{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WQNHMZXMXV4BBVDPDJW2WCYLDD","short_pith_number":"pith:WQNHMZXM","canonical_record":{"source":{"id":"2604.26941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-29T17:52:04Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2d1e6fb901868dadb5966479fdff3971ebbba17ec76c07ece52bc7c10491d3bd","abstract_canon_sha256":"32bfa902ff9ea4168649150dea5d9c3d241299d063725de3c86f9718475703dc"},"schema_version":"1.0"},"canonical_sha256":"b41a7666ecbd7810d46f1a6dab0b0b18f99f156f6e0ea29f5416111bd8a6f2f4","source":{"kind":"arxiv","id":"2604.26941","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.26941","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"2604.26941v2","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.26941","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"WQNHMZXMXV4B","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_16","alias_value":"WQNHMZXMXV4BBVDP","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_8","alias_value":"WQNHMZXM","created_at":"2026-05-25T02:02:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WQNHMZXMXV4BBVDPDJW2WCYLDD","target":"record","payload":{"canonical_record":{"source":{"id":"2604.26941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-29T17:52:04Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2d1e6fb901868dadb5966479fdff3971ebbba17ec76c07ece52bc7c10491d3bd","abstract_canon_sha256":"32bfa902ff9ea4168649150dea5d9c3d241299d063725de3c86f9718475703dc"},"schema_version":"1.0"},"canonical_sha256":"b41a7666ecbd7810d46f1a6dab0b0b18f99f156f6e0ea29f5416111bd8a6f2f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:15.896622Z","signature_b64":"Wd4rg2DOp4TECuTjoRlQgg2q/3rgT50EcA216u+jDY3TpYdQTT6gPIJtrXYgfKdQDbrm322flKlSC21xOpEYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b41a7666ecbd7810d46f1a6dab0b0b18f99f156f6e0ea29f5416111bd8a6f2f4","last_reissued_at":"2026-05-25T02:02:15.895971Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:15.895971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.26941","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":"2026-05-25T02:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cl5xgATLnP7ytBFLh+5dep88YHM2KSkwYZ16ZekcjU5fT4U4NWClR/7KpyGcfkeaL1gBK5YqOojSZsQcFiu9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:09:42.268264Z"},"content_sha256":"b762b475d79d1186f4eb6687b9a494124e528cfbecf8d3648c19927748cd6d6f","schema_version":"1.0","event_id":"sha256:b762b475d79d1186f4eb6687b9a494124e528cfbecf8d3648c19927748cd6d6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WQNHMZXMXV4BBVDPDJW2WCYLDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schwinger-Keldysh Path Integral for Gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state.","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Andrew J. Tolley, Greg Kaplanek, Maria Mylova","submitted_at":"2026-04-29T17:52:04Z","abstract_excerpt":"We develop the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that are gauge-fixed via the BRST method in covariant gauges. We focus on generic initial states, pure and mixed, specified at finite times suitable for non-equilibrium processes. We pay particular attention to the handling of the indefinite Hilbert space, the construction of BRST-invariant Schrodinger picture wavefunctionals, density matrices and inner product, the implementation of the Hata-Kugo prescription, and the role of boundary terms at both the initial and final times. We highlight the advanta"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The construction assumes that the indefinite Hilbert space and boundary terms at initial and final times can be handled via the Hata-Kugo prescription and Nakanishi-Lautrup fields without introducing inconsistencies for generic mixed states; non-perturbative Gribov ambiguity is acknowledged to potentially break the symmetry but is set aside.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A manifestly BRST-invariant Schwinger-Keldysh path integral is derived for non-Abelian gauge theories with generic initial states, enabling perturbative Ward-Takahashi-Slavnov-Taylor identities and Open EFT expansions that preserve a contracted Keldysh BRST symmetry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e1005b9f2bb1690faabeb99abc8d45340d71e24add22c7cdd7439747d7eb14b4"},"source":{"id":"2604.26941","kind":"arxiv","version":2},"verdict":{"id":"e077c630-8b0e-45f9-9ac1-25c0a7659772","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T08:28:29.902238Z","strongest_claim":"The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively.","one_line_summary":"A manifestly BRST-invariant Schwinger-Keldysh path integral is derived for non-Abelian gauge theories with generic initial states, enabling perturbative Ward-Takahashi-Slavnov-Taylor identities and Open EFT expansions that preserve a contracted Keldysh BRST symmetry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The construction assumes that the indefinite Hilbert space and boundary terms at initial and final times can be handled via the Hata-Kugo prescription and Nakanishi-Lautrup fields without introducing inconsistencies for generic mixed states; non-perturbative Gribov ambiguity is acknowledged to potentially break the symmetry but is set aside.","pith_extraction_headline":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26941/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:36:30.523383Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:41:42.688847Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"5f805e44b94e60684830e760e492b4bcc7d5ae99d8d990bebb87de63529a0b59"},"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":"e077c630-8b0e-45f9-9ac1-25c0a7659772"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"174U3n9skfz1EfxYSbe7ACWsAX7xiat8jISjMi1ip2/kQw0dgFIRJ5pn5T35TnrWJ3kRbcf3KoNSnfkyyVRkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:09:42.269163Z"},"content_sha256":"ad02d5a46c023c74f7c7337f0b3e328dd9c9199b13c30c7d4ab6368782785aa3","schema_version":"1.0","event_id":"sha256:ad02d5a46c023c74f7c7337f0b3e328dd9c9199b13c30c7d4ab6368782785aa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/bundle.json","state_url":"https://pith.science/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/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":"2026-06-09T21:09:42Z","links":{"resolver":"https://pith.science/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD","bundle":"https://pith.science/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/bundle.json","state":"https://pith.science/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQNHMZXMXV4BBVDPDJW2WCYLDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WQNHMZXMXV4BBVDPDJW2WCYLDD","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":"32bfa902ff9ea4168649150dea5d9c3d241299d063725de3c86f9718475703dc","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-29T17:52:04Z","title_canon_sha256":"2d1e6fb901868dadb5966479fdff3971ebbba17ec76c07ece52bc7c10491d3bd"},"schema_version":"1.0","source":{"id":"2604.26941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.26941","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"2604.26941v2","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.26941","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"WQNHMZXMXV4B","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_16","alias_value":"WQNHMZXMXV4BBVDP","created_at":"2026-05-25T02:02:15Z"},{"alias_kind":"pith_short_8","alias_value":"WQNHMZXM","created_at":"2026-05-25T02:02:15Z"}],"graph_snapshots":[{"event_id":"sha256:ad02d5a46c023c74f7c7337f0b3e328dd9c9199b13c30c7d4ab6368782785aa3","target":"graph","created_at":"2026-05-25T02:02:15Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The construction assumes that the indefinite Hilbert space and boundary terms at initial and final times can be handled via the Hata-Kugo prescription and Nakanishi-Lautrup fields without introducing inconsistencies for generic mixed states; non-perturbative Gribov ambiguity is acknowledged to potentially break the symmetry but is set aside."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A manifestly BRST-invariant Schwinger-Keldysh path integral is derived for non-Abelian gauge theories with generic initial states, enabling perturbative Ward-Takahashi-Slavnov-Taylor identities and Open EFT expansions that preserve a contracted Keldysh BRST symmetry."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state."}],"snapshot_sha256":"e1005b9f2bb1690faabeb99abc8d45340d71e24add22c7cdd7439747d7eb14b4"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T23:36:30.523383Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T19:41:42.688847Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.26941/integrity.json","findings":[],"snapshot_sha256":"5f805e44b94e60684830e760e492b4bcc7d5ae99d8d990bebb87de63529a0b59","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the Schwinger-Keldysh path-integral formalism for open non-Abelian gauge theories that are gauge-fixed via the BRST method in covariant gauges. We focus on generic initial states, pure and mixed, specified at finite times suitable for non-equilibrium processes. We pay particular attention to the handling of the indefinite Hilbert space, the construction of BRST-invariant Schrodinger picture wavefunctionals, density matrices and inner product, the implementation of the Hata-Kugo prescription, and the role of boundary terms at both the initial and final times. We highlight the advanta","authors_text":"Andrew J. Tolley, Greg Kaplanek, Maria Mylova","cross_cats":["quant-ph"],"headline":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-29T17:52:04Z","title":"Schwinger-Keldysh Path Integral for Gauge theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.26941","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T08:28:29.902238Z","id":"e077c630-8b0e-45f9-9ac1-25c0a7659772","model_set":{"reader":"grok-4.3"},"one_line_summary":"A manifestly BRST-invariant Schwinger-Keldysh path integral is derived for non-Abelian gauge theories with generic initial states, enabling perturbative Ward-Takahashi-Slavnov-Taylor identities and Open EFT expansions that preserve a contracted Keldysh BRST symmetry.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Schwinger-Keldysh path integrals for non-Abelian gauge theories preserve a retarded BRST symmetry for any initial state.","strongest_claim":"The resulting Schwinger-Keldysh path integral is manifestly invariant under a diagonal (retarded) BRST symmetry for arbitrary physical initial states, whether pure or mixed. From this, we obtain the corresponding Ward-Takahashi-Slavnov-Taylor identities, valid perturbatively.","weakest_assumption":"The construction assumes that the indefinite Hilbert space and boundary terms at initial and final times can be handled via the Hata-Kugo prescription and Nakanishi-Lautrup fields without introducing inconsistencies for generic mixed states; non-perturbative Gribov ambiguity is acknowledged to potentially break the symmetry but is set aside."}},"verdict_id":"e077c630-8b0e-45f9-9ac1-25c0a7659772"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b762b475d79d1186f4eb6687b9a494124e528cfbecf8d3648c19927748cd6d6f","target":"record","created_at":"2026-05-25T02:02:15Z","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":"32bfa902ff9ea4168649150dea5d9c3d241299d063725de3c86f9718475703dc","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-29T17:52:04Z","title_canon_sha256":"2d1e6fb901868dadb5966479fdff3971ebbba17ec76c07ece52bc7c10491d3bd"},"schema_version":"1.0","source":{"id":"2604.26941","kind":"arxiv","version":2}},"canonical_sha256":"b41a7666ecbd7810d46f1a6dab0b0b18f99f156f6e0ea29f5416111bd8a6f2f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41a7666ecbd7810d46f1a6dab0b0b18f99f156f6e0ea29f5416111bd8a6f2f4","first_computed_at":"2026-05-25T02:02:15.895971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:15.895971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wd4rg2DOp4TECuTjoRlQgg2q/3rgT50EcA216u+jDY3TpYdQTT6gPIJtrXYgfKdQDbrm322flKlSC21xOpEYAQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:15.896622Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.26941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b762b475d79d1186f4eb6687b9a494124e528cfbecf8d3648c19927748cd6d6f","sha256:ad02d5a46c023c74f7c7337f0b3e328dd9c9199b13c30c7d4ab6368782785aa3"],"state_sha256":"da29eeba1a7eaaf716befee3d4f5adfd1f302684279916633e7950526b5f46a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aGaDaN3hKXbuK89w7Gro47QvDZHYvVP86EVic4HVobPJj3o3xZw1ZIw62GS0HVmLTm0o+9nf2t8twRXFr/mDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:09:42.273248Z","bundle_sha256":"aa5fe91550ba7c2c9c3d5454e04c5bb708e949a3411b7bd0d519eaa827630118"}}