{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KORR4U3SHCNIPW32SQX56JWSG7","short_pith_number":"pith:KORR4U3S","canonical_record":{"source":{"id":"1002.0015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-29T21:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"dbe0476774878dcd54fa50535055fb273a0568729f9bc2de85d1ccdb73b66d7c","abstract_canon_sha256":"6528a949c87b5cc98f71d75bb07548cc417b00aa2df044fe311cd82b4e170da7"},"schema_version":"1.0"},"canonical_sha256":"53a31e5372389a87db7a942fdf26d237ec7f9ededabd6148b67bc6b3df01819a","source":{"kind":"arxiv","id":"1002.0015","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0015","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0015v2","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0015","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"KORR4U3SHCNI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KORR4U3SHCNIPW32","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KORR4U3S","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KORR4U3SHCNIPW32SQX56JWSG7","target":"record","payload":{"canonical_record":{"source":{"id":"1002.0015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-29T21:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"dbe0476774878dcd54fa50535055fb273a0568729f9bc2de85d1ccdb73b66d7c","abstract_canon_sha256":"6528a949c87b5cc98f71d75bb07548cc417b00aa2df044fe311cd82b4e170da7"},"schema_version":"1.0"},"canonical_sha256":"53a31e5372389a87db7a942fdf26d237ec7f9ededabd6148b67bc6b3df01819a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:30.064696Z","signature_b64":"Owlm/yTya4SimbTL7RsA5IGuxiP04/PmveJNv8Qerlf9wD5FvGzmUBPW7OGbzIgTjrFzGpjT/Sktsiv7/XxCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53a31e5372389a87db7a942fdf26d237ec7f9ededabd6148b67bc6b3df01819a","last_reissued_at":"2026-05-18T04:21:30.064214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:30.064214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.0015","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":"2026-05-18T04:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"67k8SUIwB0U201jSC/2d4y7ndMhFnyuAuNQJYXncCZkkDeN/+V6iPJUC7YcpI4CxZFHD7nsOoOvQ+EUyMsN3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:54:44.405603Z"},"content_sha256":"28fb721918b6a728184009f27eb52e867406854bc2179bd0b26a6ea96d501caf","schema_version":"1.0","event_id":"sha256:28fb721918b6a728184009f27eb52e867406854bc2179bd0b26a6ea96d501caf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KORR4U3SHCNIPW32SQX56JWSG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Filtrations and Distortion in Infinite-Dimensional Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexander Olshanskii, Yuri Bahturin","submitted_at":"2010-01-29T21:37:55Z","abstract_excerpt":"A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The notion of tame filtration is useful in the study of possible distortion of degrees of elements when one algebra is embedded as a subalgebra in another. A geometric analogue is the distortion of the (Riemannian) metric of a (Lie) subgroup when compared to the metric induced from the ambient (Lie) group. The distortion of a subalgebra in an algebra also refle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0015","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":"2026-05-18T04:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0e6wA5JJCDcy9nm/uCO59b1rZ47lx/MYEdEm1UpM8wZ6+xtxd93ul6Gb4w57tX0qQTcRGJ05GqbBhyG/BYC5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:54:44.405948Z"},"content_sha256":"8f1e9dac3ddddc60c8d0765508401d895e30d7e34db91ad38703e8a25019101a","schema_version":"1.0","event_id":"sha256:8f1e9dac3ddddc60c8d0765508401d895e30d7e34db91ad38703e8a25019101a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KORR4U3SHCNIPW32SQX56JWSG7/bundle.json","state_url":"https://pith.science/pith/KORR4U3SHCNIPW32SQX56JWSG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KORR4U3SHCNIPW32SQX56JWSG7/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":"2026-06-03T05:54:44Z","links":{"resolver":"https://pith.science/pith/KORR4U3SHCNIPW32SQX56JWSG7","bundle":"https://pith.science/pith/KORR4U3SHCNIPW32SQX56JWSG7/bundle.json","state":"https://pith.science/pith/KORR4U3SHCNIPW32SQX56JWSG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KORR4U3SHCNIPW32SQX56JWSG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KORR4U3SHCNIPW32SQX56JWSG7","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":"6528a949c87b5cc98f71d75bb07548cc417b00aa2df044fe311cd82b4e170da7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-29T21:37:55Z","title_canon_sha256":"dbe0476774878dcd54fa50535055fb273a0568729f9bc2de85d1ccdb73b66d7c"},"schema_version":"1.0","source":{"id":"1002.0015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0015","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0015v2","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0015","created_at":"2026-05-18T04:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"KORR4U3SHCNI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KORR4U3SHCNIPW32","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KORR4U3S","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:8f1e9dac3ddddc60c8d0765508401d895e30d7e34db91ad38703e8a25019101a","target":"graph","created_at":"2026-05-18T04:21:30Z","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":"A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The notion of tame filtration is useful in the study of possible distortion of degrees of elements when one algebra is embedded as a subalgebra in another. A geometric analogue is the distortion of the (Riemannian) metric of a (Lie) subgroup when compared to the metric induced from the ambient (Lie) group. The distortion of a subalgebra in an algebra also refle","authors_text":"Alexander Olshanskii, Yuri Bahturin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-29T21:37:55Z","title":"Filtrations and Distortion in Infinite-Dimensional Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0015","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":"sha256:28fb721918b6a728184009f27eb52e867406854bc2179bd0b26a6ea96d501caf","target":"record","created_at":"2026-05-18T04:21:30Z","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":"6528a949c87b5cc98f71d75bb07548cc417b00aa2df044fe311cd82b4e170da7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-29T21:37:55Z","title_canon_sha256":"dbe0476774878dcd54fa50535055fb273a0568729f9bc2de85d1ccdb73b66d7c"},"schema_version":"1.0","source":{"id":"1002.0015","kind":"arxiv","version":2}},"canonical_sha256":"53a31e5372389a87db7a942fdf26d237ec7f9ededabd6148b67bc6b3df01819a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53a31e5372389a87db7a942fdf26d237ec7f9ededabd6148b67bc6b3df01819a","first_computed_at":"2026-05-18T04:21:30.064214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:30.064214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Owlm/yTya4SimbTL7RsA5IGuxiP04/PmveJNv8Qerlf9wD5FvGzmUBPW7OGbzIgTjrFzGpjT/Sktsiv7/XxCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:30.064696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28fb721918b6a728184009f27eb52e867406854bc2179bd0b26a6ea96d501caf","sha256:8f1e9dac3ddddc60c8d0765508401d895e30d7e34db91ad38703e8a25019101a"],"state_sha256":"8289422433541600ff967911ca0c9a2aad5240adcea4834ba03519aab7ea4973"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYFvEVRTxJY7Cx/cVeFZdavxdBICcVG0cabp0MymHkXpvOQQFKmVwJGceIbwsVTu1DubA5YjGUXHFQB/zzXVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:54:44.407876Z","bundle_sha256":"ba9435fe02f78895ddc613d2eca2e6975db5e71ceaf73ffed8c77c746c197089"}}