{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CD35ZB5AHRPW76VFPHQ5NRCJGU","short_pith_number":"pith:CD35ZB5A","canonical_record":{"source":{"id":"1506.06278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-06-20T18:40:48Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"f43a75f7fcdd5b713919143aada71c6faa2630bdf54d5446755e5fb1b7873ac3","abstract_canon_sha256":"674be133e6bc34257daed202a279de759f1c6c497ccfc2b0174f26f33f899d0e"},"schema_version":"1.0"},"canonical_sha256":"10f7dc87a03c5f6ffaa579e1d6c449352e7ba999d64877dd29bd0246623ef1ba","source":{"kind":"arxiv","id":"1506.06278","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06278","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06278v2","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06278","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"CD35ZB5AHRPW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CD35ZB5AHRPW76VF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CD35ZB5A","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CD35ZB5AHRPW76VFPHQ5NRCJGU","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-06-20T18:40:48Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"f43a75f7fcdd5b713919143aada71c6faa2630bdf54d5446755e5fb1b7873ac3","abstract_canon_sha256":"674be133e6bc34257daed202a279de759f1c6c497ccfc2b0174f26f33f899d0e"},"schema_version":"1.0"},"canonical_sha256":"10f7dc87a03c5f6ffaa579e1d6c449352e7ba999d64877dd29bd0246623ef1ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:18.879584Z","signature_b64":"FoQ4SaYlvBQcVPc3u6JNc6wl2nWEW9R3U8EMkcw6G1cd5ZlqAfrSnEHz7+nSlPt9TwDqf32s7PYidBzypWZ+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f7dc87a03c5f6ffaa579e1d6c449352e7ba999d64877dd29bd0246623ef1ba","last_reissued_at":"2026-05-18T01:24:18.879128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:18.879128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06278","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":"2026-05-18T01:24:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eZ7LydTcg8cZug5qWLUDrNjgOyLtna17ih1YbSiE0vPQVlPT1c63jOd1L+UKnBPO2o40VvELJO5amM+ryzkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:16:30.765913Z"},"content_sha256":"939f57ffef5508dc53c4e2f67de276e6ab626f3389fda24b9ed0cea9b71748df","schema_version":"1.0","event_id":"sha256:939f57ffef5508dc53c4e2f67de276e6ab626f3389fda24b9ed0cea9b71748df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CD35ZB5AHRPW76VFPHQ5NRCJGU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Growing Multiplex Networks with Arbitrary Number of Layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Babak Fotouhi, Naghmeh Momeni","submitted_at":"2015-06-20T18:40:48Z","abstract_excerpt":"This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes diff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06278","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":"2026-05-18T01:24:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FDlSXXds4/3WlAOWnO5ZT1tSnUpu6erZOajDe9uCAIurZISOidbV6yHqCaN690nJBQFhepS2KMlpw5afrF5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:16:30.766642Z"},"content_sha256":"6ffd51a75c2244ae91ab426fd1d8a4b4a11d3911559a1421338108a9d8225fa5","schema_version":"1.0","event_id":"sha256:6ffd51a75c2244ae91ab426fd1d8a4b4a11d3911559a1421338108a9d8225fa5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/bundle.json","state_url":"https://pith.science/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/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":"2026-05-26T05:16:30Z","links":{"resolver":"https://pith.science/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU","bundle":"https://pith.science/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/bundle.json","state":"https://pith.science/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CD35ZB5AHRPW76VFPHQ5NRCJGU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CD35ZB5AHRPW76VFPHQ5NRCJGU","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":"674be133e6bc34257daed202a279de759f1c6c497ccfc2b0174f26f33f899d0e","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-06-20T18:40:48Z","title_canon_sha256":"f43a75f7fcdd5b713919143aada71c6faa2630bdf54d5446755e5fb1b7873ac3"},"schema_version":"1.0","source":{"id":"1506.06278","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06278","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06278v2","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06278","created_at":"2026-05-18T01:24:18Z"},{"alias_kind":"pith_short_12","alias_value":"CD35ZB5AHRPW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CD35ZB5AHRPW76VF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CD35ZB5A","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:6ffd51a75c2244ae91ab426fd1d8a4b4a11d3911559a1421338108a9d8225fa5","target":"graph","created_at":"2026-05-18T01:24:18Z","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":"This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes diff","authors_text":"Babak Fotouhi, Naghmeh Momeni","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-06-20T18:40:48Z","title":"Growing Multiplex Networks with Arbitrary Number of Layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06278","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":"sha256:939f57ffef5508dc53c4e2f67de276e6ab626f3389fda24b9ed0cea9b71748df","target":"record","created_at":"2026-05-18T01:24:18Z","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":"674be133e6bc34257daed202a279de759f1c6c497ccfc2b0174f26f33f899d0e","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-06-20T18:40:48Z","title_canon_sha256":"f43a75f7fcdd5b713919143aada71c6faa2630bdf54d5446755e5fb1b7873ac3"},"schema_version":"1.0","source":{"id":"1506.06278","kind":"arxiv","version":2}},"canonical_sha256":"10f7dc87a03c5f6ffaa579e1d6c449352e7ba999d64877dd29bd0246623ef1ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10f7dc87a03c5f6ffaa579e1d6c449352e7ba999d64877dd29bd0246623ef1ba","first_computed_at":"2026-05-18T01:24:18.879128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:18.879128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FoQ4SaYlvBQcVPc3u6JNc6wl2nWEW9R3U8EMkcw6G1cd5ZlqAfrSnEHz7+nSlPt9TwDqf32s7PYidBzypWZ+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:18.879584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06278","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:939f57ffef5508dc53c4e2f67de276e6ab626f3389fda24b9ed0cea9b71748df","sha256:6ffd51a75c2244ae91ab426fd1d8a4b4a11d3911559a1421338108a9d8225fa5"],"state_sha256":"2d7ffacc983aa09a2762f1c26874e01e116cda5f555e92af3c6fc9e7cda82ef4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjVL/P/V2A9BTmgABvBvxixm/H+8E+aem5M9dH4XE4vVf30CBEg5JeNsxCLuKucVyruRKL32n6tUEtPn1fCTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:16:30.770362Z","bundle_sha256":"12ff0ac89fd1baf240ff4d696f30c55bb7cc8643f369473cd76dd44cb7f4f15d"}}