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4267","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4267v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4267","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"6FXAWAGXELOQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6FXAWAGXELOQWS3E","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6FXAWAGX","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6FXAWAGXELOQWS3EBXRRDUT73L","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-22T10:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"7b1aa0e42098e1a4dcbe6874f992cb5ac3e03a221cb852c149036035ad168224","abstract_canon_sha256":"a7d1d724a9fe12e26023d67449786c456b490f2c5311e3feaa5ecb61876e7594"},"schema_version":"1.0"},"canonical_sha256":"f16e0b00d722dd0b4b640de311d27fdafc6955f3cbdfab136dd1cd6a92c89d6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.597887Z","signature_b64":"3IZgqZpFz0aEBURKz1InuUwwsMgXcy10DKiU6Gks8oiSmO0FMdfyNrrLYi1WkvCmKa32iUy+K81AgF93iHFjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f16e0b00d722dd0b4b640de311d27fdafc6955f3cbdfab136dd1cd6a92c89d6b","last_reissued_at":"2026-05-18T01:11:55.597547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.597547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4267","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIoYaKTr3Y3pE7WBKH6yz5wqU5K+uGxmb3ZiKeUT2Fs+e2mZz8uvbmYono3Um0AMSyEDMmtbse2XcIF1pgCyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:48:45.547641Z"},"content_sha256":"f29b0d6d87a2ad70eff5203db69b9cd014c48c5e5cb73604cd71c24b8cf1165a","schema_version":"1.0","event_id":"sha256:f29b0d6d87a2ad70eff5203db69b9cd014c48c5e5cb73604cd71c24b8cf1165a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6FXAWAGXELOQWS3EBXRRDUT73L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Images of Golod-Shafarevich algebras with small growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Agata Smoktunowicz, Laurent Bartholdi","submitted_at":"2011-08-22T10:13:53Z","abstract_excerpt":"We show that Golod-Shafarevich algebras can be homomorphically mapped onto infinite-dimensional algebras with polynomial growth, under mild assumptions of the number of relations of given degrees.\n  In case these algebras are finitely presented, we show they can be mapped onto an infinite dimensional algebras with quadratic growth. This answers a guestion by Zelmanov.\n  We then show, by an elementary construction, that any sufficiently regular function at least $n^{\\log n}$ may occur as the growth of an algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4267","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vytZHA7YK8ttz7XasGPSP2W/9d0ok+JudPAQEU2T+rVr3bgumqimmJFGJQTPoN6jb57qqOvAaLm4JiaFB/p0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:48:45.548354Z"},"content_sha256":"9d068449cbf58137bb00535ddb53bfb3cd8ce8f11f86371bf312d00eb2593b5b","schema_version":"1.0","event_id":"sha256:9d068449cbf58137bb00535ddb53bfb3cd8ce8f11f86371bf312d00eb2593b5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FXAWAGXELOQWS3EBXRRDUT73L/bundle.json","state_url":"https://pith.science/pith/6FXAWAGXELOQWS3EBXRRDUT73L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FXAWAGXELOQWS3EBXRRDUT73L/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":"2026-05-27T06:48:45Z","links":{"resolver":"https://pith.science/pith/6FXAWAGXELOQWS3EBXRRDUT73L","bundle":"https://pith.science/pith/6FXAWAGXELOQWS3EBXRRDUT73L/bundle.json","state":"https://pith.science/pith/6FXAWAGXELOQWS3EBXRRDUT73L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FXAWAGXELOQWS3EBXRRDUT73L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6FXAWAGXELOQWS3EBXRRDUT73L","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":"a7d1d724a9fe12e26023d67449786c456b490f2c5311e3feaa5ecb61876e7594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-22T10:13:53Z","title_canon_sha256":"7b1aa0e42098e1a4dcbe6874f992cb5ac3e03a221cb852c149036035ad168224"},"schema_version":"1.0","source":{"id":"1108.4267","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4267","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4267v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4267","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"6FXAWAGXELOQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6FXAWAGXELOQWS3E","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6FXAWAGX","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:9d068449cbf58137bb00535ddb53bfb3cd8ce8f11f86371bf312d00eb2593b5b","target":"graph","created_at":"2026-05-18T01:11:55Z","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"},"paper":{"abstract_excerpt":"We show that Golod-Shafarevich algebras can be homomorphically mapped onto infinite-dimensional algebras with polynomial growth, under mild assumptions of the number of relations of given degrees.\n  In case these algebras are finitely presented, we show they can be mapped onto an infinite dimensional algebras with quadratic growth. This answers a guestion by Zelmanov.\n  We then show, by an elementary construction, that any sufficiently regular function at least $n^{\\log n}$ may occur as the growth of an algebra.","authors_text":"Agata Smoktunowicz, Laurent Bartholdi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-22T10:13:53Z","title":"Images of Golod-Shafarevich algebras with small growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4267","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:f29b0d6d87a2ad70eff5203db69b9cd014c48c5e5cb73604cd71c24b8cf1165a","target":"record","created_at":"2026-05-18T01:11:55Z","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":"a7d1d724a9fe12e26023d67449786c456b490f2c5311e3feaa5ecb61876e7594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-22T10:13:53Z","title_canon_sha256":"7b1aa0e42098e1a4dcbe6874f992cb5ac3e03a221cb852c149036035ad168224"},"schema_version":"1.0","source":{"id":"1108.4267","kind":"arxiv","version":2}},"canonical_sha256":"f16e0b00d722dd0b4b640de311d27fdafc6955f3cbdfab136dd1cd6a92c89d6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f16e0b00d722dd0b4b640de311d27fdafc6955f3cbdfab136dd1cd6a92c89d6b","first_computed_at":"2026-05-18T01:11:55.597547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.597547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3IZgqZpFz0aEBURKz1InuUwwsMgXcy10DKiU6Gks8oiSmO0FMdfyNrrLYi1WkvCmKa32iUy+K81AgF93iHFjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.597887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4267","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29b0d6d87a2ad70eff5203db69b9cd014c48c5e5cb73604cd71c24b8cf1165a","sha256:9d068449cbf58137bb00535ddb53bfb3cd8ce8f11f86371bf312d00eb2593b5b"],"state_sha256":"4293e62ed3cd46ec23efc7408febaf90319808b91031f81bcb8cd33dfc6af0c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWkwEvXLXTwqweUpd2Rd5n4t6yY6Nt0SLnoc8E9YyTNxUFVX+LousZgG0+qUFd2SusiZ75MBwnXr9rJmIoSMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:48:45.552378Z","bundle_sha256":"881581c9c4975399b56d518bbf2ed2656b8794f916118b449dfc8832641e969a"}}