{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DFSUY2WHJ5THN4YSXSNGVUH45C","short_pith_number":"pith:DFSUY2WH","canonical_record":{"source":{"id":"1112.5739","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-24T16:54:52Z","cross_cats_sorted":[],"title_canon_sha256":"b1ef63362e34c3404978b48a154dab7e9c98318a1c5d554683496b53e24071b4","abstract_canon_sha256":"96211287f7a22fee1edddd3a7798d5f17b9101c41ef0c879334efd43a54fec6e"},"schema_version":"1.0"},"canonical_sha256":"19654c6ac74f6676f312bc9a6ad0fce8991b1a2de176d8e7a92274223cbe1ae0","source":{"kind":"arxiv","id":"1112.5739","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5739","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5739v2","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5739","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"DFSUY2WHJ5TH","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFSUY2WHJ5THN4YS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFSUY2WH","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DFSUY2WHJ5THN4YSXSNGVUH45C","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5739","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-24T16:54:52Z","cross_cats_sorted":[],"title_canon_sha256":"b1ef63362e34c3404978b48a154dab7e9c98318a1c5d554683496b53e24071b4","abstract_canon_sha256":"96211287f7a22fee1edddd3a7798d5f17b9101c41ef0c879334efd43a54fec6e"},"schema_version":"1.0"},"canonical_sha256":"19654c6ac74f6676f312bc9a6ad0fce8991b1a2de176d8e7a92274223cbe1ae0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:53.600191Z","signature_b64":"FPcR2/E3aKJvfWJKLHx3mKfaBfonsZukNWWXBF9Jrpadtc5ayfL8xgVG1HUuWR2TmH9ufsYDuvthQnGKFGGSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19654c6ac74f6676f312bc9a6ad0fce8991b1a2de176d8e7a92274223cbe1ae0","last_reissued_at":"2026-05-18T03:22:53.599704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:53.599704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5739","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":"2026-05-18T03:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSQaR0aGMz9/RFxVhSGnRWtDi9aM0fmDq0OJgTGvdDXZ7V39x7Q5Poer+Sv39i4tUw7/EWX4aiBDFGe5JghnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:58:53.702790Z"},"content_sha256":"cf42d013cf9fbef79d39a8f1130f90ce430f2296ceabf0604b7bdfd72727f24e","schema_version":"1.0","event_id":"sha256:cf42d013cf9fbef79d39a8f1130f90ce430f2296ceabf0604b7bdfd72727f24e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DFSUY2WHJ5THN4YSXSNGVUH45C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The K\\\"all\\'en-Lehmann representation for Lorentz-violating field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Robertus Potting","submitted_at":"2011-12-24T16:54:52Z","abstract_excerpt":"We consider field-theoretic models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. We show that the exact propagators can be cast in the form of a K\\\"all\\'en-Lehmann representation. We work out the resulting form of the Feynman propagators and the equal-time field commutators, and derive sum rules for the spectral density functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5739","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":"2026-05-18T03:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9jqS06g4oZ+OSV1bT54VM4MDqhGkO7JO0aqOfxHWle/vJKZeg8fn4cfO489ieVYixVZlstrHKAUJUgD9+F1oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:58:53.703132Z"},"content_sha256":"fbfaf4da88baace37884184db76803d3acff38e7146d66c445804cfdbac66d14","schema_version":"1.0","event_id":"sha256:fbfaf4da88baace37884184db76803d3acff38e7146d66c445804cfdbac66d14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/bundle.json","state_url":"https://pith.science/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/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":"2026-07-07T09:58:53Z","links":{"resolver":"https://pith.science/pith/DFSUY2WHJ5THN4YSXSNGVUH45C","bundle":"https://pith.science/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/bundle.json","state":"https://pith.science/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFSUY2WHJ5THN4YSXSNGVUH45C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DFSUY2WHJ5THN4YSXSNGVUH45C","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":"96211287f7a22fee1edddd3a7798d5f17b9101c41ef0c879334efd43a54fec6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-24T16:54:52Z","title_canon_sha256":"b1ef63362e34c3404978b48a154dab7e9c98318a1c5d554683496b53e24071b4"},"schema_version":"1.0","source":{"id":"1112.5739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5739","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5739v2","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5739","created_at":"2026-05-18T03:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"DFSUY2WHJ5TH","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFSUY2WHJ5THN4YS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFSUY2WH","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:fbfaf4da88baace37884184db76803d3acff38e7146d66c445804cfdbac66d14","target":"graph","created_at":"2026-05-18T03:22:53Z","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 consider field-theoretic models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. We show that the exact propagators can be cast in the form of a K\\\"all\\'en-Lehmann representation. We work out the resulting form of the Feynman propagators and the equal-time field commutators, and derive sum rules for the spectral density functions.","authors_text":"Robertus Potting","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-24T16:54:52Z","title":"The K\\\"all\\'en-Lehmann representation for Lorentz-violating field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5739","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:cf42d013cf9fbef79d39a8f1130f90ce430f2296ceabf0604b7bdfd72727f24e","target":"record","created_at":"2026-05-18T03:22:53Z","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":"96211287f7a22fee1edddd3a7798d5f17b9101c41ef0c879334efd43a54fec6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-12-24T16:54:52Z","title_canon_sha256":"b1ef63362e34c3404978b48a154dab7e9c98318a1c5d554683496b53e24071b4"},"schema_version":"1.0","source":{"id":"1112.5739","kind":"arxiv","version":2}},"canonical_sha256":"19654c6ac74f6676f312bc9a6ad0fce8991b1a2de176d8e7a92274223cbe1ae0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19654c6ac74f6676f312bc9a6ad0fce8991b1a2de176d8e7a92274223cbe1ae0","first_computed_at":"2026-05-18T03:22:53.599704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:53.599704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FPcR2/E3aKJvfWJKLHx3mKfaBfonsZukNWWXBF9Jrpadtc5ayfL8xgVG1HUuWR2TmH9ufsYDuvthQnGKFGGSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:53.600191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf42d013cf9fbef79d39a8f1130f90ce430f2296ceabf0604b7bdfd72727f24e","sha256:fbfaf4da88baace37884184db76803d3acff38e7146d66c445804cfdbac66d14"],"state_sha256":"03bee73449f0399b882af2eecce4ac33c5a62fda3d5421ffa9f61516ebdbcdc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYbHZ3CxwJgOjzboLJomnRZOlsaMZX5NrjXampp64J7LCKXZXBr1HrqE1JCdeONR/fwQ9/PeOWRYzYpdsA7YAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:58:53.705651Z","bundle_sha256":"10464c074a6b21cb00193f2c97d7cf391a34070ac8c6da987cdc21d2bc19fc6f"}}