{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:I6BAFDNSVKQW5G7ETZQLXZ2RNI","short_pith_number":"pith:I6BAFDNS","canonical_record":{"source":{"id":"1505.06450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-24T15:51:57Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"c4a5f84292ce41c7c65604c4f328859ac63854381f16eb114feb45cfc277b72e","abstract_canon_sha256":"ca61168dffffe0289ae150ba7fedabdc1dbc3316d3e411897e93ea65fb932e6e"},"schema_version":"1.0"},"canonical_sha256":"4782028db2aaa16e9be49e60bbe7516a063f4ecbd9debf792f02c4394d6965bb","source":{"kind":"arxiv","id":"1505.06450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06450","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06450v1","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06450","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"I6BAFDNSVKQW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I6BAFDNSVKQW5G7E","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I6BAFDNS","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:I6BAFDNSVKQW5G7ETZQLXZ2RNI","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-24T15:51:57Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"c4a5f84292ce41c7c65604c4f328859ac63854381f16eb114feb45cfc277b72e","abstract_canon_sha256":"ca61168dffffe0289ae150ba7fedabdc1dbc3316d3e411897e93ea65fb932e6e"},"schema_version":"1.0"},"canonical_sha256":"4782028db2aaa16e9be49e60bbe7516a063f4ecbd9debf792f02c4394d6965bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:45.713772Z","signature_b64":"EOT7OAyhC/6bpsvf234uvu2Q7NGIWgnqUl4ckNp3DRbD27MNA+rqmmvtqzmUpTAkRUrWec5jcV/9V7i+2PWVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4782028db2aaa16e9be49e60bbe7516a063f4ecbd9debf792f02c4394d6965bb","last_reissued_at":"2026-05-18T02:03:45.713101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:45.713101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06450","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":"2026-05-18T02:03:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBC3nGsMf4XkgkM/h4m5tU7ibB3jfN+16kKRu45Idjrtbbiho1MHlZqJ7pq9M2paTaIdhbVZr59mnFG/uXKmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:15:08.551962Z"},"content_sha256":"8bd8b62f570102cfbbcb511a63a4a408115263d7d1a68d0158988b0ae7d6b533","schema_version":"1.0","event_id":"sha256:8bd8b62f570102cfbbcb511a63a4a408115263d7d1a68d0158988b0ae7d6b533"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:I6BAFDNSVKQW5G7ETZQLXZ2RNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"History effects on network growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Amir Hossein Shirazi, Gholamreza Jafari, Hadiseh Safdari, Milad Zare Kamali, Moein Khaliqi","submitted_at":"2015-05-24T15:51:57Z","abstract_excerpt":"Growth dynamic of real networks because of emerging complexities is an open and interesting question. Indeed it is not realistic to ignore history impact on the current events. The mystery behind that complexity could be in the role of history in some how. To regard this point, the average effect of history has been included by a kernel function in differential equation of Barabasi Albert (BA) model . This approach leads to a fractional order BA differential equation as a generalization of BA model. As opposed to unlimited growth for degree of nodes, our results show that over time the memory "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06450","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":"2026-05-18T02:03:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ec0EfiSe9MPXwz04eLcQHzVnRrYxeYTGYMNwBz/2pcSA2mq/QhmDXM12bNI3DZJm5/miQfV4oJ0uFS4tUkaLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:15:08.552307Z"},"content_sha256":"01b31f4a84701fd272bd42cbc196e2ba89ae4db5ea643d0112539a43464a4ee3","schema_version":"1.0","event_id":"sha256:01b31f4a84701fd272bd42cbc196e2ba89ae4db5ea643d0112539a43464a4ee3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/bundle.json","state_url":"https://pith.science/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/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":"2026-06-30T13:15:08Z","links":{"resolver":"https://pith.science/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI","bundle":"https://pith.science/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/bundle.json","state":"https://pith.science/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6BAFDNSVKQW5G7ETZQLXZ2RNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I6BAFDNSVKQW5G7ETZQLXZ2RNI","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":"ca61168dffffe0289ae150ba7fedabdc1dbc3316d3e411897e93ea65fb932e6e","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-24T15:51:57Z","title_canon_sha256":"c4a5f84292ce41c7c65604c4f328859ac63854381f16eb114feb45cfc277b72e"},"schema_version":"1.0","source":{"id":"1505.06450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06450","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06450v1","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06450","created_at":"2026-05-18T02:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"I6BAFDNSVKQW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I6BAFDNSVKQW5G7E","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I6BAFDNS","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:01b31f4a84701fd272bd42cbc196e2ba89ae4db5ea643d0112539a43464a4ee3","target":"graph","created_at":"2026-05-18T02:03:45Z","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":"Growth dynamic of real networks because of emerging complexities is an open and interesting question. Indeed it is not realistic to ignore history impact on the current events. The mystery behind that complexity could be in the role of history in some how. To regard this point, the average effect of history has been included by a kernel function in differential equation of Barabasi Albert (BA) model . This approach leads to a fractional order BA differential equation as a generalization of BA model. As opposed to unlimited growth for degree of nodes, our results show that over time the memory ","authors_text":"Amir Hossein Shirazi, Gholamreza Jafari, Hadiseh Safdari, Milad Zare Kamali, Moein Khaliqi","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-24T15:51:57Z","title":"History effects on network growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06450","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":"sha256:8bd8b62f570102cfbbcb511a63a4a408115263d7d1a68d0158988b0ae7d6b533","target":"record","created_at":"2026-05-18T02:03:45Z","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":"ca61168dffffe0289ae150ba7fedabdc1dbc3316d3e411897e93ea65fb932e6e","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-24T15:51:57Z","title_canon_sha256":"c4a5f84292ce41c7c65604c4f328859ac63854381f16eb114feb45cfc277b72e"},"schema_version":"1.0","source":{"id":"1505.06450","kind":"arxiv","version":1}},"canonical_sha256":"4782028db2aaa16e9be49e60bbe7516a063f4ecbd9debf792f02c4394d6965bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4782028db2aaa16e9be49e60bbe7516a063f4ecbd9debf792f02c4394d6965bb","first_computed_at":"2026-05-18T02:03:45.713101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:45.713101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EOT7OAyhC/6bpsvf234uvu2Q7NGIWgnqUl4ckNp3DRbD27MNA+rqmmvtqzmUpTAkRUrWec5jcV/9V7i+2PWVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:45.713772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bd8b62f570102cfbbcb511a63a4a408115263d7d1a68d0158988b0ae7d6b533","sha256:01b31f4a84701fd272bd42cbc196e2ba89ae4db5ea643d0112539a43464a4ee3"],"state_sha256":"8365ef64f1e5e6b240ec5968eaa8584eebccb360f957cf90392a1d18844a75df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dd0GL4MWw8qGaZEHNtcnQx23xIQvaF7eW6AXk8Je5rl9cGL3WwVG6K0o2maBbPPAj+LFzOYu6dscKaFCWawmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T13:15:08.554513Z","bundle_sha256":"b2590cc2a1c1537a23d0b84dfbee26bb9ea02320aab2fe6a317c343b6c9134af"}}