{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:YP6ACGYIMMPIH7OIUHACIRLTBE","short_pith_number":"pith:YP6ACGYI","canonical_record":{"source":{"id":"0705.3340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-05-23T11:33:38Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"6521bc6ba31c1f8300cc3cd43d0f4ced28b33a23a9b21b1b86e172612c28278a","abstract_canon_sha256":"157bddbc44a7d516b56ba3bbf753cdce13a8d2ffb8e038cd8024a911a1568acb"},"schema_version":"1.0"},"canonical_sha256":"c3fc011b08631e83fdc8a1c02445730905e151845ee43a8289eee729a3a08c7d","source":{"kind":"arxiv","id":"0705.3340","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3340","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3340v4","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3340","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"YP6ACGYIMMPI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YP6ACGYIMMPIH7OI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YP6ACGYI","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:YP6ACGYIMMPIH7OIUHACIRLTBE","target":"record","payload":{"canonical_record":{"source":{"id":"0705.3340","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-05-23T11:33:38Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"6521bc6ba31c1f8300cc3cd43d0f4ced28b33a23a9b21b1b86e172612c28278a","abstract_canon_sha256":"157bddbc44a7d516b56ba3bbf753cdce13a8d2ffb8e038cd8024a911a1568acb"},"schema_version":"1.0"},"canonical_sha256":"c3fc011b08631e83fdc8a1c02445730905e151845ee43a8289eee729a3a08c7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:05.503834Z","signature_b64":"cogQxOYw9ogl1j6hllHhPsD4sb7U0o1IAzNSz+Neo9ZicgYmXasuYeUuC0e6plWIEOah1yHvEd+FOnPATMRPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3fc011b08631e83fdc8a1c02445730905e151845ee43a8289eee729a3a08c7d","last_reissued_at":"2026-05-18T00:21:05.503278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:05.503278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.3340","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5exchgmemYgoi1hmx0HU9XvDyD5nEd9FXa6mCgGtcdRaUrXMatnpQJFxMK4JrQQOsmFp5/1dLPMSbdVVwF0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:06:26.464192Z"},"content_sha256":"ed1ed988e4a7d65b6e429a383b9e82df19302902cf5fe85ac56eee383c206206","schema_version":"1.0","event_id":"sha256:ed1ed988e4a7d65b6e429a383b9e82df19302902cf5fe85ac56eee383c206206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:YP6ACGYIMMPIH7OIUHACIRLTBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renormalized Quantum Yang-Mills Fields in Curved Spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Stefan Hollands","submitted_at":"2007-05-23T11:33:38Z","abstract_excerpt":"We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3340","kind":"arxiv","version":4},"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":"2026-05-18T00:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7enNLnMrMbCNVQmNm+CgDk5kjVh/BwMQRGsQnsJOaCjG/R1kOAEsw9tP7DKIvR2dbtv8Ht4mhRZ89nLtBoHbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:06:26.464640Z"},"content_sha256":"04892a16e82167953bcd828b2bde869c6e115da5d47b7ee9e0772b9a14fae199","schema_version":"1.0","event_id":"sha256:04892a16e82167953bcd828b2bde869c6e115da5d47b7ee9e0772b9a14fae199"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/bundle.json","state_url":"https://pith.science/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/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":"2026-08-14T23:06:26Z","links":{"resolver":"https://pith.science/pith/YP6ACGYIMMPIH7OIUHACIRLTBE","bundle":"https://pith.science/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/bundle.json","state":"https://pith.science/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YP6ACGYIMMPIH7OIUHACIRLTBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:YP6ACGYIMMPIH7OIUHACIRLTBE","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":"157bddbc44a7d516b56ba3bbf753cdce13a8d2ffb8e038cd8024a911a1568acb","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-05-23T11:33:38Z","title_canon_sha256":"6521bc6ba31c1f8300cc3cd43d0f4ced28b33a23a9b21b1b86e172612c28278a"},"schema_version":"1.0","source":{"id":"0705.3340","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3340","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3340v4","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3340","created_at":"2026-05-18T00:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"YP6ACGYIMMPI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YP6ACGYIMMPIH7OI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YP6ACGYI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:04892a16e82167953bcd828b2bde869c6e115da5d47b7ee9e0772b9a14fae199","target":"graph","created_at":"2026-05-18T00:21:05Z","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 present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be ","authors_text":"Stefan Hollands","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-05-23T11:33:38Z","title":"Renormalized Quantum Yang-Mills Fields in Curved Spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3340","kind":"arxiv","version":4},"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:ed1ed988e4a7d65b6e429a383b9e82df19302902cf5fe85ac56eee383c206206","target":"record","created_at":"2026-05-18T00:21:05Z","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":"157bddbc44a7d516b56ba3bbf753cdce13a8d2ffb8e038cd8024a911a1568acb","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-05-23T11:33:38Z","title_canon_sha256":"6521bc6ba31c1f8300cc3cd43d0f4ced28b33a23a9b21b1b86e172612c28278a"},"schema_version":"1.0","source":{"id":"0705.3340","kind":"arxiv","version":4}},"canonical_sha256":"c3fc011b08631e83fdc8a1c02445730905e151845ee43a8289eee729a3a08c7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3fc011b08631e83fdc8a1c02445730905e151845ee43a8289eee729a3a08c7d","first_computed_at":"2026-05-18T00:21:05.503278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:05.503278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cogQxOYw9ogl1j6hllHhPsD4sb7U0o1IAzNSz+Neo9ZicgYmXasuYeUuC0e6plWIEOah1yHvEd+FOnPATMRPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:05.503834Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.3340","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1ed988e4a7d65b6e429a383b9e82df19302902cf5fe85ac56eee383c206206","sha256:04892a16e82167953bcd828b2bde869c6e115da5d47b7ee9e0772b9a14fae199"],"state_sha256":"47dee1b58309119c26f238a8a74c9075b576066e95168a74acaa686a5e3844e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oy4yFqF5w97yGu784xXccz1pLTKQyPNmK5c+dgdZk3/XkpR1M7iEyS0rNoZD987v2QqrP24h/29Oyi4vX80CCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:06:26.468020Z","bundle_sha256":"c3b28f44e5843bd114ac9292abc05601f8b683ea9c5df3ab58ce6c56ea01c35e"}}