{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z3FGI7OJJZVOK24MJ363NNUYX7","short_pith_number":"pith:Z3FGI7OJ","canonical_record":{"source":{"id":"1508.03379","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2015-08-13T22:53:42Z","cross_cats_sorted":["math.PR","physics.soc-ph"],"title_canon_sha256":"7450573584f6d2e9fcbd604b8e5a1c3d79d417ec803314b24422dd8a3b0188c3","abstract_canon_sha256":"cd2c3e5bce94f828d82639c527b66a1b256d301336fc8ed949620e2a5f844a1d"},"schema_version":"1.0"},"canonical_sha256":"ceca647dc94e6ae56b8c4efdb6b698bffee50265a7357e4137968ea7a1997901","source":{"kind":"arxiv","id":"1508.03379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03379","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03379v3","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03379","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"Z3FGI7OJJZVO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3FGI7OJJZVOK24M","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3FGI7OJ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z3FGI7OJJZVOK24MJ363NNUYX7","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03379","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2015-08-13T22:53:42Z","cross_cats_sorted":["math.PR","physics.soc-ph"],"title_canon_sha256":"7450573584f6d2e9fcbd604b8e5a1c3d79d417ec803314b24422dd8a3b0188c3","abstract_canon_sha256":"cd2c3e5bce94f828d82639c527b66a1b256d301336fc8ed949620e2a5f844a1d"},"schema_version":"1.0"},"canonical_sha256":"ceca647dc94e6ae56b8c4efdb6b698bffee50265a7357e4137968ea7a1997901","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:09.904504Z","signature_b64":"RldAjAAPVmDBSxwPsitBnJA34ha3QR4xSQrW+lvmNDJqOjbxvXZzfQiAVJKTuVJYgFn6RBV6ueLVgPh+u9h/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceca647dc94e6ae56b8c4efdb6b698bffee50265a7357e4137968ea7a1997901","last_reissued_at":"2026-05-18T00:50:09.903911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:09.903911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zPST/vE4ZxHOEc8ctdEpVjqz4hmOMRa8TNkfOJ5CdjcnN7iXFnk16toXSvHnJubLtFQ6fvYlI0+W7XIYaxA5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:23:58.818780Z"},"content_sha256":"253c2f55d1d8a1b3d9548ff54db42d0a70ac8cac1d41d63bc8bd9653222b2fb9","schema_version":"1.0","event_id":"sha256:253c2f55d1d8a1b3d9548ff54db42d0a70ac8cac1d41d63bc8bd9653222b2fb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z3FGI7OJJZVOK24MJ363NNUYX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The impact of degree variability on connectivity properties of large networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Hoa Ngo, Lasse Leskel\\\"a","submitted_at":"2015-08-13T22:53:42Z","abstract_excerpt":"The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree sequence. We analyze the effect of the degree variability on the approximate size of the largest connected component using stochastic ordering techniques. A counterexample shows that a higher degree variability may lead to a larger connected component, contrary to basic intuition about branching processes. When certain extremal cases are ruled out, the higher de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03379","kind":"arxiv","version":3},"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":"2026-05-18T00:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSBYTRepm0qR/7di7/8oNsxq8Wu9Qkn4S+ZNe69SS0LzI6TVD4LzcIS1KrA/baZNKa/asFKuBDpFxIXHSvG5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:23:58.819425Z"},"content_sha256":"bebfdb75278fe6ee0d84d3f7be8478e703ed66e0827ddeba3edbebb35ce3c03d","schema_version":"1.0","event_id":"sha256:bebfdb75278fe6ee0d84d3f7be8478e703ed66e0827ddeba3edbebb35ce3c03d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/bundle.json","state_url":"https://pith.science/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/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":"2026-05-30T13:23:58Z","links":{"resolver":"https://pith.science/pith/Z3FGI7OJJZVOK24MJ363NNUYX7","bundle":"https://pith.science/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/bundle.json","state":"https://pith.science/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3FGI7OJJZVOK24MJ363NNUYX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z3FGI7OJJZVOK24MJ363NNUYX7","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":"cd2c3e5bce94f828d82639c527b66a1b256d301336fc8ed949620e2a5f844a1d","cross_cats_sorted":["math.PR","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2015-08-13T22:53:42Z","title_canon_sha256":"7450573584f6d2e9fcbd604b8e5a1c3d79d417ec803314b24422dd8a3b0188c3"},"schema_version":"1.0","source":{"id":"1508.03379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03379","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03379v3","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03379","created_at":"2026-05-18T00:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"Z3FGI7OJJZVO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3FGI7OJJZVOK24M","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3FGI7OJ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:bebfdb75278fe6ee0d84d3f7be8478e703ed66e0827ddeba3edbebb35ce3c03d","target":"graph","created_at":"2026-05-18T00:50:09Z","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":"The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree sequence. We analyze the effect of the degree variability on the approximate size of the largest connected component using stochastic ordering techniques. A counterexample shows that a higher degree variability may lead to a larger connected component, contrary to basic intuition about branching processes. When certain extremal cases are ruled out, the higher de","authors_text":"Hoa Ngo, Lasse Leskel\\\"a","cross_cats":["math.PR","physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2015-08-13T22:53:42Z","title":"The impact of degree variability on connectivity properties of large networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03379","kind":"arxiv","version":3},"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":"sha256:253c2f55d1d8a1b3d9548ff54db42d0a70ac8cac1d41d63bc8bd9653222b2fb9","target":"record","created_at":"2026-05-18T00:50:09Z","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":"cd2c3e5bce94f828d82639c527b66a1b256d301336fc8ed949620e2a5f844a1d","cross_cats_sorted":["math.PR","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2015-08-13T22:53:42Z","title_canon_sha256":"7450573584f6d2e9fcbd604b8e5a1c3d79d417ec803314b24422dd8a3b0188c3"},"schema_version":"1.0","source":{"id":"1508.03379","kind":"arxiv","version":3}},"canonical_sha256":"ceca647dc94e6ae56b8c4efdb6b698bffee50265a7357e4137968ea7a1997901","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceca647dc94e6ae56b8c4efdb6b698bffee50265a7357e4137968ea7a1997901","first_computed_at":"2026-05-18T00:50:09.903911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:09.903911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RldAjAAPVmDBSxwPsitBnJA34ha3QR4xSQrW+lvmNDJqOjbxvXZzfQiAVJKTuVJYgFn6RBV6ueLVgPh+u9h/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:09.904504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:253c2f55d1d8a1b3d9548ff54db42d0a70ac8cac1d41d63bc8bd9653222b2fb9","sha256:bebfdb75278fe6ee0d84d3f7be8478e703ed66e0827ddeba3edbebb35ce3c03d"],"state_sha256":"2d7b16b59ee8eaf442363c99746a1356d41d29baa904436b14c71fe5bb7bda43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UbcGb4BzLmhxVQadJvNAw3c18GT64rfLDs2b4di4AgbIR9YqcHnJ+m/FTB2HLKR+Id0o8qz5dwt1hL8SMV/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:23:58.821981Z","bundle_sha256":"cf8abc7e2a577525566cd791e35af33233781adf33153ed057b11b3c1d6e18ea"}}