{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KOA32IGWA4JNWWEU54JCFHI7QA","short_pith_number":"pith:KOA32IGW","canonical_record":{"source":{"id":"1208.2992","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T23:18:57Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"e1e3d35420d5e8031c4d6642397b459ce4f6323f739f171894453515381a610e","abstract_canon_sha256":"ce2b3eed1bfa55e581cd90c2608bf484e13f2b9fcab7c46db54a0687e89d17fd"},"schema_version":"1.0"},"canonical_sha256":"5381bd20d60712db5894ef12229d1f800b39323c164e7b3ba81864242e149caf","source":{"kind":"arxiv","id":"1208.2992","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2992","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2992v3","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2992","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"KOA32IGWA4JN","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KOA32IGWA4JNWWEU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KOA32IGW","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KOA32IGWA4JNWWEU54JCFHI7QA","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2992","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T23:18:57Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"e1e3d35420d5e8031c4d6642397b459ce4f6323f739f171894453515381a610e","abstract_canon_sha256":"ce2b3eed1bfa55e581cd90c2608bf484e13f2b9fcab7c46db54a0687e89d17fd"},"schema_version":"1.0"},"canonical_sha256":"5381bd20d60712db5894ef12229d1f800b39323c164e7b3ba81864242e149caf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:15.888252Z","signature_b64":"OB1IG5ALjeVoGkycWi7UDBOfWvw9i9jR1zySNiiLNbX95IK9Sa+iDldSALCmYfEHTaQsAubbsGDHVAI0uYkBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5381bd20d60712db5894ef12229d1f800b39323c164e7b3ba81864242e149caf","last_reissued_at":"2026-05-18T01:55:15.887731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:15.887731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2992","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":"2026-05-18T01:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwY4v/5H0+ORh75PnotD0SKXGORkZGbv6oOZGPd/QwmH410U+Nywq1PvzMgDAe5pU8z7dOCQmwArdBdNaQikCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T02:31:09.145916Z"},"content_sha256":"d771ab86c96717ff0e214cda26d1dadc0cbc7a9bd0afba6189996c3ab9f156b2","schema_version":"1.0","event_id":"sha256:d771ab86c96717ff0e214cda26d1dadc0cbc7a9bd0afba6189996c3ab9f156b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KOA32IGWA4JNWWEU54JCFHI7QA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical phenomena in exponential random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Mei Yin","submitted_at":"2012-08-14T23:18:57Z","abstract_excerpt":"The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2992","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":"2026-05-18T01:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqTFGyxKHhR3BmIFSfmYWVvW7567g5lJ73JQq+vZYUFSg4GR2ciiRlfLvdNrgJdlufrrrzvT48AKtbfLN/UzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T02:31:09.146281Z"},"content_sha256":"22a8ad33494ba3c779ec99d20dabd592d42da3f0f2f7e9fb1c7acc46c06da08c","schema_version":"1.0","event_id":"sha256:22a8ad33494ba3c779ec99d20dabd592d42da3f0f2f7e9fb1c7acc46c06da08c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOA32IGWA4JNWWEU54JCFHI7QA/bundle.json","state_url":"https://pith.science/pith/KOA32IGWA4JNWWEU54JCFHI7QA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOA32IGWA4JNWWEU54JCFHI7QA/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":"2026-07-08T02:31:09Z","links":{"resolver":"https://pith.science/pith/KOA32IGWA4JNWWEU54JCFHI7QA","bundle":"https://pith.science/pith/KOA32IGWA4JNWWEU54JCFHI7QA/bundle.json","state":"https://pith.science/pith/KOA32IGWA4JNWWEU54JCFHI7QA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOA32IGWA4JNWWEU54JCFHI7QA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KOA32IGWA4JNWWEU54JCFHI7QA","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":"ce2b3eed1bfa55e581cd90c2608bf484e13f2b9fcab7c46db54a0687e89d17fd","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T23:18:57Z","title_canon_sha256":"e1e3d35420d5e8031c4d6642397b459ce4f6323f739f171894453515381a610e"},"schema_version":"1.0","source":{"id":"1208.2992","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2992","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2992v3","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2992","created_at":"2026-05-18T01:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"KOA32IGWA4JN","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KOA32IGWA4JNWWEU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KOA32IGW","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:22a8ad33494ba3c779ec99d20dabd592d42da3f0f2f7e9fb1c7acc46c06da08c","target":"graph","created_at":"2026-05-18T01:55:15Z","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 exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating ","authors_text":"Mei Yin","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T23:18:57Z","title":"Critical phenomena in exponential random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2992","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:d771ab86c96717ff0e214cda26d1dadc0cbc7a9bd0afba6189996c3ab9f156b2","target":"record","created_at":"2026-05-18T01:55:15Z","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":"ce2b3eed1bfa55e581cd90c2608bf484e13f2b9fcab7c46db54a0687e89d17fd","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T23:18:57Z","title_canon_sha256":"e1e3d35420d5e8031c4d6642397b459ce4f6323f739f171894453515381a610e"},"schema_version":"1.0","source":{"id":"1208.2992","kind":"arxiv","version":3}},"canonical_sha256":"5381bd20d60712db5894ef12229d1f800b39323c164e7b3ba81864242e149caf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5381bd20d60712db5894ef12229d1f800b39323c164e7b3ba81864242e149caf","first_computed_at":"2026-05-18T01:55:15.887731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:15.887731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OB1IG5ALjeVoGkycWi7UDBOfWvw9i9jR1zySNiiLNbX95IK9Sa+iDldSALCmYfEHTaQsAubbsGDHVAI0uYkBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:15.888252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2992","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d771ab86c96717ff0e214cda26d1dadc0cbc7a9bd0afba6189996c3ab9f156b2","sha256:22a8ad33494ba3c779ec99d20dabd592d42da3f0f2f7e9fb1c7acc46c06da08c"],"state_sha256":"e95a62767ae02e91afaed4ac0f1aec351366c170abf794803c2d41855d39007b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Jy6zlCoWj2MWI2tmdjBMeDiBtPgnXVVbCxkxrXqJ7BLgWiAuMQ/En6Xq3usssPTdINmDNdvrMD2d1ZCp8oNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T02:31:09.149212Z","bundle_sha256":"1bd1e9f493401d7894e6f79f220002db3b6079abd1f602eff134a1180e9000de"}}