{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WTIDFMG57SXRE3EBN6Q2DHRJKK","short_pith_number":"pith:WTIDFMG5","canonical_record":{"source":{"id":"1704.08276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T18:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"110d202c4186815cbf9b968eae8532b915899d2ab9c0320bc31d88b9abe03efb","abstract_canon_sha256":"51c1e51307736e8e9e2e0c0ccb8ac80a6b414d540c9ffc7601542dbac9f3f452"},"schema_version":"1.0"},"canonical_sha256":"b4d032b0ddfcaf126c816fa1a19e2952b3dd1e227413a37b87dffe3419aa34ea","source":{"kind":"arxiv","id":"1704.08276","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08276","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08276v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08276","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTIDFMG57SXR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WTIDFMG57SXRE3EB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WTIDFMG5","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WTIDFMG57SXRE3EBN6Q2DHRJKK","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T18:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"110d202c4186815cbf9b968eae8532b915899d2ab9c0320bc31d88b9abe03efb","abstract_canon_sha256":"51c1e51307736e8e9e2e0c0ccb8ac80a6b414d540c9ffc7601542dbac9f3f452"},"schema_version":"1.0"},"canonical_sha256":"b4d032b0ddfcaf126c816fa1a19e2952b3dd1e227413a37b87dffe3419aa34ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.667539Z","signature_b64":"QInZy4Ox/tId9AQVJ+BxpjnkN3cDJDglmQOim8NhVm7XWhBfHlAldDHMO+S7G3sYaArjO/4aGxVCszdxKe6fCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4d032b0ddfcaf126c816fa1a19e2952b3dd1e227413a37b87dffe3419aa34ea","last_reissued_at":"2026-05-17T23:56:48.667049Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.667049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08276","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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iznSVbNn9NXeYbPKq3XYkMXexK4m6Gj2KlXQ4MoDJFHRHBk+J0bpy2rpp272E6LJTjhlj62L3JqmGMU+w+nCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:47:24.720203Z"},"content_sha256":"94f15ad609bab021c1678cc6a053fadcdf734711cc1af412226405d8d8bbef4c","schema_version":"1.0","event_id":"sha256:94f15ad609bab021c1678cc6a053fadcdf734711cc1af412226405d8d8bbef4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WTIDFMG57SXRE3EBN6Q2DHRJKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preferential Attachment Random Graphs with Edge-Step Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Caio Alves, Remy Sanchis, Rodrigo Ribeiro","submitted_at":"2017-04-26T18:16:04Z","abstract_excerpt":"We propose a random graph model with preferential attachment rule and \\emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random graphs. More specifically, we prove that when the edge-step function $f$ is a \\emph{monotone regularly varying function} at infinity, the sequence of graphs associated to it obeys a power-law degree distribution whose exponent is related to the index of regular variation of $f$ at infinity whenever said index is greater than $-1$. When the regularly variation in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08276","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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrEUzbTPtYIeX3e6y+E4rNvyjP7MEi1SuP6o1tekre0TGE7qItp/AfyVi5h3hBXN7kuLXZoz7/WNmh7HYQsdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:47:24.720931Z"},"content_sha256":"1235feed099d12ead58f8b3164cbe0ac9b97cd9e52cefe3d216b4056e173ea09","schema_version":"1.0","event_id":"sha256:1235feed099d12ead58f8b3164cbe0ac9b97cd9e52cefe3d216b4056e173ea09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/bundle.json","state_url":"https://pith.science/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/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":"2026-06-07T01:47:24Z","links":{"resolver":"https://pith.science/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK","bundle":"https://pith.science/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/bundle.json","state":"https://pith.science/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTIDFMG57SXRE3EBN6Q2DHRJKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WTIDFMG57SXRE3EBN6Q2DHRJKK","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":"51c1e51307736e8e9e2e0c0ccb8ac80a6b414d540c9ffc7601542dbac9f3f452","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T18:16:04Z","title_canon_sha256":"110d202c4186815cbf9b968eae8532b915899d2ab9c0320bc31d88b9abe03efb"},"schema_version":"1.0","source":{"id":"1704.08276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08276","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08276v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08276","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTIDFMG57SXR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WTIDFMG57SXRE3EB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WTIDFMG5","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:1235feed099d12ead58f8b3164cbe0ac9b97cd9e52cefe3d216b4056e173ea09","target":"graph","created_at":"2026-05-17T23:56:48Z","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 random graph model with preferential attachment rule and \\emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random graphs. More specifically, we prove that when the edge-step function $f$ is a \\emph{monotone regularly varying function} at infinity, the sequence of graphs associated to it obeys a power-law degree distribution whose exponent is related to the index of regular variation of $f$ at infinity whenever said index is greater than $-1$. When the regularly variation in","authors_text":"Caio Alves, Remy Sanchis, Rodrigo Ribeiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T18:16:04Z","title":"Preferential Attachment Random Graphs with Edge-Step Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08276","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":"sha256:94f15ad609bab021c1678cc6a053fadcdf734711cc1af412226405d8d8bbef4c","target":"record","created_at":"2026-05-17T23:56:48Z","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":"51c1e51307736e8e9e2e0c0ccb8ac80a6b414d540c9ffc7601542dbac9f3f452","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T18:16:04Z","title_canon_sha256":"110d202c4186815cbf9b968eae8532b915899d2ab9c0320bc31d88b9abe03efb"},"schema_version":"1.0","source":{"id":"1704.08276","kind":"arxiv","version":2}},"canonical_sha256":"b4d032b0ddfcaf126c816fa1a19e2952b3dd1e227413a37b87dffe3419aa34ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4d032b0ddfcaf126c816fa1a19e2952b3dd1e227413a37b87dffe3419aa34ea","first_computed_at":"2026-05-17T23:56:48.667049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:48.667049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QInZy4Ox/tId9AQVJ+BxpjnkN3cDJDglmQOim8NhVm7XWhBfHlAldDHMO+S7G3sYaArjO/4aGxVCszdxKe6fCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:48.667539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f15ad609bab021c1678cc6a053fadcdf734711cc1af412226405d8d8bbef4c","sha256:1235feed099d12ead58f8b3164cbe0ac9b97cd9e52cefe3d216b4056e173ea09"],"state_sha256":"965aa62c28d74f1bf633718a99e0e73f1280d614cad8dbdabc1d88b076326d69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4pyGUJv9TD1+ta8admjBTp5Sh6WP71uMkLjsL9kSa8h/WLyG8HZkjJzSEsRGmbP/MRX0q0ZSrstHXhrviTYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:47:24.725095Z","bundle_sha256":"d09de140cb895370b77ab62323d7207a8e9bd6e8caa0d0a70ebd180ea60e91f8"}}