{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U6FVC5FICTATR6E7VERDNA7Y7N","short_pith_number":"pith:U6FVC5FI","canonical_record":{"source":{"id":"1307.6126","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-23T15:39:19Z","cross_cats_sorted":[],"title_canon_sha256":"c80980dcc8f30f0be5aec350d988af961a5e033acaf1ecbf31e36452600b0d09","abstract_canon_sha256":"c41fecb2922b01de2d0dc04b6bae011f4572543ffb82305095bec736f32374b7"},"schema_version":"1.0"},"canonical_sha256":"a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df","source":{"kind":"arxiv","id":"1307.6126","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6126","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6126v4","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6126","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"U6FVC5FICTAT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U6FVC5FICTATR6E7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U6FVC5FI","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U6FVC5FICTATR6E7VERDNA7Y7N","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6126","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-23T15:39:19Z","cross_cats_sorted":[],"title_canon_sha256":"c80980dcc8f30f0be5aec350d988af961a5e033acaf1ecbf31e36452600b0d09","abstract_canon_sha256":"c41fecb2922b01de2d0dc04b6bae011f4572543ffb82305095bec736f32374b7"},"schema_version":"1.0"},"canonical_sha256":"a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:57.780112Z","signature_b64":"XZVQXocgA7xs2bHWBBsjPAEohuKNIBHw4cjmiq1/CWAo2zfsvWhi0/gVjcr9QosLnCrH0W87baPwsCdHCWdSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df","last_reissued_at":"2026-05-18T03:13:57.779571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:57.779571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6126","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cz4f0HhtoLIo/fmZGHtJM+8mR5xjpl/e6Q2gr8ujNA0sA6nMIhYb8NCl90sFRhCrMgdjbPQXAZ4WfHK58rHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:29:12.763068Z"},"content_sha256":"37205330b0e2b089c6166d33a8d19824e92e5e0dece8fda1230d418a07a4b7a6","schema_version":"1.0","event_id":"sha256:37205330b0e2b089c6166d33a8d19824e92e5e0dece8fda1230d418a07a4b7a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U6FVC5FICTATR6E7VERDNA7Y7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congruences of the fork extensions. II. The congruence gamma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"George Gr\\\"atzer","submitted_at":"2013-07-23T15:39:19Z","abstract_excerpt":"G. Cz\\'edli and E.\\,T. Schmidt introduced in 2012 the fork extension. Continuing from Part I, we investigate the congruences of a fork extension. This paper has been merged with Part I, under the title Congruences of fork extensions of slim semimodular lattices, see arXiv: 1307.8404"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6126","kind":"arxiv","version":4},"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":"2026-05-18T03:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbecJye6C/O3hDjAOdqgNtemLG+VDaIOyrW9pdWS3ZbJy6AvB63HsCg0apuSoDypNyKNZHjg5S1CsFj5oeBiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:29:12.763419Z"},"content_sha256":"ded7575c2cb6547f5e4924ffb1e64f384d354a25e0ad3f138989da3bc6c87337","schema_version":"1.0","event_id":"sha256:ded7575c2cb6547f5e4924ffb1e64f384d354a25e0ad3f138989da3bc6c87337"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6FVC5FICTATR6E7VERDNA7Y7N/bundle.json","state_url":"https://pith.science/pith/U6FVC5FICTATR6E7VERDNA7Y7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6FVC5FICTATR6E7VERDNA7Y7N/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":"2026-06-21T20:29:12Z","links":{"resolver":"https://pith.science/pith/U6FVC5FICTATR6E7VERDNA7Y7N","bundle":"https://pith.science/pith/U6FVC5FICTATR6E7VERDNA7Y7N/bundle.json","state":"https://pith.science/pith/U6FVC5FICTATR6E7VERDNA7Y7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6FVC5FICTATR6E7VERDNA7Y7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U6FVC5FICTATR6E7VERDNA7Y7N","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":"c41fecb2922b01de2d0dc04b6bae011f4572543ffb82305095bec736f32374b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-23T15:39:19Z","title_canon_sha256":"c80980dcc8f30f0be5aec350d988af961a5e033acaf1ecbf31e36452600b0d09"},"schema_version":"1.0","source":{"id":"1307.6126","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6126","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6126v4","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6126","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"U6FVC5FICTAT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U6FVC5FICTATR6E7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U6FVC5FI","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:ded7575c2cb6547f5e4924ffb1e64f384d354a25e0ad3f138989da3bc6c87337","target":"graph","created_at":"2026-05-18T03:13:57Z","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":"G. Cz\\'edli and E.\\,T. Schmidt introduced in 2012 the fork extension. Continuing from Part I, we investigate the congruences of a fork extension. This paper has been merged with Part I, under the title Congruences of fork extensions of slim semimodular lattices, see arXiv: 1307.8404","authors_text":"George Gr\\\"atzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-23T15:39:19Z","title":"Congruences of the fork extensions. II. The congruence gamma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6126","kind":"arxiv","version":4},"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":"sha256:37205330b0e2b089c6166d33a8d19824e92e5e0dece8fda1230d418a07a4b7a6","target":"record","created_at":"2026-05-18T03:13:57Z","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":"c41fecb2922b01de2d0dc04b6bae011f4572543ffb82305095bec736f32374b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-23T15:39:19Z","title_canon_sha256":"c80980dcc8f30f0be5aec350d988af961a5e033acaf1ecbf31e36452600b0d09"},"schema_version":"1.0","source":{"id":"1307.6126","kind":"arxiv","version":4}},"canonical_sha256":"a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df","first_computed_at":"2026-05-18T03:13:57.779571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:57.779571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZVQXocgA7xs2bHWBBsjPAEohuKNIBHw4cjmiq1/CWAo2zfsvWhi0/gVjcr9QosLnCrH0W87baPwsCdHCWdSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:57.780112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6126","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37205330b0e2b089c6166d33a8d19824e92e5e0dece8fda1230d418a07a4b7a6","sha256:ded7575c2cb6547f5e4924ffb1e64f384d354a25e0ad3f138989da3bc6c87337"],"state_sha256":"76caf142667467f51c0f4df490512fc1a63725301bd08f7d9dddb2dc1451b55f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWgRr6uPLgOC/B/g1+m4UMDBBryNN8LPPYUvwCOMvN6EHZQTT4MAPFMNucfGhF1GyQ4+lRrcfJa0f8QiiAfjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:29:12.765305Z","bundle_sha256":"a3c3d781c84c004be2a7ae6d8e6cb3664e0ef1dc05aec6db52718f77acdda6d3"}}