{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3AHYMJV5VYVWS6W7RBF3W24NT5","short_pith_number":"pith:3AHYMJV5","canonical_record":{"source":{"id":"1509.05468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-17T22:59:04Z","cross_cats_sorted":[],"title_canon_sha256":"691e1d309bc1cfcc46023518e36a59d7bc11a50750e1fa0bb220cf54e2c45d72","abstract_canon_sha256":"430b5e38c8932c602c4024a087ef3aa2cf010befc6af446ea071ec3e13de4920"},"schema_version":"1.0"},"canonical_sha256":"d80f8626bdae2b697adf884bbb6b8d9f6009a89d0aedc05e1f5648aa0287cab4","source":{"kind":"arxiv","id":"1509.05468","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05468","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05468v1","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05468","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"3AHYMJV5VYVW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3AHYMJV5VYVWS6W7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3AHYMJV5","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3AHYMJV5VYVWS6W7RBF3W24NT5","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-17T22:59:04Z","cross_cats_sorted":[],"title_canon_sha256":"691e1d309bc1cfcc46023518e36a59d7bc11a50750e1fa0bb220cf54e2c45d72","abstract_canon_sha256":"430b5e38c8932c602c4024a087ef3aa2cf010befc6af446ea071ec3e13de4920"},"schema_version":"1.0"},"canonical_sha256":"d80f8626bdae2b697adf884bbb6b8d9f6009a89d0aedc05e1f5648aa0287cab4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:43.116452Z","signature_b64":"yfnJR/2UsYSoE4vAFpaKkr1v64xfwg6hzt41aUX2srauAyAZGJFIze1aE4SeqWWSRk6LFHncUA/4Sp9fytoPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80f8626bdae2b697adf884bbb6b8d9f6009a89d0aedc05e1f5648aa0287cab4","last_reissued_at":"2026-05-18T01:32:43.116014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:43.116014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05468","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":"2026-05-18T01:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GE+JvJtC0n1ON+zJkvM2Ke6rBnQFi7Wg0jZgm0JDhRK/csQmaMoTvlvbCLZGX/yKtjxNXkOyjspPmrQlzbEZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:35:33.341571Z"},"content_sha256":"ba342ce76ed700e9961e6cb3233a09071b53eccf4507799a4a622bd355e3596c","schema_version":"1.0","event_id":"sha256:ba342ce76ed700e9961e6cb3233a09071b53eccf4507799a4a622bd355e3596c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3AHYMJV5VYVWS6W7RBF3W24NT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loops with abelian inner mapping groups: An application of automated deduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael Kinyon, Petr Vojt\\v{e}chovsk\\'y, Robert Veroff","submitted_at":"2015-09-17T22:59:04Z","abstract_excerpt":"We describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If $Q$ is a loop with commuting inner mappings, does it follow that $Q$ modulo its center is a group and $Q$ modulo its nucleus is an abelian group? This problem has been answered affirmatively in several varieties of loops. The solution usually involves sophisticated techniques of automated deduction, and the resulting derivations are very long, often with no higher-level human proofs available."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05468","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":"2026-05-18T01:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6CZK132DN5H1P4nif4ltKG6No2g2v9DdJvnafRS7UPVaF+qulMHyUo+kcP7KN3EPsxlTYXUR9V71oyRpz42AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:35:33.342378Z"},"content_sha256":"a8704705deea33ec2f7de0075c1b6973d45d790d5acd163ecba0193202e6da57","schema_version":"1.0","event_id":"sha256:a8704705deea33ec2f7de0075c1b6973d45d790d5acd163ecba0193202e6da57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/bundle.json","state_url":"https://pith.science/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/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":"2026-06-01T02:35:33Z","links":{"resolver":"https://pith.science/pith/3AHYMJV5VYVWS6W7RBF3W24NT5","bundle":"https://pith.science/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/bundle.json","state":"https://pith.science/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AHYMJV5VYVWS6W7RBF3W24NT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3AHYMJV5VYVWS6W7RBF3W24NT5","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":"430b5e38c8932c602c4024a087ef3aa2cf010befc6af446ea071ec3e13de4920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-17T22:59:04Z","title_canon_sha256":"691e1d309bc1cfcc46023518e36a59d7bc11a50750e1fa0bb220cf54e2c45d72"},"schema_version":"1.0","source":{"id":"1509.05468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05468","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05468v1","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05468","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"3AHYMJV5VYVW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3AHYMJV5VYVWS6W7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3AHYMJV5","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:a8704705deea33ec2f7de0075c1b6973d45d790d5acd163ecba0193202e6da57","target":"graph","created_at":"2026-05-18T01:32:43Z","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 describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If $Q$ is a loop with commuting inner mappings, does it follow that $Q$ modulo its center is a group and $Q$ modulo its nucleus is an abelian group? This problem has been answered affirmatively in several varieties of loops. The solution usually involves sophisticated techniques of automated deduction, and the resulting derivations are very long, often with no higher-level human proofs available.","authors_text":"Michael Kinyon, Petr Vojt\\v{e}chovsk\\'y, Robert Veroff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-17T22:59:04Z","title":"Loops with abelian inner mapping groups: An application of automated deduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05468","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:ba342ce76ed700e9961e6cb3233a09071b53eccf4507799a4a622bd355e3596c","target":"record","created_at":"2026-05-18T01:32:43Z","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":"430b5e38c8932c602c4024a087ef3aa2cf010befc6af446ea071ec3e13de4920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-17T22:59:04Z","title_canon_sha256":"691e1d309bc1cfcc46023518e36a59d7bc11a50750e1fa0bb220cf54e2c45d72"},"schema_version":"1.0","source":{"id":"1509.05468","kind":"arxiv","version":1}},"canonical_sha256":"d80f8626bdae2b697adf884bbb6b8d9f6009a89d0aedc05e1f5648aa0287cab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d80f8626bdae2b697adf884bbb6b8d9f6009a89d0aedc05e1f5648aa0287cab4","first_computed_at":"2026-05-18T01:32:43.116014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:43.116014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yfnJR/2UsYSoE4vAFpaKkr1v64xfwg6hzt41aUX2srauAyAZGJFIze1aE4SeqWWSRk6LFHncUA/4Sp9fytoPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:43.116452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba342ce76ed700e9961e6cb3233a09071b53eccf4507799a4a622bd355e3596c","sha256:a8704705deea33ec2f7de0075c1b6973d45d790d5acd163ecba0193202e6da57"],"state_sha256":"7da6ca5a0b1c0589722f48b4ad05125f4d4475160fc20475a93441991848f6e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uMhe8DQangAlz1fgei6w/AAHmHrS/HQF1pxb2jepXe370HQ0OJ9j1vUZuS5NvDUvVqEiryQFxpnoO70ePWoXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:35:33.346826Z","bundle_sha256":"433cd061830131af31faef97ced024dc0fb6c6536bc2ada6ca24bd780bfc17e3"}}