{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:6CNRXXZLN5ESA5RNQH27Z24H64","short_pith_number":"pith:6CNRXXZL","canonical_record":{"source":{"id":"gr-qc/0512076","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-12-13T10:41:12Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"49371ec659134c60a051a2bc94f2acf10526bad99edccb104ab3d2194aa02f5e","abstract_canon_sha256":"6b89c4d14c75baa982ed6c89dba2396a01908fbfcd45cfb2ab14bcb84743dd01"},"schema_version":"1.0"},"canonical_sha256":"f09b1bdf2b6f4920762d81f5fceb87f70cbc23a9c41ef962f43468192dd79140","source":{"kind":"arxiv","id":"gr-qc/0512076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0512076","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0512076v1","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0512076","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"pith_short_12","alias_value":"6CNRXXZLN5ES","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6CNRXXZLN5ESA5RN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6CNRXXZL","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:6CNRXXZLN5ESA5RNQH27Z24H64","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0512076","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-12-13T10:41:12Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"49371ec659134c60a051a2bc94f2acf10526bad99edccb104ab3d2194aa02f5e","abstract_canon_sha256":"6b89c4d14c75baa982ed6c89dba2396a01908fbfcd45cfb2ab14bcb84743dd01"},"schema_version":"1.0"},"canonical_sha256":"f09b1bdf2b6f4920762d81f5fceb87f70cbc23a9c41ef962f43468192dd79140","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:20.216793Z","signature_b64":"oEc/MdNQRYMpGOJ+u5Sky3OSvgPNV5AvzYDy5JWwV5OKyjLv7t0CnOj1b3J3XKzqGUk7j9SETY6NuKVZRBk5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f09b1bdf2b6f4920762d81f5fceb87f70cbc23a9c41ef962f43468192dd79140","last_reissued_at":"2026-05-18T01:39:20.216141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:20.216141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0512076","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":"2026-05-18T01:39:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZmk25cL/iw6lQc1sX+jOslBuArm8PO3lt4a31kgnbsN1LJQ/IyAudeEL9BHPX9672/wlpx/WOhmqv8C1pRZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:43:16.557565Z"},"content_sha256":"8dac5904ca0f3feb16ea3fe85bc76c9b2ed8489ebafd459b0afa0ffc0255d5bf","schema_version":"1.0","event_id":"sha256:8dac5904ca0f3feb16ea3fe85bc76c9b2ed8489ebafd459b0afa0ffc0255d5bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:6CNRXXZLN5ESA5RNQH27Z24H64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group averaging, positive definiteness and superselection sectors","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Jorma Louko","submitted_at":"2005-12-13T10:41:12Z","abstract_excerpt":"I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective physical inner product and the emergence of superselection sectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0512076","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":"2026-05-18T01:39:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"70aLmhSj7QLPkSetuja47b2nobddEr4FmFtmWRPUxAK/RJwheO+zsWufWH1AwvFr/699bMKxAw0urekCAt0hDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:43:16.557909Z"},"content_sha256":"931981a37e0f5977720a8042233be143f57cbd057417d3a4205491454c0c4a7f","schema_version":"1.0","event_id":"sha256:931981a37e0f5977720a8042233be143f57cbd057417d3a4205491454c0c4a7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CNRXXZLN5ESA5RNQH27Z24H64/bundle.json","state_url":"https://pith.science/pith/6CNRXXZLN5ESA5RNQH27Z24H64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CNRXXZLN5ESA5RNQH27Z24H64/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":"2026-06-04T12:43:16Z","links":{"resolver":"https://pith.science/pith/6CNRXXZLN5ESA5RNQH27Z24H64","bundle":"https://pith.science/pith/6CNRXXZLN5ESA5RNQH27Z24H64/bundle.json","state":"https://pith.science/pith/6CNRXXZLN5ESA5RNQH27Z24H64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CNRXXZLN5ESA5RNQH27Z24H64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:6CNRXXZLN5ESA5RNQH27Z24H64","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":"6b89c4d14c75baa982ed6c89dba2396a01908fbfcd45cfb2ab14bcb84743dd01","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-12-13T10:41:12Z","title_canon_sha256":"49371ec659134c60a051a2bc94f2acf10526bad99edccb104ab3d2194aa02f5e"},"schema_version":"1.0","source":{"id":"gr-qc/0512076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0512076","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0512076v1","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0512076","created_at":"2026-05-18T01:39:20Z"},{"alias_kind":"pith_short_12","alias_value":"6CNRXXZLN5ES","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6CNRXXZLN5ESA5RN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6CNRXXZL","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:931981a37e0f5977720a8042233be143f57cbd057417d3a4205491454c0c4a7f","target":"graph","created_at":"2026-05-18T01:39:20Z","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":"I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective physical inner product and the emergence of superselection sectors.","authors_text":"Jorma Louko","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2005-12-13T10:41:12Z","title":"Group averaging, positive definiteness and superselection sectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0512076","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":"sha256:8dac5904ca0f3feb16ea3fe85bc76c9b2ed8489ebafd459b0afa0ffc0255d5bf","target":"record","created_at":"2026-05-18T01:39:20Z","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":"6b89c4d14c75baa982ed6c89dba2396a01908fbfcd45cfb2ab14bcb84743dd01","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-12-13T10:41:12Z","title_canon_sha256":"49371ec659134c60a051a2bc94f2acf10526bad99edccb104ab3d2194aa02f5e"},"schema_version":"1.0","source":{"id":"gr-qc/0512076","kind":"arxiv","version":1}},"canonical_sha256":"f09b1bdf2b6f4920762d81f5fceb87f70cbc23a9c41ef962f43468192dd79140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f09b1bdf2b6f4920762d81f5fceb87f70cbc23a9c41ef962f43468192dd79140","first_computed_at":"2026-05-18T01:39:20.216141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:20.216141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oEc/MdNQRYMpGOJ+u5Sky3OSvgPNV5AvzYDy5JWwV5OKyjLv7t0CnOj1b3J3XKzqGUk7j9SETY6NuKVZRBk5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:20.216793Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0512076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dac5904ca0f3feb16ea3fe85bc76c9b2ed8489ebafd459b0afa0ffc0255d5bf","sha256:931981a37e0f5977720a8042233be143f57cbd057417d3a4205491454c0c4a7f"],"state_sha256":"4dcbbd5662f384e1682432b65874792db3be4a2374ea8f141c75d45d8ff0405d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJw11O5W5ti7D9ANlC2KREnDyWkZZrCALv54xk69cVS94tQI0CORjVzzETuKOw0YzI77zAFYUtjEvKliP3xxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:43:16.559828Z","bundle_sha256":"6087609dccf88e36bc3095dadda4e1f6a22b71f90a4cc73f000458140357a39e"}}