{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MOD7PG3Y5A4HFG4VNRXUECT3XC","short_pith_number":"pith:MOD7PG3Y","canonical_record":{"source":{"id":"2607.09444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-07-10T14:15:25Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"047a4ec44eef8fecebd69ef4f4ad7cfd757d3f335da9e8bb52308fbde1aee4db","abstract_canon_sha256":"c9c6ac44f27f3da167f397297906a7c6607089ced23f17ce9b8a4eb491c2da7f"},"schema_version":"1.0"},"canonical_sha256":"6387f79b78e838729b956c6f420a7bb8927c8eb9c087349d5efef047a26c9252","source":{"kind":"arxiv","id":"2607.09444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09444","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09444v1","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09444","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"MOD7PG3Y5A4H","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"MOD7PG3Y5A4HFG4V","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"MOD7PG3Y","created_at":"2026-07-13T01:19:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MOD7PG3Y5A4HFG4VNRXUECT3XC","target":"record","payload":{"canonical_record":{"source":{"id":"2607.09444","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-07-10T14:15:25Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"047a4ec44eef8fecebd69ef4f4ad7cfd757d3f335da9e8bb52308fbde1aee4db","abstract_canon_sha256":"c9c6ac44f27f3da167f397297906a7c6607089ced23f17ce9b8a4eb491c2da7f"},"schema_version":"1.0"},"canonical_sha256":"6387f79b78e838729b956c6f420a7bb8927c8eb9c087349d5efef047a26c9252","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:19:15.519999Z","signature_b64":"i6cWWvFosAnxhnYqwVam3ToDhJTavons3nWhaSY//m5mItOF1kQq0QCkMnUjpHqkhDlGI74l7SmmlkJSDo6LAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6387f79b78e838729b956c6f420a7bb8927c8eb9c087349d5efef047a26c9252","last_reissued_at":"2026-07-13T01:19:15.518935Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:19:15.518935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.09444","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":"2026-07-13T01:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2EUlsDM8b/E8tHOk7MfJKvuFrcbSTKmZ6Z+j3hWsbkcQK4FmDdTCINImYwirvpZDOQ9i1twf2cmsJfg4uGOCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:21:57.815729Z"},"content_sha256":"c6711b90199c1f8297814ab0573b056f269b39b03161d0e6045ff9444b74eaf1","schema_version":"1.0","event_id":"sha256:c6711b90199c1f8297814ab0573b056f269b39b03161d0e6045ff9444b74eaf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MOD7PG3Y5A4HFG4VNRXUECT3XC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level statistics in the fractal phase of generalized Rosenzweig--Porter models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Alexander K. Hartmann, Davide Venturelli, Leticia F. Cugliandolo, Marco Tarzia, Victor Delapalme","submitted_at":"2026-07-10T14:15:25Z","abstract_excerpt":"The Rosenzweig--Porter (RP) random matrix ensemble has emerged as a minimal model for the integrability-to-chaos crossover in quantum many-body systems. Its phase diagram features a region with fractal eigenstates, exhibiting intermediate spectral and localization properties between the fully localized and fully delocalized regimes. In this work, we explore several generalizations of the RP model and determine their level statistics at the scale of the Thouless energy $E_T$, which characterizes the crossover. Using tools from free probability theory and the replica method, we compute the full "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09444","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/2607.09444/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":"2026-07-13T01:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goOPnlRxldkhaSXOQ5SH+bi16rb/3oBupwtgXtDESi5NX4NyDgw1Y8ebLmdH6/UgLAqcQ9RwC6p/sDjG9BZGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:21:57.816250Z"},"content_sha256":"1f1048c59f68a9b17d1cec40b8c27648bce836283077388c905ab706bb9917c2","schema_version":"1.0","event_id":"sha256:1f1048c59f68a9b17d1cec40b8c27648bce836283077388c905ab706bb9917c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/bundle.json","state_url":"https://pith.science/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/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":"2026-08-04T14:21:57Z","links":{"resolver":"https://pith.science/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC","bundle":"https://pith.science/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/bundle.json","state":"https://pith.science/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOD7PG3Y5A4HFG4VNRXUECT3XC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MOD7PG3Y5A4HFG4VNRXUECT3XC","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":"c9c6ac44f27f3da167f397297906a7c6607089ced23f17ce9b8a4eb491c2da7f","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-07-10T14:15:25Z","title_canon_sha256":"047a4ec44eef8fecebd69ef4f4ad7cfd757d3f335da9e8bb52308fbde1aee4db"},"schema_version":"1.0","source":{"id":"2607.09444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09444","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09444v1","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09444","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"MOD7PG3Y5A4H","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"MOD7PG3Y5A4HFG4V","created_at":"2026-07-13T01:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"MOD7PG3Y","created_at":"2026-07-13T01:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:1f1048c59f68a9b17d1cec40b8c27648bce836283077388c905ab706bb9917c2","target":"graph","created_at":"2026-07-13T01:19:15Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.09444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Rosenzweig--Porter (RP) random matrix ensemble has emerged as a minimal model for the integrability-to-chaos crossover in quantum many-body systems. Its phase diagram features a region with fractal eigenstates, exhibiting intermediate spectral and localization properties between the fully localized and fully delocalized regimes. In this work, we explore several generalizations of the RP model and determine their level statistics at the scale of the Thouless energy $E_T$, which characterizes the crossover. Using tools from free probability theory and the replica method, we compute the full ","authors_text":"Alexander K. Hartmann, Davide Venturelli, Leticia F. Cugliandolo, Marco Tarzia, Victor Delapalme","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-07-10T14:15:25Z","title":"Level statistics in the fractal phase of generalized Rosenzweig--Porter models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09444","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:c6711b90199c1f8297814ab0573b056f269b39b03161d0e6045ff9444b74eaf1","target":"record","created_at":"2026-07-13T01:19:15Z","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":"c9c6ac44f27f3da167f397297906a7c6607089ced23f17ce9b8a4eb491c2da7f","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-07-10T14:15:25Z","title_canon_sha256":"047a4ec44eef8fecebd69ef4f4ad7cfd757d3f335da9e8bb52308fbde1aee4db"},"schema_version":"1.0","source":{"id":"2607.09444","kind":"arxiv","version":1}},"canonical_sha256":"6387f79b78e838729b956c6f420a7bb8927c8eb9c087349d5efef047a26c9252","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6387f79b78e838729b956c6f420a7bb8927c8eb9c087349d5efef047a26c9252","first_computed_at":"2026-07-13T01:19:15.518935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:19:15.518935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6cWWvFosAnxhnYqwVam3ToDhJTavons3nWhaSY//m5mItOF1kQq0QCkMnUjpHqkhDlGI74l7SmmlkJSDo6LAQ==","signature_status":"signed_v1","signed_at":"2026-07-13T01:19:15.519999Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6711b90199c1f8297814ab0573b056f269b39b03161d0e6045ff9444b74eaf1","sha256:1f1048c59f68a9b17d1cec40b8c27648bce836283077388c905ab706bb9917c2"],"state_sha256":"b079bb2869cd8aaf898731ac391df08aab0f4c37a9f3f979486d5af4bec7384d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUi9efV7L4WE5taUiBNCW4y21UAY7ZSegHtwCUhDHQ9I3fRyUiUPlRDnuzoxgCYGYHAt/jkkYe+rYHxxdQwmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T14:21:57.821297Z","bundle_sha256":"5ce461cfa417c4718568c2a75e5e3eb44ea64ce43a5c0b486fa7f81bfe179e69"}}