{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:34Q6MRJVRGH4TYKLC6LVAOAA73","short_pith_number":"pith:34Q6MRJV","canonical_record":{"source":{"id":"1208.4383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-21T20:50:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"befb46de8363a622d61f51908758167775a39649dea7184dbbbc8ac337e94302","abstract_canon_sha256":"445e110e904d69959eb22ef8e06144713a57d97004a6c82e368965a0a7fdd55e"},"schema_version":"1.0"},"canonical_sha256":"df21e64535898fc9e14b1797503800fec208ecfeccfabe3402f83e760245ec06","source":{"kind":"arxiv","id":"1208.4383","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4383","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4383v1","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4383","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"34Q6MRJVRGH4","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"34Q6MRJVRGH4TYKL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"34Q6MRJV","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:34Q6MRJVRGH4TYKLC6LVAOAA73","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-21T20:50:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"befb46de8363a622d61f51908758167775a39649dea7184dbbbc8ac337e94302","abstract_canon_sha256":"445e110e904d69959eb22ef8e06144713a57d97004a6c82e368965a0a7fdd55e"},"schema_version":"1.0"},"canonical_sha256":"df21e64535898fc9e14b1797503800fec208ecfeccfabe3402f83e760245ec06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:12.913348Z","signature_b64":"wJreGqr8nQg3Csog35+Y34Iy/6jEkwWMlIjyPQVa/4IbbZChArM+5Q+9QD34n9GR2R0HAaa4jZ0rRMVu143vDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df21e64535898fc9e14b1797503800fec208ecfeccfabe3402f83e760245ec06","last_reissued_at":"2026-05-18T02:54:12.912703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:12.912703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4383","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":"2026-05-18T02:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ittuo5N5GZn1czl/fQVPZLNp8PTjzJi4lRpPqAW8GmA0eJ3blQn3uoU/dMclHFjRTrJCrwFSlIoZqESQ1ppsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:40:51.126439Z"},"content_sha256":"d6c8e166222e54e919846866ac2e3de6ced2c15f20c1b5ad6abbbbd196ce3137","schema_version":"1.0","event_id":"sha256:d6c8e166222e54e919846866ac2e3de6ced2c15f20c1b5ad6abbbbd196ce3137"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:34Q6MRJVRGH4TYKLC6LVAOAA73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coclass theory for nilpotent semigroups via their associated algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Andreas Distler, Bettina Eick","submitted_at":"2012-08-21T20:50:38Z","abstract_excerpt":"Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in that we additionally use certain algebras associated to the considered semigroups. We propose a series of conjectures on our suggested approach. If these become theorems, then this would reduce the classification of nilpotent semigroups of a fixed coclass to a finite calculation. Our conjectures are supported by the classification of nilpotent semigroups of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4383","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":"2026-05-18T02:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHpq42KtwtoMnEz89GN98gvpiOiNq0UBepJ5cd5ZeQJxbBrDaMNlqw4uWC6mm486ukGkuUiKleHbuPUoEjQnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:40:51.126785Z"},"content_sha256":"210975a9c03344895f5c1b30472a298d86c655dc12ae4d80c253c259360edf70","schema_version":"1.0","event_id":"sha256:210975a9c03344895f5c1b30472a298d86c655dc12ae4d80c253c259360edf70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/bundle.json","state_url":"https://pith.science/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/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":"2026-05-31T15:40:51Z","links":{"resolver":"https://pith.science/pith/34Q6MRJVRGH4TYKLC6LVAOAA73","bundle":"https://pith.science/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/bundle.json","state":"https://pith.science/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34Q6MRJVRGH4TYKLC6LVAOAA73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:34Q6MRJVRGH4TYKLC6LVAOAA73","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":"445e110e904d69959eb22ef8e06144713a57d97004a6c82e368965a0a7fdd55e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-21T20:50:38Z","title_canon_sha256":"befb46de8363a622d61f51908758167775a39649dea7184dbbbc8ac337e94302"},"schema_version":"1.0","source":{"id":"1208.4383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4383","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4383v1","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4383","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"34Q6MRJVRGH4","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"34Q6MRJVRGH4TYKL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"34Q6MRJV","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:210975a9c03344895f5c1b30472a298d86c655dc12ae4d80c253c259360edf70","target":"graph","created_at":"2026-05-18T02:54:12Z","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":"Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in that we additionally use certain algebras associated to the considered semigroups. We propose a series of conjectures on our suggested approach. If these become theorems, then this would reduce the classification of nilpotent semigroups of a fixed coclass to a finite calculation. Our conjectures are supported by the classification of nilpotent semigroups of ","authors_text":"Andreas Distler, Bettina Eick","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-21T20:50:38Z","title":"Coclass theory for nilpotent semigroups via their associated algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4383","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:d6c8e166222e54e919846866ac2e3de6ced2c15f20c1b5ad6abbbbd196ce3137","target":"record","created_at":"2026-05-18T02:54:12Z","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":"445e110e904d69959eb22ef8e06144713a57d97004a6c82e368965a0a7fdd55e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-08-21T20:50:38Z","title_canon_sha256":"befb46de8363a622d61f51908758167775a39649dea7184dbbbc8ac337e94302"},"schema_version":"1.0","source":{"id":"1208.4383","kind":"arxiv","version":1}},"canonical_sha256":"df21e64535898fc9e14b1797503800fec208ecfeccfabe3402f83e760245ec06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df21e64535898fc9e14b1797503800fec208ecfeccfabe3402f83e760245ec06","first_computed_at":"2026-05-18T02:54:12.912703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:12.912703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wJreGqr8nQg3Csog35+Y34Iy/6jEkwWMlIjyPQVa/4IbbZChArM+5Q+9QD34n9GR2R0HAaa4jZ0rRMVu143vDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:12.913348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c8e166222e54e919846866ac2e3de6ced2c15f20c1b5ad6abbbbd196ce3137","sha256:210975a9c03344895f5c1b30472a298d86c655dc12ae4d80c253c259360edf70"],"state_sha256":"3731ac14869969ff03f606c6ce862337a0bd52c796bb63df0d487fa1b6e604af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YefdUZtzwDS2qXEQAfwO2C0wI8z9IeOB3dnrx8aR5rWKEeVuu/53ylTi0fxrGFoOoAOw79bjtodc8vQDm6wzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:40:51.128941Z","bundle_sha256":"c4e347b87e8b74601f0260b2ef6139e0886c06dceaa4b56e24e716b06a9195b0"}}