{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:DQQEYSHG7MC7BI5TQIGKC3GQBW","short_pith_number":"pith:DQQEYSHG","canonical_record":{"source":{"id":"hep-th/9512087","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-12-12T20:01:52Z","cross_cats_sorted":["cond-mat"],"title_canon_sha256":"b3f915311ce85c3783beb710082935711d014f197150587feb15101a6d5d9c4e","abstract_canon_sha256":"3e4b462a3330de763fabeadceb8525cbdf63c3bac7fe88e1da98d85136409f21"},"schema_version":"1.0"},"canonical_sha256":"1c204c48e6fb05f0a3b3820ca16cd00dbf765e875f787285d8b11e988c466cda","source":{"kind":"arxiv","id":"hep-th/9512087","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9512087","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9512087v2","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9512087","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"DQQEYSHG7MC7","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_16","alias_value":"DQQEYSHG7MC7BI5T","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_8","alias_value":"DQQEYSHG","created_at":"2026-07-04T15:59:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:DQQEYSHG7MC7BI5TQIGKC3GQBW","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9512087","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-12-12T20:01:52Z","cross_cats_sorted":["cond-mat"],"title_canon_sha256":"b3f915311ce85c3783beb710082935711d014f197150587feb15101a6d5d9c4e","abstract_canon_sha256":"3e4b462a3330de763fabeadceb8525cbdf63c3bac7fe88e1da98d85136409f21"},"schema_version":"1.0"},"canonical_sha256":"1c204c48e6fb05f0a3b3820ca16cd00dbf765e875f787285d8b11e988c466cda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:59:48.014597Z","signature_b64":"dKpvnLEOEbCTYiY/k+5X7/mbqcXqJQtwqaWjDA+USHBm/14yF8pvXYzMv3f8MonZmINvTsF6VlrhgBYdaDJ3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c204c48e6fb05f0a3b3820ca16cd00dbf765e875f787285d8b11e988c466cda","last_reissued_at":"2026-07-04T15:59:48.014235Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:59:48.014235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9512087","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":"2026-07-04T15:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/Au2xwBffVMe83uD7FOXkc7xkc42NqSVWlUb+zGd+QJ8jhG2wEMUabZ8UCCDo2iFUczRC7EG2slTAGNMZF4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T21:25:51.950652Z"},"content_sha256":"3840756cf32997df550f43778cb36aa9a93a923d61b2c1b6868b692b12baa8a0","schema_version":"1.0","event_id":"sha256:3840756cf32997df550f43778cb36aa9a93a923d61b2c1b6868b692b12baa8a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:DQQEYSHG7MC7BI5TQIGKC3GQBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomly coupled minimal models","license":"","headline":"","cross_cats":["cond-mat"],"primary_cat":"hep-th","authors_text":"Marco Picco, Pierre Pujol, Vladimir Dotsenko","submitted_at":"1995-12-12T20:01:52Z","abstract_excerpt":"Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9512087","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/9512087/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":"2026-07-04T15:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KcyN+gcUz9/UCbF4gTXdCQF7SBMVPFKhAmxs1YAMoXO4hhbHTuTnzFbOlLzJDUBWOB54BBCoZL56tnXctkCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T21:25:51.951353Z"},"content_sha256":"0e0c490f5fcf2ec23b98d9ea315a71a3825bd2792ccb0b76ff7cc717bd582883","schema_version":"1.0","event_id":"sha256:0e0c490f5fcf2ec23b98d9ea315a71a3825bd2792ccb0b76ff7cc717bd582883"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/bundle.json","state_url":"https://pith.science/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/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":"2026-08-20T21:25:51Z","links":{"resolver":"https://pith.science/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW","bundle":"https://pith.science/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/bundle.json","state":"https://pith.science/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQQEYSHG7MC7BI5TQIGKC3GQBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:DQQEYSHG7MC7BI5TQIGKC3GQBW","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":"3e4b462a3330de763fabeadceb8525cbdf63c3bac7fe88e1da98d85136409f21","cross_cats_sorted":["cond-mat"],"license":"","primary_cat":"hep-th","submitted_at":"1995-12-12T20:01:52Z","title_canon_sha256":"b3f915311ce85c3783beb710082935711d014f197150587feb15101a6d5d9c4e"},"schema_version":"1.0","source":{"id":"hep-th/9512087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9512087","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9512087v2","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9512087","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"DQQEYSHG7MC7","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_16","alias_value":"DQQEYSHG7MC7BI5T","created_at":"2026-07-04T15:59:48Z"},{"alias_kind":"pith_short_8","alias_value":"DQQEYSHG","created_at":"2026-07-04T15:59:48Z"}],"graph_snapshots":[{"event_id":"sha256:0e0c490f5fcf2ec23b98d9ea315a71a3825bd2792ccb0b76ff7cc717bd582883","target":"graph","created_at":"2026-07-04T15:59:48Z","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/9512087/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$.","authors_text":"Marco Picco, Pierre Pujol, Vladimir Dotsenko","cross_cats":["cond-mat"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1995-12-12T20:01:52Z","title":"Randomly coupled minimal models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9512087","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":"sha256:3840756cf32997df550f43778cb36aa9a93a923d61b2c1b6868b692b12baa8a0","target":"record","created_at":"2026-07-04T15:59:48Z","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":"3e4b462a3330de763fabeadceb8525cbdf63c3bac7fe88e1da98d85136409f21","cross_cats_sorted":["cond-mat"],"license":"","primary_cat":"hep-th","submitted_at":"1995-12-12T20:01:52Z","title_canon_sha256":"b3f915311ce85c3783beb710082935711d014f197150587feb15101a6d5d9c4e"},"schema_version":"1.0","source":{"id":"hep-th/9512087","kind":"arxiv","version":2}},"canonical_sha256":"1c204c48e6fb05f0a3b3820ca16cd00dbf765e875f787285d8b11e988c466cda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c204c48e6fb05f0a3b3820ca16cd00dbf765e875f787285d8b11e988c466cda","first_computed_at":"2026-07-04T15:59:48.014235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:59:48.014235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKpvnLEOEbCTYiY/k+5X7/mbqcXqJQtwqaWjDA+USHBm/14yF8pvXYzMv3f8MonZmINvTsF6VlrhgBYdaDJ3Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T15:59:48.014597Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9512087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3840756cf32997df550f43778cb36aa9a93a923d61b2c1b6868b692b12baa8a0","sha256:0e0c490f5fcf2ec23b98d9ea315a71a3825bd2792ccb0b76ff7cc717bd582883"],"state_sha256":"bb9037146fad44782694e90f67875995e7a5360e553cdcb32a35b0dac8aa96e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHydJYKDA0r5wHZ9ltNzrCExvb11x2xU3hmvdGueTXgSkoObgI/TuJ5xaCjAY9u7vOQ2rZfVwMDTNX2MsBLWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T21:25:51.955562Z","bundle_sha256":"15db584054de750bf09b88e64640a9ef87a229644cfee0c34c5c5e5c0b822372"}}