{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TBCQGSUBUBNQFJPUESGA6D4EKX","short_pith_number":"pith:TBCQGSUB","canonical_record":{"source":{"id":"1505.05484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-20T18:50:52Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"60515f81940cd578c50d1f3b0e385bb65f8ed51aa178755bcfa42dafc4621b04","abstract_canon_sha256":"e211aeb1aeb433e92f8ac6eec466a9968417ac31508817ece2a5dad65d5d5a97"},"schema_version":"1.0"},"canonical_sha256":"9845034a81a05b02a5f4248c0f0f8455c30bb24ddf09b84742b0c596b0998089","source":{"kind":"arxiv","id":"1505.05484","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05484","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05484v1","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05484","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"TBCQGSUBUBNQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBCQGSUBUBNQFJPU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBCQGSUB","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TBCQGSUBUBNQFJPUESGA6D4EKX","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-20T18:50:52Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"60515f81940cd578c50d1f3b0e385bb65f8ed51aa178755bcfa42dafc4621b04","abstract_canon_sha256":"e211aeb1aeb433e92f8ac6eec466a9968417ac31508817ece2a5dad65d5d5a97"},"schema_version":"1.0"},"canonical_sha256":"9845034a81a05b02a5f4248c0f0f8455c30bb24ddf09b84742b0c596b0998089","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:54.557692Z","signature_b64":"Lr2o+9CpfZA1FoyMV2qp4rGo0/tEeiV4fO/ROyhbnW+/W9BdGiSY2CeABacYrb6wAk8Lr6S81rRsLlLHj6QWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9845034a81a05b02a5f4248c0f0f8455c30bb24ddf09b84742b0c596b0998089","last_reissued_at":"2026-05-18T01:34:54.557044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:54.557044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05484","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":"2026-05-18T01:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qY4eGaQ/BYEJUcsH/v9izfItdG6+hVTurBRvbhw/Bhmg6bb6ZcGpX4W3989DI2+H2WLJNaS9A+4p58WHlS4+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:32:53.578950Z"},"content_sha256":"0d897be2c5cdc824af4d39a7d0cb3052184b93506e9fba4bb258a6ab6d63a7e6","schema_version":"1.0","event_id":"sha256:0d897be2c5cdc824af4d39a7d0cb3052184b93506e9fba4bb258a6ab6d63a7e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TBCQGSUBUBNQFJPUESGA6D4EKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical dynamics of the k-core pruning process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other"],"primary_cat":"cond-mat.dis-nn","authors_text":"A. V. Goltsev, G. J. Baxter, J. F. F. Mendes, K.-E. Lee, S. N. Dorogovtsev","submitted_at":"2015-05-20T18:50:52Z","abstract_excerpt":"We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree <q> of the initial network is above, equal to, or below the threshold <q>_c corresponding to the emergence of the giant k-core. We find that above the threshold the network rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05484","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":"2026-05-18T01:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wciWqR36zBrTBXuzQbBxEIG33CkVJbm71on1Vuo2D6PW9HmO/LZXrgvoFcXWin06whCCH585gDL5Cu8O31XRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:32:53.579692Z"},"content_sha256":"4182540dbdca600eff32551ae91643fb753f45a5aced776fa212aac753e023e5","schema_version":"1.0","event_id":"sha256:4182540dbdca600eff32551ae91643fb753f45a5aced776fa212aac753e023e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/bundle.json","state_url":"https://pith.science/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/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":"2026-05-30T23:32:53Z","links":{"resolver":"https://pith.science/pith/TBCQGSUBUBNQFJPUESGA6D4EKX","bundle":"https://pith.science/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/bundle.json","state":"https://pith.science/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TBCQGSUBUBNQFJPUESGA6D4EKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TBCQGSUBUBNQFJPUESGA6D4EKX","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":"e211aeb1aeb433e92f8ac6eec466a9968417ac31508817ece2a5dad65d5d5a97","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-20T18:50:52Z","title_canon_sha256":"60515f81940cd578c50d1f3b0e385bb65f8ed51aa178755bcfa42dafc4621b04"},"schema_version":"1.0","source":{"id":"1505.05484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05484","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05484v1","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05484","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"TBCQGSUBUBNQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBCQGSUBUBNQFJPU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBCQGSUB","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:4182540dbdca600eff32551ae91643fb753f45a5aced776fa212aac753e023e5","target":"graph","created_at":"2026-05-18T01:34:54Z","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 present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree <q> of the initial network is above, equal to, or below the threshold <q>_c corresponding to the emergence of the giant k-core. We find that above the threshold the network rel","authors_text":"A. V. Goltsev, G. J. Baxter, J. F. F. Mendes, K.-E. Lee, S. N. Dorogovtsev","cross_cats":["cond-mat.other"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-20T18:50:52Z","title":"Critical dynamics of the k-core pruning process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05484","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":"sha256:0d897be2c5cdc824af4d39a7d0cb3052184b93506e9fba4bb258a6ab6d63a7e6","target":"record","created_at":"2026-05-18T01:34:54Z","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":"e211aeb1aeb433e92f8ac6eec466a9968417ac31508817ece2a5dad65d5d5a97","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-05-20T18:50:52Z","title_canon_sha256":"60515f81940cd578c50d1f3b0e385bb65f8ed51aa178755bcfa42dafc4621b04"},"schema_version":"1.0","source":{"id":"1505.05484","kind":"arxiv","version":1}},"canonical_sha256":"9845034a81a05b02a5f4248c0f0f8455c30bb24ddf09b84742b0c596b0998089","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9845034a81a05b02a5f4248c0f0f8455c30bb24ddf09b84742b0c596b0998089","first_computed_at":"2026-05-18T01:34:54.557044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:54.557044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lr2o+9CpfZA1FoyMV2qp4rGo0/tEeiV4fO/ROyhbnW+/W9BdGiSY2CeABacYrb6wAk8Lr6S81rRsLlLHj6QWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:54.557692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d897be2c5cdc824af4d39a7d0cb3052184b93506e9fba4bb258a6ab6d63a7e6","sha256:4182540dbdca600eff32551ae91643fb753f45a5aced776fa212aac753e023e5"],"state_sha256":"ef40c6be230f9e5b904dd1443964278cca374985bd521a401a11534250733372"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KxdS8oZMGCyXYqjOjfPcTK0JzrPJKWc4nBEAjgAyJ6dtOPvfX/f9Y1CpLhY0ikxX5NDYYQ8cpxOxwbSCRnLXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:32:53.583357Z","bundle_sha256":"0197ea14161fccf4b8acb40cadabd5ccbfd5e9acfc8676845af3662f3cc5c67a"}}