{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:2KTPCQCUC7BMJFY346X5GKKZMK","short_pith_number":"pith:2KTPCQCU","canonical_record":{"source":{"id":"cond-mat/0506395","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-16T09:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"0bb452de212f155016499ab678029b6beefc625ae1dbdb0b1db308f91e62fce3","abstract_canon_sha256":"c31c50268eef84d61815af4f4c7c04c87241e8c6baef5d4d17585de280d6d0d4"},"schema_version":"1.0"},"canonical_sha256":"d2a6f1405417c2c4971be7afd3295962b69496b4eb066c9ead55cf270851280c","source":{"kind":"arxiv","id":"cond-mat/0506395","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0506395","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0506395v2","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0506395","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"2KTPCQCUC7BM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2KTPCQCUC7BMJFY3","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2KTPCQCU","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:2KTPCQCUC7BMJFY346X5GKKZMK","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0506395","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-16T09:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"0bb452de212f155016499ab678029b6beefc625ae1dbdb0b1db308f91e62fce3","abstract_canon_sha256":"c31c50268eef84d61815af4f4c7c04c87241e8c6baef5d4d17585de280d6d0d4"},"schema_version":"1.0"},"canonical_sha256":"d2a6f1405417c2c4971be7afd3295962b69496b4eb066c9ead55cf270851280c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:52.571936Z","signature_b64":"7TCpEnGavgZv+5BFpfXytvnuBOXOjcmZVjTbVQPovWBsg7AjDzdW5SeLYtaiUdjlETFcktFSa9eEFRiBV1+3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a6f1405417c2c4971be7afd3295962b69496b4eb066c9ead55cf270851280c","last_reissued_at":"2026-05-18T01:06:52.571410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:52.571410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0506395","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":"2026-05-18T01:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ivjDHQ+5ibXtbanclsKvI8FmcAlk8AMYO3Tiuq91JflgblqXk3mGEvoWV5vd84YJae65ZOxHw7Ltloo5/DB3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:48:28.396724Z"},"content_sha256":"6b94af28322dd8f490de63a286ee9d0f579b56b2a1350640569a1690c8e5a3f4","schema_version":"1.0","event_id":"sha256:6b94af28322dd8f490de63a286ee9d0f579b56b2a1350640569a1690c8e5a3f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:2KTPCQCUC7BMJFY346X5GKKZMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The effect of disorder on the hierarchical modularity in complex systems","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"David Nagy, Gergely Tibely, Janos Kertesz","submitted_at":"2005-06-16T09:30:34Z","abstract_excerpt":"We consider a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the Vicsek snowflake or the deterministic scale free network by Ravasz et al. we first characterize the hierarchical modularity by the periodicity of some properties on a logarithmic scale indicating separation of scales. Then we introduce randomness by keeping the scale freeness and other important characteristics of the objects and monitor the changes in the modul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0506395","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":"2026-05-18T01:06:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YIBo14+gMJE/0OadDKhQQVDANSJFHRLqs2OP/ifFchDl+y87KEo6OtS31ssJBGM/i6tbtZdyVcUrROg4aQQlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:48:28.397134Z"},"content_sha256":"fef316c0a395ebb01312d71b740b90a7ad1cfe55c6b0b676229d7fe7e4372bfe","schema_version":"1.0","event_id":"sha256:fef316c0a395ebb01312d71b740b90a7ad1cfe55c6b0b676229d7fe7e4372bfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KTPCQCUC7BMJFY346X5GKKZMK/bundle.json","state_url":"https://pith.science/pith/2KTPCQCUC7BMJFY346X5GKKZMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KTPCQCUC7BMJFY346X5GKKZMK/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":"2026-06-01T11:48:28Z","links":{"resolver":"https://pith.science/pith/2KTPCQCUC7BMJFY346X5GKKZMK","bundle":"https://pith.science/pith/2KTPCQCUC7BMJFY346X5GKKZMK/bundle.json","state":"https://pith.science/pith/2KTPCQCUC7BMJFY346X5GKKZMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KTPCQCUC7BMJFY346X5GKKZMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2KTPCQCUC7BMJFY346X5GKKZMK","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":"c31c50268eef84d61815af4f4c7c04c87241e8c6baef5d4d17585de280d6d0d4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-16T09:30:34Z","title_canon_sha256":"0bb452de212f155016499ab678029b6beefc625ae1dbdb0b1db308f91e62fce3"},"schema_version":"1.0","source":{"id":"cond-mat/0506395","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0506395","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0506395v2","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0506395","created_at":"2026-05-18T01:06:52Z"},{"alias_kind":"pith_short_12","alias_value":"2KTPCQCUC7BM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2KTPCQCUC7BMJFY3","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2KTPCQCU","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:fef316c0a395ebb01312d71b740b90a7ad1cfe55c6b0b676229d7fe7e4372bfe","target":"graph","created_at":"2026-05-18T01:06:52Z","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 a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the Vicsek snowflake or the deterministic scale free network by Ravasz et al. we first characterize the hierarchical modularity by the periodicity of some properties on a logarithmic scale indicating separation of scales. Then we introduce randomness by keeping the scale freeness and other important characteristics of the objects and monitor the changes in the modul","authors_text":"David Nagy, Gergely Tibely, Janos Kertesz","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-16T09:30:34Z","title":"The effect of disorder on the hierarchical modularity in complex systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0506395","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":"sha256:6b94af28322dd8f490de63a286ee9d0f579b56b2a1350640569a1690c8e5a3f4","target":"record","created_at":"2026-05-18T01:06:52Z","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":"c31c50268eef84d61815af4f4c7c04c87241e8c6baef5d4d17585de280d6d0d4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-06-16T09:30:34Z","title_canon_sha256":"0bb452de212f155016499ab678029b6beefc625ae1dbdb0b1db308f91e62fce3"},"schema_version":"1.0","source":{"id":"cond-mat/0506395","kind":"arxiv","version":2}},"canonical_sha256":"d2a6f1405417c2c4971be7afd3295962b69496b4eb066c9ead55cf270851280c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2a6f1405417c2c4971be7afd3295962b69496b4eb066c9ead55cf270851280c","first_computed_at":"2026-05-18T01:06:52.571410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:52.571410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7TCpEnGavgZv+5BFpfXytvnuBOXOjcmZVjTbVQPovWBsg7AjDzdW5SeLYtaiUdjlETFcktFSa9eEFRiBV1+3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:52.571936Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0506395","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b94af28322dd8f490de63a286ee9d0f579b56b2a1350640569a1690c8e5a3f4","sha256:fef316c0a395ebb01312d71b740b90a7ad1cfe55c6b0b676229d7fe7e4372bfe"],"state_sha256":"7b5a15d245943ee276db723b6fb3803370a598d07eadea5ff49f063b59b20eca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZNVTLLsOdyn/hiDyOCIOwWtFIKqPQtCaZnn2ZzGhqr9gvtUGISqQTBNPBLvLlCnj5nbPND8zXjvKzIdtXihDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:48:28.399071Z","bundle_sha256":"f121a2a8e9745fa669f6b196ca11850fc5c41dca6c9d2edd6edcc5d4534104ba"}}