{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7IX6UVEL4LRCB7E37UZRY4XBSX","short_pith_number":"pith:7IX6UVEL","canonical_record":{"source":{"id":"1609.06901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-22T10:30:26Z","cross_cats_sorted":[],"title_canon_sha256":"aea0aa7b349071920f6f82dc47b5ad8c0ea12ede7982394053f5f424c17a5e51","abstract_canon_sha256":"cd89412d1dc8606ad26f40b7402ba4e7e6496abbb7f1b9ba398f37c84be6e47d"},"schema_version":"1.0"},"canonical_sha256":"fa2fea548be2e220fc9bfd331c72e195f19b1c2460d16f323a95f39655220d10","source":{"kind":"arxiv","id":"1609.06901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06901","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06901v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06901","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"7IX6UVEL4LRC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IX6UVEL4LRCB7E3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IX6UVEL","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7IX6UVEL4LRCB7E37UZRY4XBSX","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-22T10:30:26Z","cross_cats_sorted":[],"title_canon_sha256":"aea0aa7b349071920f6f82dc47b5ad8c0ea12ede7982394053f5f424c17a5e51","abstract_canon_sha256":"cd89412d1dc8606ad26f40b7402ba4e7e6496abbb7f1b9ba398f37c84be6e47d"},"schema_version":"1.0"},"canonical_sha256":"fa2fea548be2e220fc9bfd331c72e195f19b1c2460d16f323a95f39655220d10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:04.855641Z","signature_b64":"SEM4iBfv4jIxgYcC84i4u65WMthTXZf888sgvTZi21clExxGysLe81dtVXkgjYoAAcMRlgR9IC3ETZXvwFK+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa2fea548be2e220fc9bfd331c72e195f19b1c2460d16f323a95f39655220d10","last_reissued_at":"2026-05-18T01:04:04.855108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:04.855108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06901","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7yigC954WCzumoBoOLYGWdyw9VDm4Pgq4WTkuXlrmjzLHWeMwpvZqqHKiKAWeIcK/fY/w77RfJmF/h0dXYirDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:43.814499Z"},"content_sha256":"36ca68f5cc22c361eb10ea7267d763b72fdad6b91a1bc3dfdf1a10616b5482eb","schema_version":"1.0","event_id":"sha256:36ca68f5cc22c361eb10ea7267d763b72fdad6b91a1bc3dfdf1a10616b5482eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7IX6UVEL4LRCB7E37UZRY4XBSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On growth of metabelian Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dilber Kocak","submitted_at":"2016-09-22T10:30:26Z","abstract_excerpt":"For any integer $d\\geq 1$ we construct examples of finitely presented algebras with intermediate growth of type $[e^{n^{d/(d+1)}}]$. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06901","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VRwdioI9UoHfBAQLc8ljuAqN3cPhYwSA8U7npb6fpLxQBNzFUdFMA+7aI9LRsrcJIsl74HNyLcDqrN+UcNksDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:43.815174Z"},"content_sha256":"3c8f361858dfde5a3f03426d11b0c17a7a3c7af5b292fc116f865da206598008","schema_version":"1.0","event_id":"sha256:3c8f361858dfde5a3f03426d11b0c17a7a3c7af5b292fc116f865da206598008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/bundle.json","state_url":"https://pith.science/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/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":"2026-06-22T21:55:43Z","links":{"resolver":"https://pith.science/pith/7IX6UVEL4LRCB7E37UZRY4XBSX","bundle":"https://pith.science/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/bundle.json","state":"https://pith.science/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IX6UVEL4LRCB7E37UZRY4XBSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7IX6UVEL4LRCB7E37UZRY4XBSX","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":"cd89412d1dc8606ad26f40b7402ba4e7e6496abbb7f1b9ba398f37c84be6e47d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-22T10:30:26Z","title_canon_sha256":"aea0aa7b349071920f6f82dc47b5ad8c0ea12ede7982394053f5f424c17a5e51"},"schema_version":"1.0","source":{"id":"1609.06901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06901","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06901v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06901","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"7IX6UVEL4LRC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IX6UVEL4LRCB7E3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IX6UVEL","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:3c8f361858dfde5a3f03426d11b0c17a7a3c7af5b292fc116f865da206598008","target":"graph","created_at":"2026-05-18T01:04:04Z","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":"For any integer $d\\geq 1$ we construct examples of finitely presented algebras with intermediate growth of type $[e^{n^{d/(d+1)}}]$. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.","authors_text":"Dilber Kocak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-22T10:30:26Z","title":"On growth of metabelian Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06901","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":"sha256:36ca68f5cc22c361eb10ea7267d763b72fdad6b91a1bc3dfdf1a10616b5482eb","target":"record","created_at":"2026-05-18T01:04:04Z","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":"cd89412d1dc8606ad26f40b7402ba4e7e6496abbb7f1b9ba398f37c84be6e47d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-22T10:30:26Z","title_canon_sha256":"aea0aa7b349071920f6f82dc47b5ad8c0ea12ede7982394053f5f424c17a5e51"},"schema_version":"1.0","source":{"id":"1609.06901","kind":"arxiv","version":1}},"canonical_sha256":"fa2fea548be2e220fc9bfd331c72e195f19b1c2460d16f323a95f39655220d10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2fea548be2e220fc9bfd331c72e195f19b1c2460d16f323a95f39655220d10","first_computed_at":"2026-05-18T01:04:04.855108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.855108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SEM4iBfv4jIxgYcC84i4u65WMthTXZf888sgvTZi21clExxGysLe81dtVXkgjYoAAcMRlgR9IC3ETZXvwFK+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.855641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ca68f5cc22c361eb10ea7267d763b72fdad6b91a1bc3dfdf1a10616b5482eb","sha256:3c8f361858dfde5a3f03426d11b0c17a7a3c7af5b292fc116f865da206598008"],"state_sha256":"55997818f3fc99b006094124064d44fcbe8da804722c70db3bb170f267ee93dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BjURJeDFsyR9ibMj6/fTD+kCCv8wzJcfui5wpI46zQmrafhLC3uDSYCtp880OdaP8ifZbYzCa46utZMcIw/ZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:55:43.819039Z","bundle_sha256":"e683f72d34ec650601836aab615b4cbe10705c6b14761ba4df9775195cb31aeb"}}