{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:L7D65NLDAI7KCADSQL72OVQN3W","short_pith_number":"pith:L7D65NLD","canonical_record":{"source":{"id":"1509.06418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-21T22:26:14Z","cross_cats_sorted":["cs.SI","math.IT","math.ST","stat.TH"],"title_canon_sha256":"ec763ec5c99d144482ea11430844f0de075cdd2687044ff1a3664b51bdd762e9","abstract_canon_sha256":"d07f514d47f901ebe67a7d8ca675069631d0ad0e2e80629ee601e7086c837b34"},"schema_version":"1.0"},"canonical_sha256":"5fc7eeb563023ea1007282ffa7560ddda0467fe45d41f54c0d65a8da9cc3cc81","source":{"kind":"arxiv","id":"1509.06418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06418","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06418v1","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06418","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"L7D65NLDAI7K","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L7D65NLDAI7KCADS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L7D65NLD","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:L7D65NLDAI7KCADSQL72OVQN3W","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-21T22:26:14Z","cross_cats_sorted":["cs.SI","math.IT","math.ST","stat.TH"],"title_canon_sha256":"ec763ec5c99d144482ea11430844f0de075cdd2687044ff1a3664b51bdd762e9","abstract_canon_sha256":"d07f514d47f901ebe67a7d8ca675069631d0ad0e2e80629ee601e7086c837b34"},"schema_version":"1.0"},"canonical_sha256":"5fc7eeb563023ea1007282ffa7560ddda0467fe45d41f54c0d65a8da9cc3cc81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:20.388717Z","signature_b64":"98VF1xEkQkDojZ/xzVgsl4zlkI06eVbdJDc6q7poFog3hpg7+7QttDHXN36twJVgnQAS8RCpLwDHcfqAVi3LBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fc7eeb563023ea1007282ffa7560ddda0467fe45d41f54c0d65a8da9cc3cc81","last_reissued_at":"2026-05-18T01:32:20.388120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:20.388120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06418","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":"2026-05-18T01:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofC4BCfWNzZ24MXU90CfokYRtUMsQKHjaDxpU2rg31mLP/rUbemYt3yNiAF2++tZ3W+zpbwYV97DEsj4oGm+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:06:27.040347Z"},"content_sha256":"6f8d344ddc1f8323be05386d079d87cd00f71c3fd136f902ec83b0f3fc34d213","schema_version":"1.0","event_id":"sha256:6f8d344ddc1f8323be05386d079d87cd00f71c3fd136f902ec83b0f3fc34d213"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:L7D65NLDAI7KCADSQL72OVQN3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Po-Ling Loh, Varun Jog","submitted_at":"2015-09-21T22:26:14Z","abstract_excerpt":"We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maximum likelihood estimation when edge weights are drawn from discrete distributions, involves the Renyi divergence of order $\\frac{1}{2}$ between the distributions of within-community and between-community "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06418","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":"2026-05-18T01:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAaUdwzZfy60WZl7ox0Iu1dfePFmHnOFSn5ZAiB7wrjMcyRU7/JQHOtYf/O1+Cl50U5AAitKcfrT+vooHwWyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:06:27.041120Z"},"content_sha256":"f8fe626c30f7c04f1b20ac9bc332793bef48bd0ed34130b6fdefa1a91e5ee95a","schema_version":"1.0","event_id":"sha256:f8fe626c30f7c04f1b20ac9bc332793bef48bd0ed34130b6fdefa1a91e5ee95a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7D65NLDAI7KCADSQL72OVQN3W/bundle.json","state_url":"https://pith.science/pith/L7D65NLDAI7KCADSQL72OVQN3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7D65NLDAI7KCADSQL72OVQN3W/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":"2026-05-30T16:06:27Z","links":{"resolver":"https://pith.science/pith/L7D65NLDAI7KCADSQL72OVQN3W","bundle":"https://pith.science/pith/L7D65NLDAI7KCADSQL72OVQN3W/bundle.json","state":"https://pith.science/pith/L7D65NLDAI7KCADSQL72OVQN3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7D65NLDAI7KCADSQL72OVQN3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L7D65NLDAI7KCADSQL72OVQN3W","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":"d07f514d47f901ebe67a7d8ca675069631d0ad0e2e80629ee601e7086c837b34","cross_cats_sorted":["cs.SI","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-21T22:26:14Z","title_canon_sha256":"ec763ec5c99d144482ea11430844f0de075cdd2687044ff1a3664b51bdd762e9"},"schema_version":"1.0","source":{"id":"1509.06418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06418","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06418v1","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06418","created_at":"2026-05-18T01:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"L7D65NLDAI7K","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L7D65NLDAI7KCADS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L7D65NLD","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:f8fe626c30f7c04f1b20ac9bc332793bef48bd0ed34130b6fdefa1a91e5ee95a","target":"graph","created_at":"2026-05-18T01:32:20Z","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 derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maximum likelihood estimation when edge weights are drawn from discrete distributions, involves the Renyi divergence of order $\\frac{1}{2}$ between the distributions of within-community and between-community ","authors_text":"Po-Ling Loh, Varun Jog","cross_cats":["cs.SI","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-21T22:26:14Z","title":"Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06418","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":"sha256:6f8d344ddc1f8323be05386d079d87cd00f71c3fd136f902ec83b0f3fc34d213","target":"record","created_at":"2026-05-18T01:32:20Z","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":"d07f514d47f901ebe67a7d8ca675069631d0ad0e2e80629ee601e7086c837b34","cross_cats_sorted":["cs.SI","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-21T22:26:14Z","title_canon_sha256":"ec763ec5c99d144482ea11430844f0de075cdd2687044ff1a3664b51bdd762e9"},"schema_version":"1.0","source":{"id":"1509.06418","kind":"arxiv","version":1}},"canonical_sha256":"5fc7eeb563023ea1007282ffa7560ddda0467fe45d41f54c0d65a8da9cc3cc81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fc7eeb563023ea1007282ffa7560ddda0467fe45d41f54c0d65a8da9cc3cc81","first_computed_at":"2026-05-18T01:32:20.388120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:20.388120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"98VF1xEkQkDojZ/xzVgsl4zlkI06eVbdJDc6q7poFog3hpg7+7QttDHXN36twJVgnQAS8RCpLwDHcfqAVi3LBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:20.388717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f8d344ddc1f8323be05386d079d87cd00f71c3fd136f902ec83b0f3fc34d213","sha256:f8fe626c30f7c04f1b20ac9bc332793bef48bd0ed34130b6fdefa1a91e5ee95a"],"state_sha256":"6acaf0dbee7831bb09549779ec4e6a61820ac228967479de54fd39cd33a7488c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXnyYbZMKM1bihlsXtPR/wplRSstj1iuMwDEXKqzc0kPjxX0Xte40sXTDP/d928PMBkkkbc+n5Kinr005RXeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:06:27.044771Z","bundle_sha256":"bb78b3d356166ebd938d351e4a9d9a22f3e08e9e5023be123585b0a17190e39d"}}