{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:AOYPI2WHZ64QVIKEJWW6J6AH25","short_pith_number":"pith:AOYPI2WH","canonical_record":{"source":{"id":"gr-qc/9303026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1993-03-20T19:27:00Z","cross_cats_sorted":[],"title_canon_sha256":"6442e6b577b65b05c0b02faf813528b485a52a64853c0658cbebf3f9f1a826d9","abstract_canon_sha256":"97c9a76bebc84bc5b3a9f4a35ccdeab37c0fe8e0d24b866e272b708c87f48d3e"},"schema_version":"1.0"},"canonical_sha256":"03b0f46ac7cfb90aa1444dade4f807d76660367e5e2703e807ea2a899651deea","source":{"kind":"arxiv","id":"gr-qc/9303026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9303026","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9303026v1","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9303026","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"AOYPI2WHZ64Q","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_16","alias_value":"AOYPI2WHZ64QVIKE","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_8","alias_value":"AOYPI2WH","created_at":"2026-07-04T17:25:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:AOYPI2WHZ64QVIKEJWW6J6AH25","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9303026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1993-03-20T19:27:00Z","cross_cats_sorted":[],"title_canon_sha256":"6442e6b577b65b05c0b02faf813528b485a52a64853c0658cbebf3f9f1a826d9","abstract_canon_sha256":"97c9a76bebc84bc5b3a9f4a35ccdeab37c0fe8e0d24b866e272b708c87f48d3e"},"schema_version":"1.0"},"canonical_sha256":"03b0f46ac7cfb90aa1444dade4f807d76660367e5e2703e807ea2a899651deea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:25:34.750419Z","signature_b64":"SsSrBsAtNxDxcM66bOsfzlr7XrkuwgeG4txcspt2/pNz/AqW0jVMss5exOHJqFhK0wtF/KDlGQsCPGP/+xAbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03b0f46ac7cfb90aa1444dade4f807d76660367e5e2703e807ea2a899651deea","last_reissued_at":"2026-07-04T17:25:34.749942Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:25:34.749942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9303026","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":"2026-07-04T17:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYI9Tjk0rEE1ZZGIVHl4Lh957p+xc+v6u7+kK5R1yNDm63CEkmCm9A6Y20dgFE4N2wuK65nTVaqH4Gmatd2WDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:18:24.960126Z"},"content_sha256":"5fff1a06a7c03efc03890d63ae6da1edcb02181b7d82fefb87d9a2f16e3b482d","schema_version":"1.0","event_id":"sha256:5fff1a06a7c03efc03890d63ae6da1edcb02181b7d82fefb87d9a2f16e3b482d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:AOYPI2WHZ64QVIKEJWW6J6AH25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique determination of an inner product by adjointness relations in the algebra of quantum observables","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Alan D. Rendall","submitted_at":"1993-03-20T19:27:00Z","abstract_excerpt":"It is shown that if a representation of a *-algebra on a vector space $V$ is an irreducible *-representation with respect to some inner product on $V$ then under appropriate technical conditions this property determines the inner product uniquely up to a constant factor. Ashtekar has suggested using the condition that a given representation of the algebra of quantum observables is a *-representation to fix the inner product on the space of physical states. This idea is of particular interest for the quantisation of gravity where an obvious prescription for defining an inner product is lacking."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9303026","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/9303026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFtTJF26W+8H1+O8TQkQ4CjXrhExmrSOXjoOCk+XIyk/xnl9BLk3iCcpDem+MKcYYio8k5jr5Y3pVLyiBLX+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:18:24.960503Z"},"content_sha256":"b196258b6b1b049f293c5f0eadefb5087a60d06f11b8ca2c061a03c74b1cd1d5","schema_version":"1.0","event_id":"sha256:b196258b6b1b049f293c5f0eadefb5087a60d06f11b8ca2c061a03c74b1cd1d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/bundle.json","state_url":"https://pith.science/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/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":"2026-07-05T04:18:24Z","links":{"resolver":"https://pith.science/pith/AOYPI2WHZ64QVIKEJWW6J6AH25","bundle":"https://pith.science/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/bundle.json","state":"https://pith.science/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOYPI2WHZ64QVIKEJWW6J6AH25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:AOYPI2WHZ64QVIKEJWW6J6AH25","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":"97c9a76bebc84bc5b3a9f4a35ccdeab37c0fe8e0d24b866e272b708c87f48d3e","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1993-03-20T19:27:00Z","title_canon_sha256":"6442e6b577b65b05c0b02faf813528b485a52a64853c0658cbebf3f9f1a826d9"},"schema_version":"1.0","source":{"id":"gr-qc/9303026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9303026","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9303026v1","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9303026","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"AOYPI2WHZ64Q","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_16","alias_value":"AOYPI2WHZ64QVIKE","created_at":"2026-07-04T17:25:34Z"},{"alias_kind":"pith_short_8","alias_value":"AOYPI2WH","created_at":"2026-07-04T17:25:34Z"}],"graph_snapshots":[{"event_id":"sha256:b196258b6b1b049f293c5f0eadefb5087a60d06f11b8ca2c061a03c74b1cd1d5","target":"graph","created_at":"2026-07-04T17:25:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/gr-qc/9303026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that if a representation of a *-algebra on a vector space $V$ is an irreducible *-representation with respect to some inner product on $V$ then under appropriate technical conditions this property determines the inner product uniquely up to a constant factor. Ashtekar has suggested using the condition that a given representation of the algebra of quantum observables is a *-representation to fix the inner product on the space of physical states. This idea is of particular interest for the quantisation of gravity where an obvious prescription for defining an inner product is lacking.","authors_text":"Alan D. Rendall","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1993-03-20T19:27:00Z","title":"Unique determination of an inner product by adjointness relations in the algebra of quantum observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9303026","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":"sha256:5fff1a06a7c03efc03890d63ae6da1edcb02181b7d82fefb87d9a2f16e3b482d","target":"record","created_at":"2026-07-04T17:25:34Z","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":"97c9a76bebc84bc5b3a9f4a35ccdeab37c0fe8e0d24b866e272b708c87f48d3e","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1993-03-20T19:27:00Z","title_canon_sha256":"6442e6b577b65b05c0b02faf813528b485a52a64853c0658cbebf3f9f1a826d9"},"schema_version":"1.0","source":{"id":"gr-qc/9303026","kind":"arxiv","version":1}},"canonical_sha256":"03b0f46ac7cfb90aa1444dade4f807d76660367e5e2703e807ea2a899651deea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03b0f46ac7cfb90aa1444dade4f807d76660367e5e2703e807ea2a899651deea","first_computed_at":"2026-07-04T17:25:34.749942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:25:34.749942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SsSrBsAtNxDxcM66bOsfzlr7XrkuwgeG4txcspt2/pNz/AqW0jVMss5exOHJqFhK0wtF/KDlGQsCPGP/+xAbBg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:25:34.750419Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9303026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fff1a06a7c03efc03890d63ae6da1edcb02181b7d82fefb87d9a2f16e3b482d","sha256:b196258b6b1b049f293c5f0eadefb5087a60d06f11b8ca2c061a03c74b1cd1d5"],"state_sha256":"b410355c1584f3618bad211c1b64d172a7504504ad1e5f26300a3514ac3df489"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSy3D9A0+cVg0ZzrLvY5fqDdHTLEZ9yqdy1lneULZI/PJYyyCqT76zo83VRNaCaKwtxVoM+RHJMmQiHkTPMfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T04:18:24.962255Z","bundle_sha256":"4009c1a45add13aaa0ed450ab14333c410c93f2c4ef123c36d77eac319918938"}}