{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2NUNKE5CPCZ5S34AX2OGM2AKUD","short_pith_number":"pith:2NUNKE5C","canonical_record":{"source":{"id":"1511.05271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-17T04:58:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"title_canon_sha256":"a19a19697322339ccf2e4344d80378a00e70ed6e7d6be77325d4159522e61eeb","abstract_canon_sha256":"293abe58d61fa59c19978dad892cc6a0a92560a9091450f636b2c2b4396f1d04"},"schema_version":"1.0"},"canonical_sha256":"d368d513a278b3d96f80be9c66680aa0d7bd20029c875d01fb06f3caf308260b","source":{"kind":"arxiv","id":"1511.05271","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05271","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05271v3","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05271","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"2NUNKE5CPCZ5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NUNKE5CPCZ5S34A","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NUNKE5C","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2NUNKE5CPCZ5S34AX2OGM2AKUD","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-17T04:58:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"title_canon_sha256":"a19a19697322339ccf2e4344d80378a00e70ed6e7d6be77325d4159522e61eeb","abstract_canon_sha256":"293abe58d61fa59c19978dad892cc6a0a92560a9091450f636b2c2b4396f1d04"},"schema_version":"1.0"},"canonical_sha256":"d368d513a278b3d96f80be9c66680aa0d7bd20029c875d01fb06f3caf308260b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:49.473998Z","signature_b64":"n95fpnrLmMUwMLf7aA4yEQyhHe1mdgTyBzkjQiSa1L9xNVlIHNkv4B7T72mne9IlMkhOyVzw04sbH4YDC9w3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d368d513a278b3d96f80be9c66680aa0d7bd20029c875d01fb06f3caf308260b","last_reissued_at":"2026-05-18T01:12:49.473653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:49.473653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05271","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":"2026-05-18T01:12:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aahbChxzac9rNtoqM1Kkqb0JjWsvtmTATWGcGTC4KsF5EVD7+VXNVRjQpc3vmIBtJkE3zBj9qzxISyTxk04nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:02:01.338127Z"},"content_sha256":"14ed59ae9c5792a7307243b8185cb94832c8ce18852162110f4e1b2cc124fb98","schema_version":"1.0","event_id":"sha256:14ed59ae9c5792a7307243b8185cb94832c8ce18852162110f4e1b2cc124fb98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2NUNKE5CPCZ5S34AX2OGM2AKUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enhanced detectability of community structure in multilayer networks through layer aggregation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"primary_cat":"physics.soc-ph","authors_text":"Dane Taylor, Natalie Stanley, Peter J. Mucha, Saray Shai","submitted_at":"2015-11-17T04:58:35Z","abstract_excerpt":"Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matrix theory, we analyze detectability limitations for multilayer (specifically, multiplex) stochastic block models (SBMs) in which L layers are derived from a common SBM. We study the effect of layer aggregation on detectability for several aggregation methods, including summation of the layers' adjac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05271","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":"2026-05-18T01:12:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4YF27e+w8sECxUrTvCuLUp7mc6rEwKwvqPIHRzrGRHZSh23I1iqiA/GmBMfeTyspcqofnfgF1TKe5oFvoXtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:02:01.338621Z"},"content_sha256":"88f4e9fddd630dfbaa9639059023786b1ddade31bcaa09a70ac0ca3a805fb428","schema_version":"1.0","event_id":"sha256:88f4e9fddd630dfbaa9639059023786b1ddade31bcaa09a70ac0ca3a805fb428"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/bundle.json","state_url":"https://pith.science/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/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":"2026-05-24T06:02:01Z","links":{"resolver":"https://pith.science/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD","bundle":"https://pith.science/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/bundle.json","state":"https://pith.science/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2NUNKE5CPCZ5S34AX2OGM2AKUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NUNKE5CPCZ5S34AX2OGM2AKUD","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":"293abe58d61fa59c19978dad892cc6a0a92560a9091450f636b2c2b4396f1d04","cross_cats_sorted":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-17T04:58:35Z","title_canon_sha256":"a19a19697322339ccf2e4344d80378a00e70ed6e7d6be77325d4159522e61eeb"},"schema_version":"1.0","source":{"id":"1511.05271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05271","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05271v3","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05271","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"2NUNKE5CPCZ5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NUNKE5CPCZ5S34A","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NUNKE5C","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:88f4e9fddd630dfbaa9639059023786b1ddade31bcaa09a70ac0ca3a805fb428","target":"graph","created_at":"2026-05-18T01:12:49Z","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":"Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matrix theory, we analyze detectability limitations for multilayer (specifically, multiplex) stochastic block models (SBMs) in which L layers are derived from a common SBM. We study the effect of layer aggregation on detectability for several aggregation methods, including summation of the layers' adjac","authors_text":"Dane Taylor, Natalie Stanley, Peter J. Mucha, Saray Shai","cross_cats":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-17T04:58:35Z","title":"Enhanced detectability of community structure in multilayer networks through layer aggregation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05271","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":"sha256:14ed59ae9c5792a7307243b8185cb94832c8ce18852162110f4e1b2cc124fb98","target":"record","created_at":"2026-05-18T01:12:49Z","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":"293abe58d61fa59c19978dad892cc6a0a92560a9091450f636b2c2b4396f1d04","cross_cats_sorted":["cond-mat.dis-nn","cs.SI","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-17T04:58:35Z","title_canon_sha256":"a19a19697322339ccf2e4344d80378a00e70ed6e7d6be77325d4159522e61eeb"},"schema_version":"1.0","source":{"id":"1511.05271","kind":"arxiv","version":3}},"canonical_sha256":"d368d513a278b3d96f80be9c66680aa0d7bd20029c875d01fb06f3caf308260b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d368d513a278b3d96f80be9c66680aa0d7bd20029c875d01fb06f3caf308260b","first_computed_at":"2026-05-18T01:12:49.473653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:49.473653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n95fpnrLmMUwMLf7aA4yEQyhHe1mdgTyBzkjQiSa1L9xNVlIHNkv4B7T72mne9IlMkhOyVzw04sbH4YDC9w3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:49.473998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14ed59ae9c5792a7307243b8185cb94832c8ce18852162110f4e1b2cc124fb98","sha256:88f4e9fddd630dfbaa9639059023786b1ddade31bcaa09a70ac0ca3a805fb428"],"state_sha256":"b4d4f42cfcca8649d6af1552a5e2ef06a3d47f750c9d357c5eb400056b0d8488"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGdfDb/2Hhh5AhhDAuX0CjoB0cxLy0OeUhrlVuiwz870P5ZTtbJ08hy8P9B1+vDdfSoEXsgcKXXJ0a7B9jb5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T06:02:01.341128Z","bundle_sha256":"a3ac0ba56f618835506bcbe5c7599ab1c4326b92efc3fd2a003f3172342a78aa"}}