{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:7DDURZY3YDGO5POPITSTE3V6AB","short_pith_number":"pith:7DDURZY3","canonical_record":{"source":{"id":"gr-qc/9311010","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1993-11-07T00:45:18Z","cross_cats_sorted":["alg-geom","hep-th","math.AG"],"title_canon_sha256":"28d04f11fc7670f0a96ebca54067bb991e0378f241ef4827a846f5aea7ff5b82","abstract_canon_sha256":"77a5d78ae7cdff1ef10619cacf0a1b6492c25a023f7fb3a821c5da9a262480a1"},"schema_version":"1.0"},"canonical_sha256":"f8c748e71bc0cceebdcf44e5326ebe00599129f56947bd9ace8e0555df309f9b","source":{"kind":"arxiv","id":"gr-qc/9311010","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9311010","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9311010v2","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9311010","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"7DDURZY3YDGO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7DDURZY3YDGO5POP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7DDURZY3","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:7DDURZY3YDGO5POPITSTE3V6AB","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9311010","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1993-11-07T00:45:18Z","cross_cats_sorted":["alg-geom","hep-th","math.AG"],"title_canon_sha256":"28d04f11fc7670f0a96ebca54067bb991e0378f241ef4827a846f5aea7ff5b82","abstract_canon_sha256":"77a5d78ae7cdff1ef10619cacf0a1b6492c25a023f7fb3a821c5da9a262480a1"},"schema_version":"1.0"},"canonical_sha256":"f8c748e71bc0cceebdcf44e5326ebe00599129f56947bd9ace8e0555df309f9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:45.273657Z","signature_b64":"2e4obEACRcxN/LQRgFrsGByoaWhTJcMGcjK6c1I5BTAfvmkn474/L///unPTVFRMZNk5D8BwOL7nP9Wo4tPYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8c748e71bc0cceebdcf44e5326ebe00599129f56947bd9ace8e0555df309f9b","last_reissued_at":"2026-05-18T01:06:45.273110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:45.273110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9311010","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQSrT1nzh+mKLAKUkr14Ctu3NfU3kqXS7AAelUycOXo5wLByDbMS2vCvlsMcACY4InsfXOmSZU+u3Isz0ojEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:39:31.206664Z"},"content_sha256":"492470d54b187c2fe5df71a7405b9785982aa1fea335ef06599bf85681c35fab","schema_version":"1.0","event_id":"sha256:492470d54b187c2fe5df71a7405b9785982aa1fea335ef06599bf85681c35fab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:7DDURZY3YDGO5POPITSTE3V6AB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representation Theory of Analytic Holonomy C* Algebras","license":"","headline":"","cross_cats":["alg-geom","hep-th","math.AG"],"primary_cat":"gr-qc","authors_text":"Abhay Ashtekar, Jerzy lewandowski","submitted_at":"1993-11-07T00:45:18Z","abstract_excerpt":"Integral calculus on the space  of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of connections.\n  The general setting is provided by the abelian C* algebra of functions on the quotient space of connections  generated by Wilson loops (i.e., by the traces of holonomies of connections around closed loops). The representation theory of this algebra leads to an interesting and powerful ``duality'' between gauge--equivalence classes of connections "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9311010","kind":"arxiv","version":2},"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":"2026-05-18T01:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qcoLYbCYdOE35Swn1XOOYrrntKU0FfPNTa4IdUrepsj+kM58zfb0pPXVMpThBKQZIhFWCfUmIdUPE/MgtJauCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:39:31.207063Z"},"content_sha256":"4b0f415dd68d5605ffa1956a1ff755c02c199cf6c2ef91ed7b8813e1d96223a0","schema_version":"1.0","event_id":"sha256:4b0f415dd68d5605ffa1956a1ff755c02c199cf6c2ef91ed7b8813e1d96223a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DDURZY3YDGO5POPITSTE3V6AB/bundle.json","state_url":"https://pith.science/pith/7DDURZY3YDGO5POPITSTE3V6AB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DDURZY3YDGO5POPITSTE3V6AB/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":"2026-05-26T16:39:31Z","links":{"resolver":"https://pith.science/pith/7DDURZY3YDGO5POPITSTE3V6AB","bundle":"https://pith.science/pith/7DDURZY3YDGO5POPITSTE3V6AB/bundle.json","state":"https://pith.science/pith/7DDURZY3YDGO5POPITSTE3V6AB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DDURZY3YDGO5POPITSTE3V6AB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:7DDURZY3YDGO5POPITSTE3V6AB","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":"77a5d78ae7cdff1ef10619cacf0a1b6492c25a023f7fb3a821c5da9a262480a1","cross_cats_sorted":["alg-geom","hep-th","math.AG"],"license":"","primary_cat":"gr-qc","submitted_at":"1993-11-07T00:45:18Z","title_canon_sha256":"28d04f11fc7670f0a96ebca54067bb991e0378f241ef4827a846f5aea7ff5b82"},"schema_version":"1.0","source":{"id":"gr-qc/9311010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9311010","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9311010v2","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9311010","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"7DDURZY3YDGO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7DDURZY3YDGO5POP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7DDURZY3","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:4b0f415dd68d5605ffa1956a1ff755c02c199cf6c2ef91ed7b8813e1d96223a0","target":"graph","created_at":"2026-05-18T01:06:45Z","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":"Integral calculus on the space  of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of connections.\n  The general setting is provided by the abelian C* algebra of functions on the quotient space of connections  generated by Wilson loops (i.e., by the traces of holonomies of connections around closed loops). The representation theory of this algebra leads to an interesting and powerful ``duality'' between gauge--equivalence classes of connections ","authors_text":"Abhay Ashtekar, Jerzy lewandowski","cross_cats":["alg-geom","hep-th","math.AG"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1993-11-07T00:45:18Z","title":"Representation Theory of Analytic Holonomy C* Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9311010","kind":"arxiv","version":2},"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":"sha256:492470d54b187c2fe5df71a7405b9785982aa1fea335ef06599bf85681c35fab","target":"record","created_at":"2026-05-18T01:06:45Z","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":"77a5d78ae7cdff1ef10619cacf0a1b6492c25a023f7fb3a821c5da9a262480a1","cross_cats_sorted":["alg-geom","hep-th","math.AG"],"license":"","primary_cat":"gr-qc","submitted_at":"1993-11-07T00:45:18Z","title_canon_sha256":"28d04f11fc7670f0a96ebca54067bb991e0378f241ef4827a846f5aea7ff5b82"},"schema_version":"1.0","source":{"id":"gr-qc/9311010","kind":"arxiv","version":2}},"canonical_sha256":"f8c748e71bc0cceebdcf44e5326ebe00599129f56947bd9ace8e0555df309f9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8c748e71bc0cceebdcf44e5326ebe00599129f56947bd9ace8e0555df309f9b","first_computed_at":"2026-05-18T01:06:45.273110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:45.273110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2e4obEACRcxN/LQRgFrsGByoaWhTJcMGcjK6c1I5BTAfvmkn474/L///unPTVFRMZNk5D8BwOL7nP9Wo4tPYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:45.273657Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9311010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:492470d54b187c2fe5df71a7405b9785982aa1fea335ef06599bf85681c35fab","sha256:4b0f415dd68d5605ffa1956a1ff755c02c199cf6c2ef91ed7b8813e1d96223a0"],"state_sha256":"9d898ad52384f330dadff6ed6ec218653892c6aba6fad8029ed616fffc54a8aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGISJVrPlWGWSrJ8BJH7J4D9v5hk3nXQGr30n/Deu8iz54WY4LXeFiuZ5sLmF2LreMq6T7aCk/xU1k8jyJE0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:39:31.209435Z","bundle_sha256":"f685d3a15fa3792307a859ce2396a056eb145777875768bae66fa8c7afcd6dbf"}}