{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:GXRP6RQSPHU7B7PPTQ2BOQQAZN","short_pith_number":"pith:GXRP6RQS","canonical_record":{"source":{"id":"hep-th/9208054","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-08-21T19:13:00Z","cross_cats_sorted":[],"title_canon_sha256":"64809547c561c13f9767d756dccd592cf0ac98556a60f1fff5757521eef21a2a","abstract_canon_sha256":"cd241256ebf7b2788775266a59fb4a4e65bf9a543dafebcff07b2371cac0eb7e"},"schema_version":"1.0"},"canonical_sha256":"35e2ff461279e9f0fdef9c34174200cb42aef6be9f78ace9e35ed4e68e45d084","source":{"kind":"arxiv","id":"hep-th/9208054","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9208054","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9208054v2","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9208054","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"GXRP6RQSPHU7","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"GXRP6RQSPHU7B7PP","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"GXRP6RQS","created_at":"2026-07-04T15:55:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:GXRP6RQSPHU7B7PPTQ2BOQQAZN","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9208054","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-08-21T19:13:00Z","cross_cats_sorted":[],"title_canon_sha256":"64809547c561c13f9767d756dccd592cf0ac98556a60f1fff5757521eef21a2a","abstract_canon_sha256":"cd241256ebf7b2788775266a59fb4a4e65bf9a543dafebcff07b2371cac0eb7e"},"schema_version":"1.0"},"canonical_sha256":"35e2ff461279e9f0fdef9c34174200cb42aef6be9f78ace9e35ed4e68e45d084","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:55:24.233219Z","signature_b64":"yDvgSG/ZtS902AUZ/G51lfnvzk91XyH1pLB1OyAaCDAv+yBLArhD8xJoyAMymSL62YEdp/Q+SG8I2hhoiCTpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e2ff461279e9f0fdef9c34174200cb42aef6be9f78ace9e35ed4e68e45d084","last_reissued_at":"2026-07-04T15:55:24.232859Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:55:24.232859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9208054","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":"2026-07-04T15:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uT1RbV6akdC/t70AHjCBH4nlSoBXUc7zzFGF71r5iAm9nP9GpC/atxwIaVsuceWsCIYm9bilG9aRSJtbTNxiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:00:57.789276Z"},"content_sha256":"3d9e053fe8733bf9b2cc8c6b654ccad631c8b8c39ec0f5ca4f9a39a230597fa5","schema_version":"1.0","event_id":"sha256:3d9e053fe8733bf9b2cc8c6b654ccad631c8b8c39ec0f5ca4f9a39a230597fa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:GXRP6RQSPHU7B7PPTQ2BOQQAZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuum Limits of ``Induced QCD\": Lessons of the Gaussian Model at d=1 and Beyond","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Morozov, G.W. Semenoff, I.I. Kogan, N. Weiss","submitted_at":"1992-08-21T19:13:00Z","abstract_excerpt":"We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\\rightarrow\\infty$, only the conventional large-$N$ limit is relevant for its {\\it continuum} limit. We also give a mean--field analysis of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9208054","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9208054/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":"2026-07-04T15:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4r0LmuQAvettC3Uwi0NCC4kDDU6r0+O9I41v7aCNgY1GuwgI7AJJl7oJqzzPG/a343Afbr6xNBsMJR9YR7JECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:00:57.789665Z"},"content_sha256":"7d048a63c1dfe73524e0b83e6ff9e7a48740697925bda44cba9fbc95c2221cb8","schema_version":"1.0","event_id":"sha256:7d048a63c1dfe73524e0b83e6ff9e7a48740697925bda44cba9fbc95c2221cb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/bundle.json","state_url":"https://pith.science/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/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":"2026-07-05T03:00:57Z","links":{"resolver":"https://pith.science/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN","bundle":"https://pith.science/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/bundle.json","state":"https://pith.science/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXRP6RQSPHU7B7PPTQ2BOQQAZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:GXRP6RQSPHU7B7PPTQ2BOQQAZN","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":"cd241256ebf7b2788775266a59fb4a4e65bf9a543dafebcff07b2371cac0eb7e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-08-21T19:13:00Z","title_canon_sha256":"64809547c561c13f9767d756dccd592cf0ac98556a60f1fff5757521eef21a2a"},"schema_version":"1.0","source":{"id":"hep-th/9208054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9208054","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9208054v2","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9208054","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"GXRP6RQSPHU7","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"GXRP6RQSPHU7B7PP","created_at":"2026-07-04T15:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"GXRP6RQS","created_at":"2026-07-04T15:55:24Z"}],"graph_snapshots":[{"event_id":"sha256:7d048a63c1dfe73524e0b83e6ff9e7a48740697925bda44cba9fbc95c2221cb8","target":"graph","created_at":"2026-07-04T15:55:24Z","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/hep-th/9208054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\\rightarrow\\infty$, only the conventional large-$N$ limit is relevant for its {\\it continuum} limit. We also give a mean--field analysis of ","authors_text":"A. Morozov, G.W. Semenoff, I.I. Kogan, N. Weiss","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1992-08-21T19:13:00Z","title":"Continuum Limits of ``Induced QCD\": Lessons of the Gaussian Model at d=1 and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9208054","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":"sha256:3d9e053fe8733bf9b2cc8c6b654ccad631c8b8c39ec0f5ca4f9a39a230597fa5","target":"record","created_at":"2026-07-04T15:55:24Z","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":"cd241256ebf7b2788775266a59fb4a4e65bf9a543dafebcff07b2371cac0eb7e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-08-21T19:13:00Z","title_canon_sha256":"64809547c561c13f9767d756dccd592cf0ac98556a60f1fff5757521eef21a2a"},"schema_version":"1.0","source":{"id":"hep-th/9208054","kind":"arxiv","version":2}},"canonical_sha256":"35e2ff461279e9f0fdef9c34174200cb42aef6be9f78ace9e35ed4e68e45d084","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e2ff461279e9f0fdef9c34174200cb42aef6be9f78ace9e35ed4e68e45d084","first_computed_at":"2026-07-04T15:55:24.232859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:55:24.232859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yDvgSG/ZtS902AUZ/G51lfnvzk91XyH1pLB1OyAaCDAv+yBLArhD8xJoyAMymSL62YEdp/Q+SG8I2hhoiCTpCA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:55:24.233219Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9208054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d9e053fe8733bf9b2cc8c6b654ccad631c8b8c39ec0f5ca4f9a39a230597fa5","sha256:7d048a63c1dfe73524e0b83e6ff9e7a48740697925bda44cba9fbc95c2221cb8"],"state_sha256":"b18a8197cf5d5388df8d02d1b93f55b529ae8f89ac019f660a9ed596d358cf46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqP6e27xcyA5PSlOCw2+u9jX2L1Zdi3wf1IgXEC/GsuWdTby0+MhZvege8EUgIXnGWTgtToEG3R/Mr5eJVPuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T03:00:57.791595Z","bundle_sha256":"955a8f3524538e6844b16f0f5479b7b3215760a15428697e7d6e69b7a3ce1fa7"}}