{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VCRNQR7G5HUQZ44QI54Z2G7QKB","short_pith_number":"pith:VCRNQR7G","canonical_record":{"source":{"id":"1312.3683","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-12-13T00:08:44Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"b789d202b0a50b63aa0ee5fcc64ca61d6ca4032004fd06965238bbae99b0ed76","abstract_canon_sha256":"9ab2539e5dfca2f86254811e790ab7d8cba8ea0a2d9f14de5e6004f72134a4d1"},"schema_version":"1.0"},"canonical_sha256":"a8a2d847e6e9e90cf39047799d1bf050434f2a277cbd5819934e76a4e426ef98","source":{"kind":"arxiv","id":"1312.3683","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3683","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3683v4","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3683","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"VCRNQR7G5HUQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VCRNQR7G5HUQZ44Q","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VCRNQR7G","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VCRNQR7G5HUQZ44QI54Z2G7QKB","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3683","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-12-13T00:08:44Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"b789d202b0a50b63aa0ee5fcc64ca61d6ca4032004fd06965238bbae99b0ed76","abstract_canon_sha256":"9ab2539e5dfca2f86254811e790ab7d8cba8ea0a2d9f14de5e6004f72134a4d1"},"schema_version":"1.0"},"canonical_sha256":"a8a2d847e6e9e90cf39047799d1bf050434f2a277cbd5819934e76a4e426ef98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:10.876420Z","signature_b64":"onxzSkrA76QNwd0jsxRZ9LhjDxGNd9AmApTHsEPhg55svNzBG2IWEd2sCklD2tN54W3IKrhWAysjralqtq35DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8a2d847e6e9e90cf39047799d1bf050434f2a277cbd5819934e76a4e426ef98","last_reissued_at":"2026-05-18T02:40:10.875824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:10.875824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3683","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZO9QY+ieUJNQbwpuS4mu//NpqM0pwa/4qm5V/iZ4SVgnVSVtHdLqbZNLZbe3wzzYCz7zO7w6hTDE/YCjMFFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:29:20.332373Z"},"content_sha256":"a5e2c83e17c08e5bdbcf036b0b8df69116eedafbd230991797c2dc86ee9fea63","schema_version":"1.0","event_id":"sha256:a5e2c83e17c08e5bdbcf036b0b8df69116eedafbd230991797c2dc86ee9fea63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VCRNQR7G5HUQZ44QI54Z2G7QKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-linear growth and condensation in multiplex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Ginestra Bianconi, Marc Barthelemy, Vincenzo Nicosia, Vito Latora","submitted_at":"2013-12-13T00:08:44Z","abstract_excerpt":"Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3683","kind":"arxiv","version":4},"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":"2026-05-18T02:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QyJw5iSHBeH5JhrFHLfwywVbTB4+V6B7/FW550jyGRfTabNyqZ2f7gncfLpbzq7wKGo89nP9MojQPfJkVLX+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:29:20.332730Z"},"content_sha256":"97693d30ae9e25fbe9a83346de8e3b81fcbe8fa1c37d9ea7984ce7188866f097","schema_version":"1.0","event_id":"sha256:97693d30ae9e25fbe9a83346de8e3b81fcbe8fa1c37d9ea7984ce7188866f097"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/bundle.json","state_url":"https://pith.science/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/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":"2026-06-01T13:29:20Z","links":{"resolver":"https://pith.science/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB","bundle":"https://pith.science/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/bundle.json","state":"https://pith.science/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCRNQR7G5HUQZ44QI54Z2G7QKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VCRNQR7G5HUQZ44QI54Z2G7QKB","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":"9ab2539e5dfca2f86254811e790ab7d8cba8ea0a2d9f14de5e6004f72134a4d1","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-12-13T00:08:44Z","title_canon_sha256":"b789d202b0a50b63aa0ee5fcc64ca61d6ca4032004fd06965238bbae99b0ed76"},"schema_version":"1.0","source":{"id":"1312.3683","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3683","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3683v4","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3683","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"VCRNQR7G5HUQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VCRNQR7G5HUQZ44Q","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VCRNQR7G","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:97693d30ae9e25fbe9a83346de8e3b81fcbe8fa1c37d9ea7984ce7188866f097","target":"graph","created_at":"2026-05-18T02:40:10Z","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":"Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed ","authors_text":"Ginestra Bianconi, Marc Barthelemy, Vincenzo Nicosia, Vito Latora","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-12-13T00:08:44Z","title":"Non-linear growth and condensation in multiplex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3683","kind":"arxiv","version":4},"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:a5e2c83e17c08e5bdbcf036b0b8df69116eedafbd230991797c2dc86ee9fea63","target":"record","created_at":"2026-05-18T02:40:10Z","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":"9ab2539e5dfca2f86254811e790ab7d8cba8ea0a2d9f14de5e6004f72134a4d1","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-12-13T00:08:44Z","title_canon_sha256":"b789d202b0a50b63aa0ee5fcc64ca61d6ca4032004fd06965238bbae99b0ed76"},"schema_version":"1.0","source":{"id":"1312.3683","kind":"arxiv","version":4}},"canonical_sha256":"a8a2d847e6e9e90cf39047799d1bf050434f2a277cbd5819934e76a4e426ef98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8a2d847e6e9e90cf39047799d1bf050434f2a277cbd5819934e76a4e426ef98","first_computed_at":"2026-05-18T02:40:10.875824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:10.875824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onxzSkrA76QNwd0jsxRZ9LhjDxGNd9AmApTHsEPhg55svNzBG2IWEd2sCklD2tN54W3IKrhWAysjralqtq35DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:10.876420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3683","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e2c83e17c08e5bdbcf036b0b8df69116eedafbd230991797c2dc86ee9fea63","sha256:97693d30ae9e25fbe9a83346de8e3b81fcbe8fa1c37d9ea7984ce7188866f097"],"state_sha256":"13e15a0120fa6450db365a605ae872d86d841ca9e9ee75407aa1f0a450b927bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+elhaNLMBqOg95Vt/gchpRXyPUyVMI0920Q48ydbdnk0rlcj+kCveHBdpCzYyhb9gfolPTm7B+jirngAQin8Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:29:20.334851Z","bundle_sha256":"bb7d76430d06ce0e662f0720a88213f239a8ee31052c8dabefaff62047a1ea55"}}