{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7BUH7CZ2QCCW7JLPPIUEFIIAUU","short_pith_number":"pith:7BUH7CZ2","canonical_record":{"source":{"id":"1408.6669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-28T10:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"e662003057cb77a227a9bf66bd122201b511d73c8e42fdd21cc536b618938395","abstract_canon_sha256":"cb284c6672dd773e3e71ae3d24407222d9c957f085e15256ae497ed455206cda"},"schema_version":"1.0"},"canonical_sha256":"f8687f8b3a80856fa56f7a2842a100a53a362ca59bb370db0bf10d0753c57561","source":{"kind":"arxiv","id":"1408.6669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6669","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6669v1","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6669","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"7BUH7CZ2QCCW","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7BUH7CZ2QCCW7JLP","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7BUH7CZ2","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7BUH7CZ2QCCW7JLPPIUEFIIAUU","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-28T10:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"e662003057cb77a227a9bf66bd122201b511d73c8e42fdd21cc536b618938395","abstract_canon_sha256":"cb284c6672dd773e3e71ae3d24407222d9c957f085e15256ae497ed455206cda"},"schema_version":"1.0"},"canonical_sha256":"f8687f8b3a80856fa56f7a2842a100a53a362ca59bb370db0bf10d0753c57561","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:01.109493Z","signature_b64":"f7UUSy89gitS6/yDkSlkjarMo8SXU7tOUOIynhFbxaK3COSrctoiymNfQGEmUrV0y4/oPANbIpdP+Diljq0YBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8687f8b3a80856fa56f7a2842a100a53a362ca59bb370db0bf10d0753c57561","last_reissued_at":"2026-05-18T02:44:01.108841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:01.108841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6669","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":"2026-05-18T02:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZUt+bxfppBHmPPX1JmHms+5a86j7lLHv/wlplhDghtoR9NAkXLYrXNx/OA/TfdS1L6lEKO5MKFhTQv67SyvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:21:56.571247Z"},"content_sha256":"d4ab5dce8af781016cb904878976fcedf4202327ee0d39f15729d17909234e1e","schema_version":"1.0","event_id":"sha256:d4ab5dce8af781016cb904878976fcedf4202327ee0d39f15729d17909234e1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7BUH7CZ2QCCW7JLPPIUEFIIAUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nilpotent group without local functional equations for pro-isomorphic subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Mark N. Berman","submitted_at":"2014-08-28T10:21:07Z","abstract_excerpt":"The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the rational primes. We manufacture the first example of a torsion-free finitely generated nilpotent group G such that the local Euler factors of its pro-isomorphic zeta function do not satisfy functional equations. The group G has nilpotency class 4 and Hirsch length 25. It is obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6669","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":"2026-05-18T02:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck/YB3GldE5rihW9fhRkgTSWdLbDCLFh5LNMNah7K/1gsIQ4xA+WpeQMc489p1ZJGELeAKKoHRaqvkGlDrDdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:21:56.571611Z"},"content_sha256":"bba35620967325cc8c226c319087da70320a877278c9eb40817cee02aeb2d2d0","schema_version":"1.0","event_id":"sha256:bba35620967325cc8c226c319087da70320a877278c9eb40817cee02aeb2d2d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/bundle.json","state_url":"https://pith.science/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/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":"2026-06-23T02:21:56Z","links":{"resolver":"https://pith.science/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU","bundle":"https://pith.science/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/bundle.json","state":"https://pith.science/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BUH7CZ2QCCW7JLPPIUEFIIAUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7BUH7CZ2QCCW7JLPPIUEFIIAUU","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":"cb284c6672dd773e3e71ae3d24407222d9c957f085e15256ae497ed455206cda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-28T10:21:07Z","title_canon_sha256":"e662003057cb77a227a9bf66bd122201b511d73c8e42fdd21cc536b618938395"},"schema_version":"1.0","source":{"id":"1408.6669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6669","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6669v1","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6669","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"7BUH7CZ2QCCW","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7BUH7CZ2QCCW7JLP","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7BUH7CZ2","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:bba35620967325cc8c226c319087da70320a877278c9eb40817cee02aeb2d2d0","target":"graph","created_at":"2026-05-18T02:44:01Z","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":"The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the rational primes. We manufacture the first example of a torsion-free finitely generated nilpotent group G such that the local Euler factors of its pro-isomorphic zeta function do not satisfy functional equations. The group G has nilpotency class 4 and Hirsch length 25. It is obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable algebra","authors_text":"Benjamin Klopsch, Mark N. Berman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-28T10:21:07Z","title":"A nilpotent group without local functional equations for pro-isomorphic subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6669","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:d4ab5dce8af781016cb904878976fcedf4202327ee0d39f15729d17909234e1e","target":"record","created_at":"2026-05-18T02:44:01Z","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":"cb284c6672dd773e3e71ae3d24407222d9c957f085e15256ae497ed455206cda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-28T10:21:07Z","title_canon_sha256":"e662003057cb77a227a9bf66bd122201b511d73c8e42fdd21cc536b618938395"},"schema_version":"1.0","source":{"id":"1408.6669","kind":"arxiv","version":1}},"canonical_sha256":"f8687f8b3a80856fa56f7a2842a100a53a362ca59bb370db0bf10d0753c57561","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8687f8b3a80856fa56f7a2842a100a53a362ca59bb370db0bf10d0753c57561","first_computed_at":"2026-05-18T02:44:01.108841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:01.108841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f7UUSy89gitS6/yDkSlkjarMo8SXU7tOUOIynhFbxaK3COSrctoiymNfQGEmUrV0y4/oPANbIpdP+Diljq0YBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:01.109493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4ab5dce8af781016cb904878976fcedf4202327ee0d39f15729d17909234e1e","sha256:bba35620967325cc8c226c319087da70320a877278c9eb40817cee02aeb2d2d0"],"state_sha256":"dce81bbf514e90a6640bb56a44250fc33c6ca15883d964b0144dcadd8d8790cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IY3PViRiP8c1jwb8nDiI0QMBbrCf6lPnLmwKpE5oWQKgkOB2ovNF5HF1l0g4+bCyjfHwgq2tqbaErzQZ2rapDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:21:56.573584Z","bundle_sha256":"ec590dd36324c05b29ef51eec379def37b6b8d6af862f893192762314e45fd57"}}