{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F2SAARDFJGKJEKNYNW26HNHBQL","short_pith_number":"pith:F2SAARDF","canonical_record":{"source":{"id":"1507.00610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-07-02T15:03:28Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"3da39e2b794fd99b1250fc5ce3a34a261985d8c66a59644c12a7a5ea7c855758","abstract_canon_sha256":"619bf3941a2e63d227e08c5485da43d67e097e9a22d7ef25033f251ef147e2ac"},"schema_version":"1.0"},"canonical_sha256":"2ea400446549949229b86db5e3b4e182ed588cd486f7415ef557f788e92bbb1c","source":{"kind":"arxiv","id":"1507.00610","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00610","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00610v1","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00610","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"F2SAARDFJGKJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F2SAARDFJGKJEKNY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F2SAARDF","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F2SAARDFJGKJEKNYNW26HNHBQL","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-07-02T15:03:28Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"3da39e2b794fd99b1250fc5ce3a34a261985d8c66a59644c12a7a5ea7c855758","abstract_canon_sha256":"619bf3941a2e63d227e08c5485da43d67e097e9a22d7ef25033f251ef147e2ac"},"schema_version":"1.0"},"canonical_sha256":"2ea400446549949229b86db5e3b4e182ed588cd486f7415ef557f788e92bbb1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:20.885559Z","signature_b64":"uYJaTTuMmNyRaMmBRV5HyflwoA0Q0ZpJfI0L5ptBSjlMeF+pIroElSmqGrmjc9cs9/MCKOophIorlR0XE0FUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea400446549949229b86db5e3b4e182ed588cd486f7415ef557f788e92bbb1c","last_reissued_at":"2026-05-18T01:22:20.884681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:20.884681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00610","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":"2026-05-18T01:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRMbt2PednP2orbEaarU11HKjehjQnj/mhP7rm8ae3n1l8CPLgCxWCVY/G5xSSOOZTVRs3isxPl0Upx3yDA/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:19.866751Z"},"content_sha256":"ce2066822511d0645d507fc0440202814500f8c912dd44e18dcbff186f3134e7","schema_version":"1.0","event_id":"sha256:ce2066822511d0645d507fc0440202814500f8c912dd44e18dcbff186f3134e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F2SAARDFJGKJEKNYNW26HNHBQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Network growth with preferential attachment and without \"rich get richer\" mechanism","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":"A. Achahbar, A. Lachgar","submitted_at":"2015-07-02T15:03:28Z","abstract_excerpt":"We propose a simple preferential attachment model of growing network using the complementary probability of Barab\\'asi-Albert (BA) model, i.e., $\\Pi(k_i) \\propto 1-\\frac{k_i}{\\sum_j k_j}$. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with \"rich get richer\" phenomena. We also calculate the average degree of a target node a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00610","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":"2026-05-18T01:22:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YCjx44A9+8RVB6TT7V12ULN88EnWdub6hNhxupA4Y65pws31LqZFWpVGWKavsjBMcz8AtJj0J0LX8ampaMcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:19.867105Z"},"content_sha256":"e2b54cfb253a105f69d366ef2d1de35fee423b4a7b2239bf503848516a00dfaf","schema_version":"1.0","event_id":"sha256:e2b54cfb253a105f69d366ef2d1de35fee423b4a7b2239bf503848516a00dfaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2SAARDFJGKJEKNYNW26HNHBQL/bundle.json","state_url":"https://pith.science/pith/F2SAARDFJGKJEKNYNW26HNHBQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2SAARDFJGKJEKNYNW26HNHBQL/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":"2026-05-27T23:18:19Z","links":{"resolver":"https://pith.science/pith/F2SAARDFJGKJEKNYNW26HNHBQL","bundle":"https://pith.science/pith/F2SAARDFJGKJEKNYNW26HNHBQL/bundle.json","state":"https://pith.science/pith/F2SAARDFJGKJEKNYNW26HNHBQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2SAARDFJGKJEKNYNW26HNHBQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F2SAARDFJGKJEKNYNW26HNHBQL","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":"619bf3941a2e63d227e08c5485da43d67e097e9a22d7ef25033f251ef147e2ac","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":"2015-07-02T15:03:28Z","title_canon_sha256":"3da39e2b794fd99b1250fc5ce3a34a261985d8c66a59644c12a7a5ea7c855758"},"schema_version":"1.0","source":{"id":"1507.00610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00610","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00610v1","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00610","created_at":"2026-05-18T01:22:20Z"},{"alias_kind":"pith_short_12","alias_value":"F2SAARDFJGKJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F2SAARDFJGKJEKNY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F2SAARDF","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:e2b54cfb253a105f69d366ef2d1de35fee423b4a7b2239bf503848516a00dfaf","target":"graph","created_at":"2026-05-18T01:22:20Z","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 propose a simple preferential attachment model of growing network using the complementary probability of Barab\\'asi-Albert (BA) model, i.e., $\\Pi(k_i) \\propto 1-\\frac{k_i}{\\sum_j k_j}$. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with \"rich get richer\" phenomena. We also calculate the average degree of a target node a","authors_text":"A. Achahbar, A. Lachgar","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":"2015-07-02T15:03:28Z","title":"Network growth with preferential attachment and without \"rich get richer\" mechanism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00610","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:ce2066822511d0645d507fc0440202814500f8c912dd44e18dcbff186f3134e7","target":"record","created_at":"2026-05-18T01:22:20Z","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":"619bf3941a2e63d227e08c5485da43d67e097e9a22d7ef25033f251ef147e2ac","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":"2015-07-02T15:03:28Z","title_canon_sha256":"3da39e2b794fd99b1250fc5ce3a34a261985d8c66a59644c12a7a5ea7c855758"},"schema_version":"1.0","source":{"id":"1507.00610","kind":"arxiv","version":1}},"canonical_sha256":"2ea400446549949229b86db5e3b4e182ed588cd486f7415ef557f788e92bbb1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ea400446549949229b86db5e3b4e182ed588cd486f7415ef557f788e92bbb1c","first_computed_at":"2026-05-18T01:22:20.884681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:20.884681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uYJaTTuMmNyRaMmBRV5HyflwoA0Q0ZpJfI0L5ptBSjlMeF+pIroElSmqGrmjc9cs9/MCKOophIorlR0XE0FUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:20.885559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce2066822511d0645d507fc0440202814500f8c912dd44e18dcbff186f3134e7","sha256:e2b54cfb253a105f69d366ef2d1de35fee423b4a7b2239bf503848516a00dfaf"],"state_sha256":"8eca30d5a78c70d57b7d9b7dd76364b47a611474a6137b8470ff31bc7a55123b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9glUQ3axA8mNvbYtG03FHtCmXxX18kEGvW/OPy7O0KdJq+67+EPyyOFeXFVCD18TlxL/T/+zvPh6BuVzy5TDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:18:19.870022Z","bundle_sha256":"6248b7d7b5b0b95ac08fb562c278dff43b6c3ba9c7163ce5918f3ff1446a72d4"}}