{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QMRHBJMFRDSXIL6DKIDYZXFL5G","short_pith_number":"pith:QMRHBJMF","canonical_record":{"source":{"id":"1804.01630","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-05T00:06:34Z","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"title_canon_sha256":"21a8477adeaaff2f8f399157bac094df3d75b5bbea2b35d4219c0f729d30bc22","abstract_canon_sha256":"0b4474d21d81d551824e63ee52194a2a73dfb4db18ccf71f9ba145342dc4719a"},"schema_version":"1.0"},"canonical_sha256":"832270a58588e5742fc352078cdcabe9b9ff99724e67ff0f76bcedb3355acea8","source":{"kind":"arxiv","id":"1804.01630","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01630","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01630v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01630","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"QMRHBJMFRDSX","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMRHBJMFRDSXIL6D","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMRHBJMF","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QMRHBJMFRDSXIL6DKIDYZXFL5G","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01630","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-05T00:06:34Z","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"title_canon_sha256":"21a8477adeaaff2f8f399157bac094df3d75b5bbea2b35d4219c0f729d30bc22","abstract_canon_sha256":"0b4474d21d81d551824e63ee52194a2a73dfb4db18ccf71f9ba145342dc4719a"},"schema_version":"1.0"},"canonical_sha256":"832270a58588e5742fc352078cdcabe9b9ff99724e67ff0f76bcedb3355acea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:23.545324Z","signature_b64":"PPc95eDCcKkwKMfLrhRSIsASSgLR8NqdTIYlxMfiteBoRpmqDNC2W6VsN9o2xvSNVqq04zZQPnRCSPhv0O+9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"832270a58588e5742fc352078cdcabe9b9ff99724e67ff0f76bcedb3355acea8","last_reissued_at":"2026-05-18T00:07:23.544774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:23.544774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01630","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RY3C2hwSdsqjh1kZNRIC+zMS7d9E+GeFuiZe1tGwgKZZO3V7Ccpj36kK5rFXikJ/VAMk+gKXapCqbK4jP/xOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:05.371854Z"},"content_sha256":"0844661fe1d7698710fad49fad33cfc41f1fe908704afb0422b301453d2dc7f9","schema_version":"1.0","event_id":"sha256:0844661fe1d7698710fad49fad33cfc41f1fe908704afb0422b301453d2dc7f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QMRHBJMFRDSXIL6DKIDYZXFL5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase diagram and metastability of the Ising model on two coupled networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Fernando L. Metz, Lucas Nicolao, Ma\\'ira Bolfe","submitted_at":"2018-04-05T00:06:34Z","abstract_excerpt":"We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\\\"os-R\\'enyi random graphs. We derive analytical expressions for the free-energy of the system and the magnetization of each graph, from which the phase diagrams, the stability of the different states, and the nature of the transitions among them, are clearly characterized. We show that a metastable state appears discontinuously by varying the model parameters, yielding a region in the phase diagram where two solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01630","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/hhBRFOdDqdPgDMIFFgw9o5u+2rc31v7qdV07DrIUfbp6eW8yEJprxPS3pcyOUrmQ5rNbSmq9DT9PIbzGsBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:05.372201Z"},"content_sha256":"a2cfaf1846d8204de7ae2be52b682b9b58534648cdb5607325683c234b0093c2","schema_version":"1.0","event_id":"sha256:a2cfaf1846d8204de7ae2be52b682b9b58534648cdb5607325683c234b0093c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/bundle.json","state_url":"https://pith.science/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/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":"2026-05-28T07:50:05Z","links":{"resolver":"https://pith.science/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G","bundle":"https://pith.science/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/bundle.json","state":"https://pith.science/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMRHBJMFRDSXIL6DKIDYZXFL5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QMRHBJMFRDSXIL6DKIDYZXFL5G","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":"0b4474d21d81d551824e63ee52194a2a73dfb4db18ccf71f9ba145342dc4719a","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-05T00:06:34Z","title_canon_sha256":"21a8477adeaaff2f8f399157bac094df3d75b5bbea2b35d4219c0f729d30bc22"},"schema_version":"1.0","source":{"id":"1804.01630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01630","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01630v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01630","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"QMRHBJMFRDSX","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMRHBJMFRDSXIL6D","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMRHBJMF","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:a2cfaf1846d8204de7ae2be52b682b9b58534648cdb5607325683c234b0093c2","target":"graph","created_at":"2026-05-18T00:07:23Z","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 explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\\\"os-R\\'enyi random graphs. We derive analytical expressions for the free-energy of the system and the magnetization of each graph, from which the phase diagrams, the stability of the different states, and the nature of the transitions among them, are clearly characterized. We show that a metastable state appears discontinuously by varying the model parameters, yielding a region in the phase diagram where two solutions","authors_text":"Fernando L. Metz, Lucas Nicolao, Ma\\'ira Bolfe","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-05T00:06:34Z","title":"Phase diagram and metastability of the Ising model on two coupled networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01630","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":"sha256:0844661fe1d7698710fad49fad33cfc41f1fe908704afb0422b301453d2dc7f9","target":"record","created_at":"2026-05-18T00:07:23Z","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":"0b4474d21d81d551824e63ee52194a2a73dfb4db18ccf71f9ba145342dc4719a","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-05T00:06:34Z","title_canon_sha256":"21a8477adeaaff2f8f399157bac094df3d75b5bbea2b35d4219c0f729d30bc22"},"schema_version":"1.0","source":{"id":"1804.01630","kind":"arxiv","version":2}},"canonical_sha256":"832270a58588e5742fc352078cdcabe9b9ff99724e67ff0f76bcedb3355acea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"832270a58588e5742fc352078cdcabe9b9ff99724e67ff0f76bcedb3355acea8","first_computed_at":"2026-05-18T00:07:23.544774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.544774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PPc95eDCcKkwKMfLrhRSIsASSgLR8NqdTIYlxMfiteBoRpmqDNC2W6VsN9o2xvSNVqq04zZQPnRCSPhv0O+9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.545324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0844661fe1d7698710fad49fad33cfc41f1fe908704afb0422b301453d2dc7f9","sha256:a2cfaf1846d8204de7ae2be52b682b9b58534648cdb5607325683c234b0093c2"],"state_sha256":"77a6970898ecc08c58a61a81ae9add0acfd025bebb9216da4f257e3c7a427617"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uicRfS90jQhevWL8BdzHIYzi8C/AftBPlGMKguUJliz1RsnknLMVyIfYptiYgIpamMsOKzC1RuxqJdxhWCsJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:50:05.374324Z","bundle_sha256":"e3b21b15eb438cd2d951703e94ea748393e0ca2cabe5dcd27ffa152b39f929c7"}}