{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:WCRW2QXDULHRGEPMP6MZLDBPAL","short_pith_number":"pith:WCRW2QXD","canonical_record":{"source":{"id":"hep-th/9210098","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-10-19T08:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"7b734cdc1075d6d2bfef47cdaa087008b69a3dbf648022c937439dc1148ddd9f","abstract_canon_sha256":"ba94e31e6d97ea0db1027d682c55f51586a63787abd297219ffbf41c144151d0"},"schema_version":"1.0"},"canonical_sha256":"b0a36d42e3a2cf1311ec7f99958c2f02e19b0f41616eeaa1ec3d2bcf764fd096","source":{"kind":"arxiv","id":"hep-th/9210098","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9210098","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9210098v1","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9210098","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"WCRW2QXDULHR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"WCRW2QXDULHRGEPM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"WCRW2QXD","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:WCRW2QXDULHRGEPMP6MZLDBPAL","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9210098","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-10-19T08:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"7b734cdc1075d6d2bfef47cdaa087008b69a3dbf648022c937439dc1148ddd9f","abstract_canon_sha256":"ba94e31e6d97ea0db1027d682c55f51586a63787abd297219ffbf41c144151d0"},"schema_version":"1.0"},"canonical_sha256":"b0a36d42e3a2cf1311ec7f99958c2f02e19b0f41616eeaa1ec3d2bcf764fd096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:43.236906Z","signature_b64":"AYT/vZGOaK/dW9keNMV747OkGB69I8ISITWb4EJ+LYWqQC+oGArdd4UvZZmOJlycirXXRwBaZRTjomyAIjZnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0a36d42e3a2cf1311ec7f99958c2f02e19b0f41616eeaa1ec3d2bcf764fd096","last_reissued_at":"2026-05-18T01:38:43.236506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:43.236506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9210098","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":"2026-05-18T01:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"susYe8AsPgLNWOzp1+eSJUCpScPgDLGdzjkNYkObPJWWPbg+jmw5Nj5mtCiRUisUo6iTN81PpJqOxe1eVp6VCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:48:46.374703Z"},"content_sha256":"ff3006ec10273c496d2fae43d02993f02c9732d6f4d91c35b8f73e86f90ab2ef","schema_version":"1.0","event_id":"sha256:ff3006ec10273c496d2fae43d02993f02c9732d6f4d91c35b8f73e86f90ab2ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:WCRW2QXDULHRGEPMP6MZLDBPAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Geometry and Gauge Theories on Discrete Groups","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Andrzej Sitarz","submitted_at":"1992-10-19T08:53:11Z","abstract_excerpt":"We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action functionals for unitary gauge theories. A detailed analysis of two simple models based on $\\z_2$ and $\\z_3$ follows. Finally we study the method of combining the discrete and continuous geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9210098","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":"2026-05-18T01:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q2WCLe3ct5mo2Ty73uoSbn3aGHD9C7x7dBxfGG5MxodlI4YqHOSHRqLVN8Ebjs/F3F5c1eln9eKgE+nar+vhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:48:46.375047Z"},"content_sha256":"360b420982328a431f0f0cac7083e3233014d0e5ed98dce05736e72e1695e3f0","schema_version":"1.0","event_id":"sha256:360b420982328a431f0f0cac7083e3233014d0e5ed98dce05736e72e1695e3f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/bundle.json","state_url":"https://pith.science/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/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":"2026-05-30T07:48:46Z","links":{"resolver":"https://pith.science/pith/WCRW2QXDULHRGEPMP6MZLDBPAL","bundle":"https://pith.science/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/bundle.json","state":"https://pith.science/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCRW2QXDULHRGEPMP6MZLDBPAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:WCRW2QXDULHRGEPMP6MZLDBPAL","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":"ba94e31e6d97ea0db1027d682c55f51586a63787abd297219ffbf41c144151d0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-10-19T08:53:11Z","title_canon_sha256":"7b734cdc1075d6d2bfef47cdaa087008b69a3dbf648022c937439dc1148ddd9f"},"schema_version":"1.0","source":{"id":"hep-th/9210098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9210098","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9210098v1","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9210098","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"WCRW2QXDULHR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"WCRW2QXDULHRGEPM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"WCRW2QXD","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:360b420982328a431f0f0cac7083e3233014d0e5ed98dce05736e72e1695e3f0","target":"graph","created_at":"2026-05-18T01:38:43Z","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 build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action functionals for unitary gauge theories. A detailed analysis of two simple models based on $\\z_2$ and $\\z_3$ follows. Finally we study the method of combining the discrete and continuous geometry.","authors_text":"Andrzej Sitarz","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1992-10-19T08:53:11Z","title":"Noncommutative Geometry and Gauge Theories on Discrete Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9210098","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:ff3006ec10273c496d2fae43d02993f02c9732d6f4d91c35b8f73e86f90ab2ef","target":"record","created_at":"2026-05-18T01:38:43Z","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":"ba94e31e6d97ea0db1027d682c55f51586a63787abd297219ffbf41c144151d0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-10-19T08:53:11Z","title_canon_sha256":"7b734cdc1075d6d2bfef47cdaa087008b69a3dbf648022c937439dc1148ddd9f"},"schema_version":"1.0","source":{"id":"hep-th/9210098","kind":"arxiv","version":1}},"canonical_sha256":"b0a36d42e3a2cf1311ec7f99958c2f02e19b0f41616eeaa1ec3d2bcf764fd096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0a36d42e3a2cf1311ec7f99958c2f02e19b0f41616eeaa1ec3d2bcf764fd096","first_computed_at":"2026-05-18T01:38:43.236506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:43.236506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AYT/vZGOaK/dW9keNMV747OkGB69I8ISITWb4EJ+LYWqQC+oGArdd4UvZZmOJlycirXXRwBaZRTjomyAIjZnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:43.236906Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9210098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff3006ec10273c496d2fae43d02993f02c9732d6f4d91c35b8f73e86f90ab2ef","sha256:360b420982328a431f0f0cac7083e3233014d0e5ed98dce05736e72e1695e3f0"],"state_sha256":"8f855133aba8388dd0df55fcb4cee71f2d099942d209aadfd5ff9aef35dea34b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgzOu5FD1IG0bwwGytgbWhaqZXx4ZmF2QMqSpGCLZyVVbu2ZWj2xloutwK6ittRtcE/VBotkE30b4A6WNvI4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:48:46.377149Z","bundle_sha256":"f2db2ea15dd738f5e7803470794934aa9a04c8a25f83742130555016d25c57b0"}}