{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:DVI33FNDHUZZ7VC77ZEP6PLLH4","short_pith_number":"pith:DVI33FND","canonical_record":{"source":{"id":"hep-th/9909026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-09-04T12:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"85653f64e4a0cb8662cff12f5c222dd13e4f29cb3383db29854a18e2dc01eb9e","abstract_canon_sha256":"cb04be34f729cc5b6111dad5e0a1e94be1a98cfc91c23ada97e5997f39e57550"},"schema_version":"1.0"},"canonical_sha256":"1d51bd95a33d339fd45ffe48ff3d6b3f02a7760dd6ead26d112160aa0a2e818d","source":{"kind":"arxiv","id":"hep-th/9909026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9909026","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9909026v1","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9909026","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"DVI33FNDHUZZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"DVI33FNDHUZZ7VC7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"DVI33FND","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:DVI33FNDHUZZ7VC77ZEP6PLLH4","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9909026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-09-04T12:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"85653f64e4a0cb8662cff12f5c222dd13e4f29cb3383db29854a18e2dc01eb9e","abstract_canon_sha256":"cb04be34f729cc5b6111dad5e0a1e94be1a98cfc91c23ada97e5997f39e57550"},"schema_version":"1.0"},"canonical_sha256":"1d51bd95a33d339fd45ffe48ff3d6b3f02a7760dd6ead26d112160aa0a2e818d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:54.231106Z","signature_b64":"tHRyeUZje6sEvxHwbkIHFMLXlbj/hG5ri+dQrWYNmdplXFmwsxbSCpDghJhmT0w4ch0qj6HeTgi7vvEGv5K2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d51bd95a33d339fd45ffe48ff3d6b3f02a7760dd6ead26d112160aa0a2e818d","last_reissued_at":"2026-05-18T02:35:54.230619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:54.230619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9909026","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":"2026-05-18T02:35:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEhAzg9bbHb1tIvwAa/Srl/fYUV/lm+gxfWxPinVrbBAZg8rPtkbg1fwbNxsP6KJ3pLyywilvsScn+Ac1W5oCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:08:14.078983Z"},"content_sha256":"00dcceac5250ee540d9340c092aa20337e147d19454bc0dc7d4e335cc234321f","schema_version":"1.0","event_id":"sha256:00dcceac5250ee540d9340c092aa20337e147d19454bc0dc7d4e335cc234321f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:DVI33FNDHUZZ7VC77ZEP6PLLH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Yoshitaka Okumura","submitted_at":"1999-09-04T12:17:04Z","abstract_excerpt":"Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\\times Z_N$ which is very close to NCG in case of $M_4\\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9909026","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":"2026-05-18T02:35:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmtvXKX6Wyii7vz5kCrrfdB9+ssoDxnKWommUkj917Kd+a9PhJ4iNTb6AvIItxhMpDJ5oT0X9VZ55bEbOPPjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:08:14.079341Z"},"content_sha256":"dc3ccf08f4b1977fcaf3353b77055a1a85cc6b527a7268919aedb318dccc217f","schema_version":"1.0","event_id":"sha256:dc3ccf08f4b1977fcaf3353b77055a1a85cc6b527a7268919aedb318dccc217f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/bundle.json","state_url":"https://pith.science/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/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":"2026-06-26T21:08:14Z","links":{"resolver":"https://pith.science/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4","bundle":"https://pith.science/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/bundle.json","state":"https://pith.science/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVI33FNDHUZZ7VC77ZEP6PLLH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:DVI33FNDHUZZ7VC77ZEP6PLLH4","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":"cb04be34f729cc5b6111dad5e0a1e94be1a98cfc91c23ada97e5997f39e57550","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-09-04T12:17:04Z","title_canon_sha256":"85653f64e4a0cb8662cff12f5c222dd13e4f29cb3383db29854a18e2dc01eb9e"},"schema_version":"1.0","source":{"id":"hep-th/9909026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9909026","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9909026v1","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9909026","created_at":"2026-05-18T02:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"DVI33FNDHUZZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"DVI33FNDHUZZ7VC7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"DVI33FND","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:dc3ccf08f4b1977fcaf3353b77055a1a85cc6b527a7268919aedb318dccc217f","target":"graph","created_at":"2026-05-18T02:35:54Z","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":"Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\\times Z_N$ which is very close to NCG in case of $M_4\\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory ba","authors_text":"Yoshitaka Okumura","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-09-04T12:17:04Z","title":"BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9909026","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":"sha256:00dcceac5250ee540d9340c092aa20337e147d19454bc0dc7d4e335cc234321f","target":"record","created_at":"2026-05-18T02:35:54Z","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":"cb04be34f729cc5b6111dad5e0a1e94be1a98cfc91c23ada97e5997f39e57550","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1999-09-04T12:17:04Z","title_canon_sha256":"85653f64e4a0cb8662cff12f5c222dd13e4f29cb3383db29854a18e2dc01eb9e"},"schema_version":"1.0","source":{"id":"hep-th/9909026","kind":"arxiv","version":1}},"canonical_sha256":"1d51bd95a33d339fd45ffe48ff3d6b3f02a7760dd6ead26d112160aa0a2e818d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d51bd95a33d339fd45ffe48ff3d6b3f02a7760dd6ead26d112160aa0a2e818d","first_computed_at":"2026-05-18T02:35:54.230619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:54.230619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tHRyeUZje6sEvxHwbkIHFMLXlbj/hG5ri+dQrWYNmdplXFmwsxbSCpDghJhmT0w4ch0qj6HeTgi7vvEGv5K2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:54.231106Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9909026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00dcceac5250ee540d9340c092aa20337e147d19454bc0dc7d4e335cc234321f","sha256:dc3ccf08f4b1977fcaf3353b77055a1a85cc6b527a7268919aedb318dccc217f"],"state_sha256":"f39d00b2b124ce04aaa4c6cdc36e8d577af75a376be323f0dff88d82258a5228"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYSRNa9LMadIy/jXe0c67fC80pmiapX2WPoIjBU3djgxRnLhp6rWd9iYMf7oFOwCQuPRqwshaTf9r4N1ORSjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:08:14.081255Z","bundle_sha256":"802dee19a5965e3bb2009693b6f732f0523f91cb9febf1af27b4fb7f7be178db"}}