{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2EGGFF4VBPAKHCTY4LH5GMNVNC","short_pith_number":"pith:2EGGFF4V","canonical_record":{"source":{"id":"1503.03155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"b7a848ccd672dafabfe2f2c1b0c97ca3f8dab4025e2a5da13daec241b223e678","abstract_canon_sha256":"fdbc0dfa83ef5acf834a6ca89d028736522dc29a4d4ed285b8b63dabfb440f65"},"schema_version":"1.0"},"canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","source":{"kind":"arxiv","id":"1503.03155","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03155","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03155v3","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03155","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"2EGGFF4VBPAK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2EGGFF4VBPAKHCTY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2EGGFF4V","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2EGGFF4VBPAKHCTY4LH5GMNVNC","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"b7a848ccd672dafabfe2f2c1b0c97ca3f8dab4025e2a5da13daec241b223e678","abstract_canon_sha256":"fdbc0dfa83ef5acf834a6ca89d028736522dc29a4d4ed285b8b63dabfb440f65"},"schema_version":"1.0"},"canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.278212Z","signature_b64":"cLBChoy5o1WI9c+/DvY+JReqFVLhnVpfKhersToF5Q6bx7C5dpd3eTqBke7aY6584X7UD4BPk74ubDPcaZhpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","last_reissued_at":"2026-05-18T00:54:58.277665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.277665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03155","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwbm33pecfUPAy1mkykzTe+R+4WuDFTpG3LkDYfu8CU2pR+hJkX5qxC529olDylD7+PfqXKY03R/sHUchjp/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:16:55.140292Z"},"content_sha256":"bce42a2c930aa3a53db3ba77462f8267ccc3a6a10d0468bd31a43de069545204","schema_version":"1.0","event_id":"sha256:bce42a2c930aa3a53db3ba77462f8267ccc3a6a10d0468bd31a43de069545204"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2EGGFF4VBPAKHCTY4LH5GMNVNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Heat Kernel Pagerank and a Local Clustering Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fan Chung, Olivia Simpson","submitted_at":"2015-03-11T02:47:50Z","abstract_excerpt":"Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time $O\\big(\\frac{\\log(\\epsilon^{-1})\\log n}{\\epsilon^3\\log\\log(\\epsilon^{-1})}\\big)$, assuming performing a random walk step and sampling from a distribution with bounded support take constant time.\n  The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03155","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAsu2BmSH0Gq5mriy6dJYivBwhZiDN8Q5kZglq9Qwam3a1XQm4f5pP1ZbuMhfEyBgMG1Ah2qHelfCLQTTQGlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:16:55.140888Z"},"content_sha256":"09307888f731f909dd3f4cb3f9ce2a5d4e62b24b841145cbcd2bf4fd729a5e67","schema_version":"1.0","event_id":"sha256:09307888f731f909dd3f4cb3f9ce2a5d4e62b24b841145cbcd2bf4fd729a5e67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/bundle.json","state_url":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/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":"2026-05-30T21:16:55Z","links":{"resolver":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC","bundle":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/bundle.json","state":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2EGGFF4VBPAKHCTY4LH5GMNVNC","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":"fdbc0dfa83ef5acf834a6ca89d028736522dc29a4d4ed285b8b63dabfb440f65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","title_canon_sha256":"b7a848ccd672dafabfe2f2c1b0c97ca3f8dab4025e2a5da13daec241b223e678"},"schema_version":"1.0","source":{"id":"1503.03155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03155","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03155v3","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03155","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"2EGGFF4VBPAK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2EGGFF4VBPAKHCTY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2EGGFF4V","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:09307888f731f909dd3f4cb3f9ce2a5d4e62b24b841145cbcd2bf4fd729a5e67","target":"graph","created_at":"2026-05-18T00:54:58Z","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":"Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time $O\\big(\\frac{\\log(\\epsilon^{-1})\\log n}{\\epsilon^3\\log\\log(\\epsilon^{-1})}\\big)$, assuming performing a random walk step and sampling from a distribution with bounded support take constant time.\n  The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms.","authors_text":"Fan Chung, Olivia Simpson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","title":"Computing Heat Kernel Pagerank and a Local Clustering Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03155","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:bce42a2c930aa3a53db3ba77462f8267ccc3a6a10d0468bd31a43de069545204","target":"record","created_at":"2026-05-18T00:54:58Z","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":"fdbc0dfa83ef5acf834a6ca89d028736522dc29a4d4ed285b8b63dabfb440f65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","title_canon_sha256":"b7a848ccd672dafabfe2f2c1b0c97ca3f8dab4025e2a5da13daec241b223e678"},"schema_version":"1.0","source":{"id":"1503.03155","kind":"arxiv","version":3}},"canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","first_computed_at":"2026-05-18T00:54:58.277665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.277665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLBChoy5o1WI9c+/DvY+JReqFVLhnVpfKhersToF5Q6bx7C5dpd3eTqBke7aY6584X7UD4BPk74ubDPcaZhpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.278212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bce42a2c930aa3a53db3ba77462f8267ccc3a6a10d0468bd31a43de069545204","sha256:09307888f731f909dd3f4cb3f9ce2a5d4e62b24b841145cbcd2bf4fd729a5e67"],"state_sha256":"83bb6b1dfdc3d5880e94be4c6d4e22ad6a76fecd2e274582fb22d7c4354d1b37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kH9qIO/lrmOm/J6DU+C+/rv0GfMyfjTxs6oRyZeGRSTJDLdas2wFVvgBuc0FEhmAnbptNHtQn5vGpEtcxjioBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:16:55.144418Z","bundle_sha256":"9885b1ae3f914722e165822442076f513d05b980013e8b921862b6fd5a69747e"}}