{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:I2DB7HOHHE7STZKLCZB5XXLY34","short_pith_number":"pith:I2DB7HOH","canonical_record":{"source":{"id":"2606.23088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-22T09:33:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eaf2e42224dbecd46831812eddf021765830950ce39ff742f5360c92f60a523b","abstract_canon_sha256":"1251a72f090fdbc40c49f671a7fc4a6fc026d35730cd17e6f2f6cfa171876059"},"schema_version":"1.0"},"canonical_sha256":"46861f9dc7393f29e54b1643dbdd78df03d5bac8350f014bfeba29c2bf7e8229","source":{"kind":"arxiv","id":"2606.23088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23088","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23088v1","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23088","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"I2DB7HOHHE7S","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_16","alias_value":"I2DB7HOHHE7STZKL","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_8","alias_value":"I2DB7HOH","created_at":"2026-06-23T03:14:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:I2DB7HOHHE7STZKLCZB5XXLY34","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-22T09:33:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eaf2e42224dbecd46831812eddf021765830950ce39ff742f5360c92f60a523b","abstract_canon_sha256":"1251a72f090fdbc40c49f671a7fc4a6fc026d35730cd17e6f2f6cfa171876059"},"schema_version":"1.0"},"canonical_sha256":"46861f9dc7393f29e54b1643dbdd78df03d5bac8350f014bfeba29c2bf7e8229","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:09.529551Z","signature_b64":"O5u+Sbk26oROe7rq8mOVqFuRF+Uqowjcz6RjTavHwoEm8kH/8TwDBsJ9qpWTWo2JsHAvXDTpIW4CLcfLxLdSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46861f9dc7393f29e54b1643dbdd78df03d5bac8350f014bfeba29c2bf7e8229","last_reissued_at":"2026-06-23T03:14:09.529154Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:09.529154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23088","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":"2026-06-23T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYLTHsSV+9QZLXertPhsuZPXJ0LH03VarZ0Q06CJkohtromk9BZsEAKdUxATGvckzTID//hIxW6lcFUtmU+bBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:17:57.778817Z"},"content_sha256":"986a2b58ed65e253924401241b764b06836d17526174424d0197c6509b0ccfa5","schema_version":"1.0","event_id":"sha256:986a2b58ed65e253924401241b764b06836d17526174424d0197c6509b0ccfa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:I2DB7HOHHE7STZKLCZB5XXLY34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On background fields and a cutoff in sigma models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"N. V. Kharuk","submitted_at":"2026-06-22T09:33:56Z","abstract_excerpt":"In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the construction of the generating functional by introducing a background field. Furthermore, we perform a one-loop renormalization of the quantum action, calculate power-law singularities in the two-loop approximation, and consider transition to an extended classical action. Finally, we study the consistency of the cutoff with special f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23088","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/2606.23088/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":"2026-06-23T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b17sy470vEtiv2tmr1+H7n8LDrMGJV4gQ2jdUaCXjUeI8HxZ9bejlXPhu0I+XbWAs9fRg7oA4V4QR0evkkEGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:17:57.779422Z"},"content_sha256":"e75fcf8f440409d8b444b16075ef82f9a76ba3f50f30445a518a20fa6b9004cd","schema_version":"1.0","event_id":"sha256:e75fcf8f440409d8b444b16075ef82f9a76ba3f50f30445a518a20fa6b9004cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2DB7HOHHE7STZKLCZB5XXLY34/bundle.json","state_url":"https://pith.science/pith/I2DB7HOHHE7STZKLCZB5XXLY34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2DB7HOHHE7STZKLCZB5XXLY34/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":"2026-06-24T15:17:57Z","links":{"resolver":"https://pith.science/pith/I2DB7HOHHE7STZKLCZB5XXLY34","bundle":"https://pith.science/pith/I2DB7HOHHE7STZKLCZB5XXLY34/bundle.json","state":"https://pith.science/pith/I2DB7HOHHE7STZKLCZB5XXLY34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2DB7HOHHE7STZKLCZB5XXLY34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I2DB7HOHHE7STZKLCZB5XXLY34","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":"1251a72f090fdbc40c49f671a7fc4a6fc026d35730cd17e6f2f6cfa171876059","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-22T09:33:56Z","title_canon_sha256":"eaf2e42224dbecd46831812eddf021765830950ce39ff742f5360c92f60a523b"},"schema_version":"1.0","source":{"id":"2606.23088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23088","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23088v1","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23088","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"I2DB7HOHHE7S","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_16","alias_value":"I2DB7HOHHE7STZKL","created_at":"2026-06-23T03:14:09Z"},{"alias_kind":"pith_short_8","alias_value":"I2DB7HOH","created_at":"2026-06-23T03:14:09Z"}],"graph_snapshots":[{"event_id":"sha256:e75fcf8f440409d8b444b16075ef82f9a76ba3f50f30445a518a20fa6b9004cd","target":"graph","created_at":"2026-06-23T03:14:09Z","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/2606.23088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the construction of the generating functional by introducing a background field. Furthermore, we perform a one-loop renormalization of the quantum action, calculate power-law singularities in the two-loop approximation, and consider transition to an extended classical action. Finally, we study the consistency of the cutoff with special f","authors_text":"N. V. Kharuk","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-22T09:33:56Z","title":"On background fields and a cutoff in sigma models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23088","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":"sha256:986a2b58ed65e253924401241b764b06836d17526174424d0197c6509b0ccfa5","target":"record","created_at":"2026-06-23T03:14:09Z","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":"1251a72f090fdbc40c49f671a7fc4a6fc026d35730cd17e6f2f6cfa171876059","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-06-22T09:33:56Z","title_canon_sha256":"eaf2e42224dbecd46831812eddf021765830950ce39ff742f5360c92f60a523b"},"schema_version":"1.0","source":{"id":"2606.23088","kind":"arxiv","version":1}},"canonical_sha256":"46861f9dc7393f29e54b1643dbdd78df03d5bac8350f014bfeba29c2bf7e8229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46861f9dc7393f29e54b1643dbdd78df03d5bac8350f014bfeba29c2bf7e8229","first_computed_at":"2026-06-23T03:14:09.529154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:09.529154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5u+Sbk26oROe7rq8mOVqFuRF+Uqowjcz6RjTavHwoEm8kH/8TwDBsJ9qpWTWo2JsHAvXDTpIW4CLcfLxLdSBQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:09.529551Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:986a2b58ed65e253924401241b764b06836d17526174424d0197c6509b0ccfa5","sha256:e75fcf8f440409d8b444b16075ef82f9a76ba3f50f30445a518a20fa6b9004cd"],"state_sha256":"16878d2456c1b75f861e7d943c6446c3eb90061e447837a035acdcf2b8ba58cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6WYLMSes0stHW5Q4Iedsy3DTJm+ICA6U3szvsVHE5fEU1r3JFzI15FBzb60zsJGXL/7SegScShyQnw05Le4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:17:57.782118Z","bundle_sha256":"3f462850b6a758f2c2aaad4b0f14c06bea5e10b2b79c7f74a29056f4b5d1f9f6"}}