{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KKZPBJJUKG7UAGPBIHBP2VJD4M","short_pith_number":"pith:KKZPBJJU","canonical_record":{"source":{"id":"1603.08759","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:15:33Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"title_canon_sha256":"924f8a330be0573e68c3244453db9bc9efdda1600c549b19f91967d308235049","abstract_canon_sha256":"dba04f9a816f924b45b8321994a66f32d7fbab10df9b9b54f61560777f3aaa43"},"schema_version":"1.0"},"canonical_sha256":"52b2f0a53451bf4019e141c2fd5523e33509f1d9fda39e01170faf7eb8e0591f","source":{"kind":"arxiv","id":"1603.08759","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08759","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08759v2","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08759","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"KKZPBJJUKG7U","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KKZPBJJUKG7UAGPB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KKZPBJJU","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KKZPBJJUKG7UAGPBIHBP2VJD4M","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08759","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:15:33Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"title_canon_sha256":"924f8a330be0573e68c3244453db9bc9efdda1600c549b19f91967d308235049","abstract_canon_sha256":"dba04f9a816f924b45b8321994a66f32d7fbab10df9b9b54f61560777f3aaa43"},"schema_version":"1.0"},"canonical_sha256":"52b2f0a53451bf4019e141c2fd5523e33509f1d9fda39e01170faf7eb8e0591f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:09.503461Z","signature_b64":"OWVD+OBHiL6zVUK3fNyvYQtvQaCspNdqN/qN2gDifRqO4yjP3eUQcemPU9jKrxy5NFAA7ovA7bnDkcukD/HPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52b2f0a53451bf4019e141c2fd5523e33509f1d9fda39e01170faf7eb8e0591f","last_reissued_at":"2026-05-18T00:43:09.502857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:09.502857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08759","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GhowwTgbII4f2T8jazy+oLdVWiNlGg/6Q91WKUmH2HwwJY8q2WmpZ2+EMHeesyr65qLQSH7sJK671r6UidUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:49:09.584353Z"},"content_sha256":"2ff7d52db05a98f3efe5d954957a21d9edad60de430ebdf494a0c168eb3be5ed","schema_version":"1.0","event_id":"sha256:2ff7d52db05a98f3efe5d954957a21d9edad60de430ebdf494a0c168eb3be5ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KKZPBJJUKG7UAGPBIHBP2VJD4M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ensemble nonequivalence in random graphs with modular structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"primary_cat":"math.PR","authors_text":"Andrea Roccaverde, Diego Garlaschelli, Frank den Hollander","submitted_at":"2016-03-29T13:15:33Z","abstract_excerpt":"Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must be met by every graph, soft constraints must be met only on average, subject to maximal entropy. In Squartini et al. (2015) it was shown that ensembles of random graphs are non-equivalent when the degrees of the nodes are constrained, in the sense of a non-zero limiting specific relative entropy as the number of nodes diverges. In that paper, the nodes were "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08759","kind":"arxiv","version":2},"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":"2026-05-18T00:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5v6eTHF551X9HUhbPTJg4zhZIl6uCaPGxiiN+rbydWXJ2RbejEI1z3SU0DGKazdSx9iUnmVkonz8uhd34zjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:49:09.585053Z"},"content_sha256":"6853d3f776acdbdb5ea8c13f6cec63020fc4756099f3d588c8a294c6c110eae5","schema_version":"1.0","event_id":"sha256:6853d3f776acdbdb5ea8c13f6cec63020fc4756099f3d588c8a294c6c110eae5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/bundle.json","state_url":"https://pith.science/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/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":"2026-05-30T12:49:09Z","links":{"resolver":"https://pith.science/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M","bundle":"https://pith.science/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/bundle.json","state":"https://pith.science/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKZPBJJUKG7UAGPBIHBP2VJD4M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KKZPBJJUKG7UAGPBIHBP2VJD4M","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":"dba04f9a816f924b45b8321994a66f32d7fbab10df9b9b54f61560777f3aaa43","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:15:33Z","title_canon_sha256":"924f8a330be0573e68c3244453db9bc9efdda1600c549b19f91967d308235049"},"schema_version":"1.0","source":{"id":"1603.08759","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08759","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08759v2","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08759","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"KKZPBJJUKG7U","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KKZPBJJUKG7UAGPB","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KKZPBJJU","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:6853d3f776acdbdb5ea8c13f6cec63020fc4756099f3d588c8a294c6c110eae5","target":"graph","created_at":"2026-05-18T00:43:09Z","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":"Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must be met by every graph, soft constraints must be met only on average, subject to maximal entropy. In Squartini et al. (2015) it was shown that ensembles of random graphs are non-equivalent when the degrees of the nodes are constrained, in the sense of a non-zero limiting specific relative entropy as the number of nodes diverges. In that paper, the nodes were ","authors_text":"Andrea Roccaverde, Diego Garlaschelli, Frank den Hollander","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:15:33Z","title":"Ensemble nonequivalence in random graphs with modular structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08759","kind":"arxiv","version":2},"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":"sha256:2ff7d52db05a98f3efe5d954957a21d9edad60de430ebdf494a0c168eb3be5ed","target":"record","created_at":"2026-05-18T00:43:09Z","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":"dba04f9a816f924b45b8321994a66f32d7fbab10df9b9b54f61560777f3aaa43","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:15:33Z","title_canon_sha256":"924f8a330be0573e68c3244453db9bc9efdda1600c549b19f91967d308235049"},"schema_version":"1.0","source":{"id":"1603.08759","kind":"arxiv","version":2}},"canonical_sha256":"52b2f0a53451bf4019e141c2fd5523e33509f1d9fda39e01170faf7eb8e0591f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52b2f0a53451bf4019e141c2fd5523e33509f1d9fda39e01170faf7eb8e0591f","first_computed_at":"2026-05-18T00:43:09.502857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:09.502857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OWVD+OBHiL6zVUK3fNyvYQtvQaCspNdqN/qN2gDifRqO4yjP3eUQcemPU9jKrxy5NFAA7ovA7bnDkcukD/HPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:09.503461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08759","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ff7d52db05a98f3efe5d954957a21d9edad60de430ebdf494a0c168eb3be5ed","sha256:6853d3f776acdbdb5ea8c13f6cec63020fc4756099f3d588c8a294c6c110eae5"],"state_sha256":"85f8f5e90b25b759ab11d2c72c51d0caf3d2ed4c0c9270672f7fe865252968f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LG5myDtmSp2F2jit9gIzQ0cnDFUFJksMcdKNiajCIKDB7QjC9AtNoagDqMNyMrbzVYpyx8an8vY0qqYShEOYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:49:09.588553Z","bundle_sha256":"62f9c8912949915cd878f759f4e5b5110d659e09fca4d6dee40c4e1bb9e4096f"}}