{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CFEOD5HJ3FJRVQU2EVZ7REDRA6","short_pith_number":"pith:CFEOD5HJ","canonical_record":{"source":{"id":"1801.02932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-09T13:45:21Z","cross_cats_sorted":[],"title_canon_sha256":"6ee732a652c21bbc48fc7ef89f37a3751be2282f16e64e7cc317eaea9e28e468","abstract_canon_sha256":"cacd340b0a37161b6ebaf1615908d57a1f8f70b874b8b1b64b20c56513dbf662"},"schema_version":"1.0"},"canonical_sha256":"1148e1f4e9d9531ac29a2573f8907107b879477d9fbb99e5423bb762aa0fb549","source":{"kind":"arxiv","id":"1801.02932","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02932","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02932v2","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02932","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"CFEOD5HJ3FJR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFEOD5HJ3FJRVQU2","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFEOD5HJ","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CFEOD5HJ3FJRVQU2EVZ7REDRA6","target":"record","payload":{"canonical_record":{"source":{"id":"1801.02932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-09T13:45:21Z","cross_cats_sorted":[],"title_canon_sha256":"6ee732a652c21bbc48fc7ef89f37a3751be2282f16e64e7cc317eaea9e28e468","abstract_canon_sha256":"cacd340b0a37161b6ebaf1615908d57a1f8f70b874b8b1b64b20c56513dbf662"},"schema_version":"1.0"},"canonical_sha256":"1148e1f4e9d9531ac29a2573f8907107b879477d9fbb99e5423bb762aa0fb549","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:44.149070Z","signature_b64":"ouxZ7YPl/Z869UOlW29tZdexCfnsISTP+ZFU2A0OHkjtlfmuhAgfqv9VnNxqQGQvy4i9Fz0t303ijvnoBXLWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1148e1f4e9d9531ac29a2573f8907107b879477d9fbb99e5423bb762aa0fb549","last_reissued_at":"2026-05-18T00:20:44.148402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:44.148402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.02932","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":"2026-05-18T00:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EV/Vu8pmUKeviRsaSArXs3Lv6l7PYJ0iw4PL1Y1Modpp5xABEH2M3XQeNjm5yYOgkY/n/LYFWvM0nXHiA6r+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:25:55.091752Z"},"content_sha256":"e7a03a245bbdc76c8c84ba38f6b73ee88c8b5158fdd4499be2a41e1e1a65c430","schema_version":"1.0","event_id":"sha256:e7a03a245bbdc76c8c84ba38f6b73ee88c8b5158fdd4499be2a41e1e1a65c430"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CFEOD5HJ3FJRVQU2EVZ7REDRA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomials describing the multiplication in finitely generated torsion free nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Cant, Bettina Eick","submitted_at":"2018-01-09T13:45:21Z","abstract_excerpt":"A famous result of Hall asserts that the multiplication and exponentiation in finitely generated torsion free nilpotent groups can be described by rational polynomials. We describe an algorithm to determine such polynomials for all torsion free nilpotent groups of given Hirsch length. We apply this to determine the Hall polynomials for all such groups of Hirsch length at most 7."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02932","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":"2026-05-18T00:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbdb/b6XM1k3OMWliMwfKwchLvKC24cmD3ELp8MA9jGf6kTobu1zriq377MGsXO8TYStDeYdZIMYGuCYGl5pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:25:55.092562Z"},"content_sha256":"3b6f1d25fa718fa15f88bb344af8c525a84d4ca7432be73a7029dddfba85b5cd","schema_version":"1.0","event_id":"sha256:3b6f1d25fa718fa15f88bb344af8c525a84d4ca7432be73a7029dddfba85b5cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/bundle.json","state_url":"https://pith.science/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/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":"2026-05-31T20:25:55Z","links":{"resolver":"https://pith.science/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6","bundle":"https://pith.science/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/bundle.json","state":"https://pith.science/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFEOD5HJ3FJRVQU2EVZ7REDRA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CFEOD5HJ3FJRVQU2EVZ7REDRA6","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":"cacd340b0a37161b6ebaf1615908d57a1f8f70b874b8b1b64b20c56513dbf662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-09T13:45:21Z","title_canon_sha256":"6ee732a652c21bbc48fc7ef89f37a3751be2282f16e64e7cc317eaea9e28e468"},"schema_version":"1.0","source":{"id":"1801.02932","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02932","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02932v2","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02932","created_at":"2026-05-18T00:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"CFEOD5HJ3FJR","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFEOD5HJ3FJRVQU2","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFEOD5HJ","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:3b6f1d25fa718fa15f88bb344af8c525a84d4ca7432be73a7029dddfba85b5cd","target":"graph","created_at":"2026-05-18T00:20:44Z","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 famous result of Hall asserts that the multiplication and exponentiation in finitely generated torsion free nilpotent groups can be described by rational polynomials. We describe an algorithm to determine such polynomials for all torsion free nilpotent groups of given Hirsch length. We apply this to determine the Hall polynomials for all such groups of Hirsch length at most 7.","authors_text":"Alexander Cant, Bettina Eick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-09T13:45:21Z","title":"Polynomials describing the multiplication in finitely generated torsion free nilpotent groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02932","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:e7a03a245bbdc76c8c84ba38f6b73ee88c8b5158fdd4499be2a41e1e1a65c430","target":"record","created_at":"2026-05-18T00:20:44Z","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":"cacd340b0a37161b6ebaf1615908d57a1f8f70b874b8b1b64b20c56513dbf662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-09T13:45:21Z","title_canon_sha256":"6ee732a652c21bbc48fc7ef89f37a3751be2282f16e64e7cc317eaea9e28e468"},"schema_version":"1.0","source":{"id":"1801.02932","kind":"arxiv","version":2}},"canonical_sha256":"1148e1f4e9d9531ac29a2573f8907107b879477d9fbb99e5423bb762aa0fb549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1148e1f4e9d9531ac29a2573f8907107b879477d9fbb99e5423bb762aa0fb549","first_computed_at":"2026-05-18T00:20:44.148402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:44.148402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ouxZ7YPl/Z869UOlW29tZdexCfnsISTP+ZFU2A0OHkjtlfmuhAgfqv9VnNxqQGQvy4i9Fz0t303ijvnoBXLWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:44.149070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02932","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a03a245bbdc76c8c84ba38f6b73ee88c8b5158fdd4499be2a41e1e1a65c430","sha256:3b6f1d25fa718fa15f88bb344af8c525a84d4ca7432be73a7029dddfba85b5cd"],"state_sha256":"441271fd6c592e78457002079c270a5dc87a83659ca4f391b79ce3a8a64e2d18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0QR0nnE0NI3IuXg68mi4847n/AhSn9NUNTbJzG2GRZyp3QRpWrjJhqMlffOcKVgezL/8eapiyBvhm8GTuIKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:25:55.096709Z","bundle_sha256":"612587be2669d5ba5d873d68fff958a818501518f55a4c70cd2141d6c39d2e88"}}