{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E5LGDBW3H4D4QF6MU5A7PTIQVN","short_pith_number":"pith:E5LGDBW3","canonical_record":{"source":{"id":"1611.04583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-11-13T03:49:58Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"582eb176512ae14b2ab9bc224c66d783b95e514448b9681570da80bc034627f5","abstract_canon_sha256":"1f4931ef159956ac78aa3b82a7e314a00717ca462c9deaae88ae0d73d3783ec2"},"schema_version":"1.0"},"canonical_sha256":"27566186db3f07c817cca741f7cd10ab723b522f49253cdea8e2327010579a37","source":{"kind":"arxiv","id":"1611.04583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04583","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04583v1","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04583","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"E5LGDBW3H4D4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5LGDBW3H4D4QF6M","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5LGDBW3","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E5LGDBW3H4D4QF6MU5A7PTIQVN","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-11-13T03:49:58Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"582eb176512ae14b2ab9bc224c66d783b95e514448b9681570da80bc034627f5","abstract_canon_sha256":"1f4931ef159956ac78aa3b82a7e314a00717ca462c9deaae88ae0d73d3783ec2"},"schema_version":"1.0"},"canonical_sha256":"27566186db3f07c817cca741f7cd10ab723b522f49253cdea8e2327010579a37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:30.382084Z","signature_b64":"bGbUdvNlN6zqt+9WseP9R3tp8huosPltj0kmL9YIn9lYXo+FPbIYN9/lKG2QSejzgQ/kEappddToPnM/nbRNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27566186db3f07c817cca741f7cd10ab723b522f49253cdea8e2327010579a37","last_reissued_at":"2026-05-18T00:56:30.380727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:30.380727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04583","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":"2026-05-18T00:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jGv4gFnrVzMmsIHi4/0/7k3+WOXjqIwntF2IznhcCGRP+1rxctXo3PlhwyD6WXpmD55HCiat594Cv+Qc5qpZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:35:27.154946Z"},"content_sha256":"6a1076aefc803858389cb3995accbe4c59d159ca74c2e28badf0f6943614db1e","schema_version":"1.0","event_id":"sha256:6a1076aefc803858389cb3995accbe4c59d159ca74c2e28badf0f6943614db1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E5LGDBW3H4D4QF6MU5A7PTIQVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks","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":"Liana Islam, Md. Kamrul Hassan, Syed Arefinul Haque","submitted_at":"2016-11-13T03:49:58Z","abstract_excerpt":"We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law $P(k)\\sim k^{-\\gamma(m)}$ with a spectrum of exponents depending on $m$. To appreciate the contrast between MDA and Barab\\'{a}si-Albert (BA) networks, we then discuss their rank-size distribution. To quantify how long a leader, the node with the maximum degree, persists in its leadership as the network evolves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04583","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":""},"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":"2026-05-18T00:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3ozics1EmOjrOgAeWwaVwuA6AeUyTa5QttMIeneWsz8l/YCGJyudXkvO0DVevBcFzbPq04bg1UazX0ofFtyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:35:27.155301Z"},"content_sha256":"135ff506164503c29f4c09ce514d70a29c8af9889eeecf93a8717bafcb8247b4","schema_version":"1.0","event_id":"sha256:135ff506164503c29f4c09ce514d70a29c8af9889eeecf93a8717bafcb8247b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/bundle.json","state_url":"https://pith.science/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/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":"2026-06-30T11:35:27Z","links":{"resolver":"https://pith.science/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN","bundle":"https://pith.science/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/bundle.json","state":"https://pith.science/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5LGDBW3H4D4QF6MU5A7PTIQVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E5LGDBW3H4D4QF6MU5A7PTIQVN","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":"1f4931ef159956ac78aa3b82a7e314a00717ca462c9deaae88ae0d73d3783ec2","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":"2016-11-13T03:49:58Z","title_canon_sha256":"582eb176512ae14b2ab9bc224c66d783b95e514448b9681570da80bc034627f5"},"schema_version":"1.0","source":{"id":"1611.04583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04583","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04583v1","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04583","created_at":"2026-05-18T00:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"E5LGDBW3H4D4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E5LGDBW3H4D4QF6M","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E5LGDBW3","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:135ff506164503c29f4c09ce514d70a29c8af9889eeecf93a8717bafcb8247b4","target":"graph","created_at":"2026-05-18T00:56:30Z","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 investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law $P(k)\\sim k^{-\\gamma(m)}$ with a spectrum of exponents depending on $m$. To appreciate the contrast between MDA and Barab\\'{a}si-Albert (BA) networks, we then discuss their rank-size distribution. To quantify how long a leader, the node with the maximum degree, persists in its leadership as the network evolves","authors_text":"Liana Islam, Md. Kamrul Hassan, Syed Arefinul Haque","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":"2016-11-13T03:49:58Z","title":"Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04583","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":"sha256:6a1076aefc803858389cb3995accbe4c59d159ca74c2e28badf0f6943614db1e","target":"record","created_at":"2026-05-18T00:56:30Z","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":"1f4931ef159956ac78aa3b82a7e314a00717ca462c9deaae88ae0d73d3783ec2","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":"2016-11-13T03:49:58Z","title_canon_sha256":"582eb176512ae14b2ab9bc224c66d783b95e514448b9681570da80bc034627f5"},"schema_version":"1.0","source":{"id":"1611.04583","kind":"arxiv","version":1}},"canonical_sha256":"27566186db3f07c817cca741f7cd10ab723b522f49253cdea8e2327010579a37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27566186db3f07c817cca741f7cd10ab723b522f49253cdea8e2327010579a37","first_computed_at":"2026-05-18T00:56:30.380727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:30.380727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bGbUdvNlN6zqt+9WseP9R3tp8huosPltj0kmL9YIn9lYXo+FPbIYN9/lKG2QSejzgQ/kEappddToPnM/nbRNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:30.382084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a1076aefc803858389cb3995accbe4c59d159ca74c2e28badf0f6943614db1e","sha256:135ff506164503c29f4c09ce514d70a29c8af9889eeecf93a8717bafcb8247b4"],"state_sha256":"d02431a698d479de3412479c60f86b32bf98b00121f26797c9407746179a37c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngGxMHvH2iosgiSa7K25CEiCgp9RlGQYW+g0I93ZsJjgM0LpkOUTTT8SS3+Fq3FOS9vasj07qaC9WvW/tn5PDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T11:35:27.157275Z","bundle_sha256":"751fce8331f7cf9d240b2483f68ab8c3aecae69059bf490edf6e6ac2b8825928"}}