{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EFJ37GY3WZ3YJVLIHNX4EHPN5Q","short_pith_number":"pith:EFJ37GY3","canonical_record":{"source":{"id":"1103.5151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-26T19:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"79481ebdf5325d670fba40bf24d1f462de039463f991836e26823512bc257b45","abstract_canon_sha256":"57ca0ee5461af69a2773016492d4f1e4b5f10cc422a052171e11d383a3d6e648"},"schema_version":"1.0"},"canonical_sha256":"2153bf9b1bb67784d5683b6fc21dedec2b8caa16b06848b8dbfe763d9ed4f6be","source":{"kind":"arxiv","id":"1103.5151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5151","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5151v1","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5151","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"EFJ37GY3WZ3Y","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFJ37GY3WZ3YJVLI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFJ37GY3","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EFJ37GY3WZ3YJVLIHNX4EHPN5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-26T19:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"79481ebdf5325d670fba40bf24d1f462de039463f991836e26823512bc257b45","abstract_canon_sha256":"57ca0ee5461af69a2773016492d4f1e4b5f10cc422a052171e11d383a3d6e648"},"schema_version":"1.0"},"canonical_sha256":"2153bf9b1bb67784d5683b6fc21dedec2b8caa16b06848b8dbfe763d9ed4f6be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:38.544009Z","signature_b64":"cJ42dgfKyFLe7TALVl9kBracgC/n6EwmmydAbnlhIZFKpUeGK3J646k1io40hqubA7QC9iRpOIqTui9aUhkzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2153bf9b1bb67784d5683b6fc21dedec2b8caa16b06848b8dbfe763d9ed4f6be","last_reissued_at":"2026-05-18T04:25:38.543583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:38.543583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5151","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":"2026-05-18T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ziiSUnmSTlEyqyE4zTLPtXDWROfzZX3pfG/8WyXzHg3ScZBG2a18vnbeHmugXpitqDuQp5OMJY4bbi4APF/wAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:59:08.393778Z"},"content_sha256":"afe357b5689f129fa8b9dfeb498aba17eb4febdd7a671d8e3785c3d087473ea3","schema_version":"1.0","event_id":"sha256:afe357b5689f129fa8b9dfeb498aba17eb4febdd7a671d8e3785c3d087473ea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EFJ37GY3WZ3YJVLIHNX4EHPN5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Baer Invariants of Free Nilpotent Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Behrooz Mashayekhy, Mohsen Parvizi","submitted_at":"2011-03-26T19:50:44Z","abstract_excerpt":"We present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\\textbf{Z}\\st{n}* \\textbf{Z}\\st{n}*...\\st{n}*\\textbf{Z}$) with respect to the variety ${\\cal V}$ with the set of words $V=\\{[\\ga_{c_1+1},\\ga_{c_2+1}]\\}$, for all $c_1\\geq c_2$ and $2c_2-c_1>2n-2$. Also, an explicit formula for the polynilpotent multiplier of a free $n$th nilpotent group is given for any class row $(c_1,c_2,...,c_t)$, where $c_1\\geq n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5151","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":"2026-05-18T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tKpGR/JcorsyrGANADQ8nJuhTwOi4eknNuN4kBLU6szjsqUUuQCOJWdGr4whkPNjyjIsLpOa62tABISOpjtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:59:08.394140Z"},"content_sha256":"de08e3af2323f665b57f99ca373d7dc44178e44c5587dde3447a5d1f5d7c4310","schema_version":"1.0","event_id":"sha256:de08e3af2323f665b57f99ca373d7dc44178e44c5587dde3447a5d1f5d7c4310"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/bundle.json","state_url":"https://pith.science/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/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":"2026-06-11T12:59:08Z","links":{"resolver":"https://pith.science/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q","bundle":"https://pith.science/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/bundle.json","state":"https://pith.science/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFJ37GY3WZ3YJVLIHNX4EHPN5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EFJ37GY3WZ3YJVLIHNX4EHPN5Q","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":"57ca0ee5461af69a2773016492d4f1e4b5f10cc422a052171e11d383a3d6e648","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-26T19:50:44Z","title_canon_sha256":"79481ebdf5325d670fba40bf24d1f462de039463f991836e26823512bc257b45"},"schema_version":"1.0","source":{"id":"1103.5151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5151","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5151v1","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5151","created_at":"2026-05-18T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"EFJ37GY3WZ3Y","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EFJ37GY3WZ3YJVLI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EFJ37GY3","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:de08e3af2323f665b57f99ca373d7dc44178e44c5587dde3447a5d1f5d7c4310","target":"graph","created_at":"2026-05-18T04:25:38Z","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 present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\\textbf{Z}\\st{n}* \\textbf{Z}\\st{n}*...\\st{n}*\\textbf{Z}$) with respect to the variety ${\\cal V}$ with the set of words $V=\\{[\\ga_{c_1+1},\\ga_{c_2+1}]\\}$, for all $c_1\\geq c_2$ and $2c_2-c_1>2n-2$. Also, an explicit formula for the polynilpotent multiplier of a free $n$th nilpotent group is given for any class row $(c_1,c_2,...,c_t)$, where $c_1\\geq n$.","authors_text":"Behrooz Mashayekhy, Mohsen Parvizi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-26T19:50:44Z","title":"Some Baer Invariants of Free Nilpotent Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5151","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:afe357b5689f129fa8b9dfeb498aba17eb4febdd7a671d8e3785c3d087473ea3","target":"record","created_at":"2026-05-18T04:25:38Z","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":"57ca0ee5461af69a2773016492d4f1e4b5f10cc422a052171e11d383a3d6e648","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-26T19:50:44Z","title_canon_sha256":"79481ebdf5325d670fba40bf24d1f462de039463f991836e26823512bc257b45"},"schema_version":"1.0","source":{"id":"1103.5151","kind":"arxiv","version":1}},"canonical_sha256":"2153bf9b1bb67784d5683b6fc21dedec2b8caa16b06848b8dbfe763d9ed4f6be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2153bf9b1bb67784d5683b6fc21dedec2b8caa16b06848b8dbfe763d9ed4f6be","first_computed_at":"2026-05-18T04:25:38.543583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:38.543583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJ42dgfKyFLe7TALVl9kBracgC/n6EwmmydAbnlhIZFKpUeGK3J646k1io40hqubA7QC9iRpOIqTui9aUhkzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:38.544009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afe357b5689f129fa8b9dfeb498aba17eb4febdd7a671d8e3785c3d087473ea3","sha256:de08e3af2323f665b57f99ca373d7dc44178e44c5587dde3447a5d1f5d7c4310"],"state_sha256":"cf1994004e1c8ba924ef187f8b14ecd8a0991b50866948f9e607310fdadc33d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fb9x8hyQsGWheYLIEff9ga8w3UtWNYGCX5Ew5M+58vV3SQgGfTKrodBRD6OJ1/M89/yynERCWvRnt+BDigcqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:59:08.396168Z","bundle_sha256":"59fe8ecf4f2031e8758d631913ead8b56d1ca4ef0ba9bc0602034415e1bd7deb"}}