{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LYMTP7ADBMFAGMOEUSVJW7HTHB","short_pith_number":"pith:LYMTP7AD","canonical_record":{"source":{"id":"1305.4970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"57cda96aca3678c9cc7bacc1c7ac79b98c76791982151b217c8a072a13610550","abstract_canon_sha256":"727f54c5fcbd8713b3fbea9644480799bc34ff9e97777880d5a841ded7245539"},"schema_version":"1.0"},"canonical_sha256":"5e1937fc030b0a0331c4a4aa9b7cf3385be1c4f917ca8bb63820f22f58e032f1","source":{"kind":"arxiv","id":"1305.4970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4970","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4970v1","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4970","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"pith_short_12","alias_value":"LYMTP7ADBMFA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LYMTP7ADBMFAGMOE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LYMTP7AD","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LYMTP7ADBMFAGMOEUSVJW7HTHB","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"57cda96aca3678c9cc7bacc1c7ac79b98c76791982151b217c8a072a13610550","abstract_canon_sha256":"727f54c5fcbd8713b3fbea9644480799bc34ff9e97777880d5a841ded7245539"},"schema_version":"1.0"},"canonical_sha256":"5e1937fc030b0a0331c4a4aa9b7cf3385be1c4f917ca8bb63820f22f58e032f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:06.992672Z","signature_b64":"/hV+K5h2MYibVZyIYbuFxyxbY640aVJkvBocJRzoqWK+1/5eJ+Z1w2GU6lDc/HW5G3kHG/IW/JcNUQHr8C60Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e1937fc030b0a0331c4a4aa9b7cf3385be1c4f917ca8bb63820f22f58e032f1","last_reissued_at":"2026-05-18T00:12:06.992158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:06.992158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4970","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":"2026-05-18T00:12:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZo2RPMsNMEVlGnsNMiMJSjPcn5whsd9S9CesK+lf+HUJLey7WjRR7etyz/OutojeGbKxUJxnszxAZ35d928AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:32:33.956372Z"},"content_sha256":"183b4e443c2c396b91b7500423254063540c651922e46847975fec9181c756cf","schema_version":"1.0","event_id":"sha256:183b4e443c2c396b91b7500423254063540c651922e46847975fec9181c756cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LYMTP7ADBMFAGMOEUSVJW7HTHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On atomicity of free algebras in Boolean algebras with operators, and a new result on Pinter's free algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tarek Sayed Ahmed","submitted_at":"2013-04-23T12:28:09Z","abstract_excerpt":"We give some general theorems on free algebras of varieties of Boolean algebras with operators; a hitherto new result is obtained for Pinter's substitution algebras. For n\\geq 3, and m>1, there is a generating set of the free algebra freely generated by m elements, which is not a free set of generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4970","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":"2026-05-18T00:12:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ztEVSuOLQl3wtBEEd+L3e+I2l7IgQTSi3fooIS5vvViLjK9qGhpMWWa2MLnVYG5A74JN91amgAXrhnRBhxVlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:32:33.956725Z"},"content_sha256":"dafa3eb08fbbcef4904b5fcdd3d07681d160b196aa1b6e96538d57c82ed689bd","schema_version":"1.0","event_id":"sha256:dafa3eb08fbbcef4904b5fcdd3d07681d160b196aa1b6e96538d57c82ed689bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/bundle.json","state_url":"https://pith.science/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/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":"2026-06-26T07:32:33Z","links":{"resolver":"https://pith.science/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB","bundle":"https://pith.science/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/bundle.json","state":"https://pith.science/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYMTP7ADBMFAGMOEUSVJW7HTHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LYMTP7ADBMFAGMOEUSVJW7HTHB","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":"727f54c5fcbd8713b3fbea9644480799bc34ff9e97777880d5a841ded7245539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:28:09Z","title_canon_sha256":"57cda96aca3678c9cc7bacc1c7ac79b98c76791982151b217c8a072a13610550"},"schema_version":"1.0","source":{"id":"1305.4970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4970","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4970v1","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4970","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"pith_short_12","alias_value":"LYMTP7ADBMFA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LYMTP7ADBMFAGMOE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LYMTP7AD","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:dafa3eb08fbbcef4904b5fcdd3d07681d160b196aa1b6e96538d57c82ed689bd","target":"graph","created_at":"2026-05-18T00:12:06Z","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 give some general theorems on free algebras of varieties of Boolean algebras with operators; a hitherto new result is obtained for Pinter's substitution algebras. For n\\geq 3, and m>1, there is a generating set of the free algebra freely generated by m elements, which is not a free set of generators.","authors_text":"Tarek Sayed Ahmed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:28:09Z","title":"On atomicity of free algebras in Boolean algebras with operators, and a new result on Pinter's free algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4970","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":"sha256:183b4e443c2c396b91b7500423254063540c651922e46847975fec9181c756cf","target":"record","created_at":"2026-05-18T00:12:06Z","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":"727f54c5fcbd8713b3fbea9644480799bc34ff9e97777880d5a841ded7245539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-23T12:28:09Z","title_canon_sha256":"57cda96aca3678c9cc7bacc1c7ac79b98c76791982151b217c8a072a13610550"},"schema_version":"1.0","source":{"id":"1305.4970","kind":"arxiv","version":1}},"canonical_sha256":"5e1937fc030b0a0331c4a4aa9b7cf3385be1c4f917ca8bb63820f22f58e032f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e1937fc030b0a0331c4a4aa9b7cf3385be1c4f917ca8bb63820f22f58e032f1","first_computed_at":"2026-05-18T00:12:06.992158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:06.992158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/hV+K5h2MYibVZyIYbuFxyxbY640aVJkvBocJRzoqWK+1/5eJ+Z1w2GU6lDc/HW5G3kHG/IW/JcNUQHr8C60Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:06.992672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:183b4e443c2c396b91b7500423254063540c651922e46847975fec9181c756cf","sha256:dafa3eb08fbbcef4904b5fcdd3d07681d160b196aa1b6e96538d57c82ed689bd"],"state_sha256":"0010e1efbf9411ac33080994f979038157b71a3009250e8a66e68d6542375335"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aA50sunWXQvoSjrT688v3rOEJYc3aS10Om1ZG7Fh8q/ky0r0C3wAJsXTt805DD61FrqVRZc7rZZzuzwfAcRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:32:33.958740Z","bundle_sha256":"16d7dac600e5ef65e994e446d419f52554a993ad73cc71af87c1ad2fa2f6bd80"}}