{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DJAS5RYENEJSYJMORRQINS3LCL","short_pith_number":"pith:DJAS5RYE","canonical_record":{"source":{"id":"1310.4164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T19:52:19Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1b71c7375ee08b31f98a82900d7c6d58a31ebd7ef5d46689f6bb3aa6e83fe429","abstract_canon_sha256":"5d2e567469ce07de5a18868f8b7b36c0fc8a66f3594820da9b145fb7210df436"},"schema_version":"1.0"},"canonical_sha256":"1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d","source":{"kind":"arxiv","id":"1310.4164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4164","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4164v1","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4164","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"DJAS5RYENEJS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJAS5RYENEJSYJMO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJAS5RYE","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DJAS5RYENEJSYJMORRQINS3LCL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T19:52:19Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1b71c7375ee08b31f98a82900d7c6d58a31ebd7ef5d46689f6bb3aa6e83fe429","abstract_canon_sha256":"5d2e567469ce07de5a18868f8b7b36c0fc8a66f3594820da9b145fb7210df436"},"schema_version":"1.0"},"canonical_sha256":"1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:24.914664Z","signature_b64":"ICCQXwXR1uvphq11IkYDK78+IZy6Di8hrTxSRhIUUDXQ0zyi6y0H1h39yT5vRU9yZGEVODaTq999mpsif2OvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d","last_reissued_at":"2026-05-18T03:10:24.913890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:24.913890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4164","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dg1qIrFVUh8Ke7EEfsTG0WNwmjG8z4N/oW4SGJhB+MIhVqMAPczwo/JRGLXXP+f9G8azi3/bDYSmxLMlmgx7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:36:45.056917Z"},"content_sha256":"fce35bdfa194eb05d384b36418d20543cccd62f6076bd34acf853dc195fe03c2","schema_version":"1.0","event_id":"sha256:fce35bdfa194eb05d384b36418d20543cccd62f6076bd34acf853dc195fe03c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DJAS5RYENEJSYJMORRQINS3LCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transition in the two star Exponential Random Graph Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sumit Mukherjee","submitted_at":"2013-10-15T19:52:19Z","abstract_excerpt":"This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the phase transition boundaries are identified, and shown to be similar as that of the Curie-Weiss model of statistical physics. Concentration results are obtained for all the degrees, which further validate the phase transition predictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4164","kind":"arxiv","version":1},"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":"2026-05-18T03:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zgkc0C5D2RYBUtZ6m1VLjr9fPmTtSaFP+3aPmkdy0zu5DvzKtm6laRaTSDcSkuzICABShMVyeBWI/rceYx7aBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:36:45.057265Z"},"content_sha256":"b481dbf7ce2b73a837db8b9191f4dbd464d924cb39ea495a1297c21c3d5c24da","schema_version":"1.0","event_id":"sha256:b481dbf7ce2b73a837db8b9191f4dbd464d924cb39ea495a1297c21c3d5c24da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJAS5RYENEJSYJMORRQINS3LCL/bundle.json","state_url":"https://pith.science/pith/DJAS5RYENEJSYJMORRQINS3LCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJAS5RYENEJSYJMORRQINS3LCL/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":"2026-05-30T18:36:45Z","links":{"resolver":"https://pith.science/pith/DJAS5RYENEJSYJMORRQINS3LCL","bundle":"https://pith.science/pith/DJAS5RYENEJSYJMORRQINS3LCL/bundle.json","state":"https://pith.science/pith/DJAS5RYENEJSYJMORRQINS3LCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJAS5RYENEJSYJMORRQINS3LCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DJAS5RYENEJSYJMORRQINS3LCL","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":"5d2e567469ce07de5a18868f8b7b36c0fc8a66f3594820da9b145fb7210df436","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T19:52:19Z","title_canon_sha256":"1b71c7375ee08b31f98a82900d7c6d58a31ebd7ef5d46689f6bb3aa6e83fe429"},"schema_version":"1.0","source":{"id":"1310.4164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4164","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4164v1","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4164","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"DJAS5RYENEJS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJAS5RYENEJSYJMO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJAS5RYE","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b481dbf7ce2b73a837db8b9191f4dbd464d924cb39ea495a1297c21c3d5c24da","target":"graph","created_at":"2026-05-18T03:10:24Z","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":"This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the phase transition boundaries are identified, and shown to be similar as that of the Curie-Weiss model of statistical physics. Concentration results are obtained for all the degrees, which further validate the phase transition predictions.","authors_text":"Sumit Mukherjee","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T19:52:19Z","title":"Phase transition in the two star Exponential Random Graph Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4164","kind":"arxiv","version":1},"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:fce35bdfa194eb05d384b36418d20543cccd62f6076bd34acf853dc195fe03c2","target":"record","created_at":"2026-05-18T03:10:24Z","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":"5d2e567469ce07de5a18868f8b7b36c0fc8a66f3594820da9b145fb7210df436","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T19:52:19Z","title_canon_sha256":"1b71c7375ee08b31f98a82900d7c6d58a31ebd7ef5d46689f6bb3aa6e83fe429"},"schema_version":"1.0","source":{"id":"1310.4164","kind":"arxiv","version":1}},"canonical_sha256":"1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a412ec70469132c258e8c6086cb6b12ca57a31b716af3361d8e3fb0ca5e9b1d","first_computed_at":"2026-05-18T03:10:24.913890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:24.913890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ICCQXwXR1uvphq11IkYDK78+IZy6Di8hrTxSRhIUUDXQ0zyi6y0H1h39yT5vRU9yZGEVODaTq999mpsif2OvCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:24.914664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fce35bdfa194eb05d384b36418d20543cccd62f6076bd34acf853dc195fe03c2","sha256:b481dbf7ce2b73a837db8b9191f4dbd464d924cb39ea495a1297c21c3d5c24da"],"state_sha256":"3b9e9226c67a15eb903312b82c4bfcd6bff07c41eab86740ec85353f941d24af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqgZq2sLxwPAU8u1VkGoIXnve5kMjZOubM3LKlzOFaz/JyVKkeCUaatCwarwuwMmyDQMq+ahQfytEq7fgii9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:36:45.059504Z","bundle_sha256":"ceca38339c7fa23d4fa4a34db874d7978c134087115f6d5d19466eb2fbbd9087"}}