{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KUQVE2ERMPID4FGJR2IB3ADYP2","short_pith_number":"pith:KUQVE2ER","canonical_record":{"source":{"id":"1109.6642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-09-29T19:54:36Z","cross_cats_sorted":["cs.IT","cs.SI","math.IT"],"title_canon_sha256":"42bd6f9ec8868b555faab2e5e11b6999d8d43ce54532923284a8affbd9329646","abstract_canon_sha256":"733c159dc376a49b90971be2d8d470e17b22a22db0a21d35483e43427073efef"},"schema_version":"1.0"},"canonical_sha256":"552152689163d03e14c98e901d80787eab3401467c5a23ecd7473cf083fcf10e","source":{"kind":"arxiv","id":"1109.6642","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6642","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6642v3","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6642","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"KUQVE2ERMPID","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KUQVE2ERMPID4FGJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KUQVE2ER","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KUQVE2ERMPID4FGJR2IB3ADYP2","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-09-29T19:54:36Z","cross_cats_sorted":["cs.IT","cs.SI","math.IT"],"title_canon_sha256":"42bd6f9ec8868b555faab2e5e11b6999d8d43ce54532923284a8affbd9329646","abstract_canon_sha256":"733c159dc376a49b90971be2d8d470e17b22a22db0a21d35483e43427073efef"},"schema_version":"1.0"},"canonical_sha256":"552152689163d03e14c98e901d80787eab3401467c5a23ecd7473cf083fcf10e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:36.041411Z","signature_b64":"5AO/JP/MBlAQFFmzN0Pm9aes35NQnjCuA0pG7lMIXFjH692VZmGZJGMDj4fOjDi9kvP9BtAvwvmVQiQ/0lcxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"552152689163d03e14c98e901d80787eab3401467c5a23ecd7473cf083fcf10e","last_reissued_at":"2026-05-18T02:21:36.040977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:36.040977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6642","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Fg6zCtcbzw9ojNcBqvY58TwLEIYlJpsqmM0ORT1I3AIkLU3d5AzLO8GS/3w3kHxEGCS3J5iQr1cfE4ytRwuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:05:45.333132Z"},"content_sha256":"cfee9504783ff44966eb70c8651162443992f193ced77abe82a15875005bb858","schema_version":"1.0","event_id":"sha256:cfee9504783ff44966eb70c8651162443992f193ced77abe82a15875005bb858"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KUQVE2ERMPID4FGJR2IB3ADYP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.SI","math.IT"],"primary_cat":"physics.soc-ph","authors_text":"Mauricio Barahona, Michael T. Schaub, Renaud Lambiotte","submitted_at":"2011-09-29T19:54:36Z","abstract_excerpt":"The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original Map co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6642","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mnUx3L+PITDLejpToQClRwdFHxPMJ86ybEkNYEzPbZdDhozdu0WuiZRhSjZZwx+0BBFgZcbr9rQuvvHL3wFQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:05:45.333857Z"},"content_sha256":"3d6ae8d8f9d66124b64396c2bd7c40a6c1e90a753adbcc06493343724c476a80","schema_version":"1.0","event_id":"sha256:3d6ae8d8f9d66124b64396c2bd7c40a6c1e90a753adbcc06493343724c476a80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/bundle.json","state_url":"https://pith.science/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/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":"2026-06-10T00:05:45Z","links":{"resolver":"https://pith.science/pith/KUQVE2ERMPID4FGJR2IB3ADYP2","bundle":"https://pith.science/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/bundle.json","state":"https://pith.science/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUQVE2ERMPID4FGJR2IB3ADYP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KUQVE2ERMPID4FGJR2IB3ADYP2","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":"733c159dc376a49b90971be2d8d470e17b22a22db0a21d35483e43427073efef","cross_cats_sorted":["cs.IT","cs.SI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-09-29T19:54:36Z","title_canon_sha256":"42bd6f9ec8868b555faab2e5e11b6999d8d43ce54532923284a8affbd9329646"},"schema_version":"1.0","source":{"id":"1109.6642","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6642","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6642v3","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6642","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"KUQVE2ERMPID","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KUQVE2ERMPID4FGJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KUQVE2ER","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:3d6ae8d8f9d66124b64396c2bd7c40a6c1e90a753adbcc06493343724c476a80","target":"graph","created_at":"2026-05-18T02:21:36Z","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 detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original Map co","authors_text":"Mauricio Barahona, Michael T. Schaub, Renaud Lambiotte","cross_cats":["cs.IT","cs.SI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-09-29T19:54:36Z","title":"Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6642","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:cfee9504783ff44966eb70c8651162443992f193ced77abe82a15875005bb858","target":"record","created_at":"2026-05-18T02:21:36Z","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":"733c159dc376a49b90971be2d8d470e17b22a22db0a21d35483e43427073efef","cross_cats_sorted":["cs.IT","cs.SI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-09-29T19:54:36Z","title_canon_sha256":"42bd6f9ec8868b555faab2e5e11b6999d8d43ce54532923284a8affbd9329646"},"schema_version":"1.0","source":{"id":"1109.6642","kind":"arxiv","version":3}},"canonical_sha256":"552152689163d03e14c98e901d80787eab3401467c5a23ecd7473cf083fcf10e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"552152689163d03e14c98e901d80787eab3401467c5a23ecd7473cf083fcf10e","first_computed_at":"2026-05-18T02:21:36.040977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:36.040977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5AO/JP/MBlAQFFmzN0Pm9aes35NQnjCuA0pG7lMIXFjH692VZmGZJGMDj4fOjDi9kvP9BtAvwvmVQiQ/0lcxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:36.041411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6642","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfee9504783ff44966eb70c8651162443992f193ced77abe82a15875005bb858","sha256:3d6ae8d8f9d66124b64396c2bd7c40a6c1e90a753adbcc06493343724c476a80"],"state_sha256":"89e48929e3816a42724abf865f707e03150cdb8932e16233d0a8bb6df3a54b91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlOw/YCc1JeGEM8LIa4wct/u3ou+dQtaNtwDo/eTwHNkYDh+yDe3DDuFfLOIkhPFXcyVOsxM61WsldjUG5NCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:05:45.338815Z","bundle_sha256":"24f9f27848367796e591c63a59dc9bcb4edf88f5e40437b148e1f80c56c35719"}}