{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZCNDZSHGV4IQTYPMFYK7FQSDQF","short_pith_number":"pith:ZCNDZSHG","canonical_record":{"source":{"id":"1404.5290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-21T19:53:27Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"84e49ffc1156f6409ccf2e7d89b915b359d89b1dd385936309cfa184ec8c2a29","abstract_canon_sha256":"60e7f5eab5eb963ea41d582b6224a8108dec93e0f59888b5d9a27d63ac7dc304"},"schema_version":"1.0"},"canonical_sha256":"c89a3cc8e6af1109e1ec2e15f2c24381646606fec46914b7ee7cb6181a0ca6ed","source":{"kind":"arxiv","id":"1404.5290","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5290","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5290v2","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5290","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZCNDZSHGV4IQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCNDZSHGV4IQTYPM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCNDZSHG","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZCNDZSHGV4IQTYPMFYK7FQSDQF","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-21T19:53:27Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"84e49ffc1156f6409ccf2e7d89b915b359d89b1dd385936309cfa184ec8c2a29","abstract_canon_sha256":"60e7f5eab5eb963ea41d582b6224a8108dec93e0f59888b5d9a27d63ac7dc304"},"schema_version":"1.0"},"canonical_sha256":"c89a3cc8e6af1109e1ec2e15f2c24381646606fec46914b7ee7cb6181a0ca6ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:28.388442Z","signature_b64":"5QlXfR/B60ozgD1QL7s+XzHWLMtBVMahdZ4A8RSdHIgf6ZWGh4Y6VC7T7rbWwWM/VQ0FxWb2lr301E3PCpMUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c89a3cc8e6af1109e1ec2e15f2c24381646606fec46914b7ee7cb6181a0ca6ed","last_reissued_at":"2026-05-18T02:53:28.387682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:28.387682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5290","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoJRp6QXU+5TSdc+eF02m3+aHGmY/zlunEjrtBy7a6RtVuE4I1u7W5QJVWlSVO+dgwPRJFKvDf70ZX68gK4kCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:47:20.127465Z"},"content_sha256":"7129c9084a2a7f07de7c56fa05d6811c05e8e2dc49f1c35e539db004c6286dd3","schema_version":"1.0","event_id":"sha256:7129c9084a2a7f07de7c56fa05d6811c05e8e2dc49f1c35e539db004c6286dd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZCNDZSHGV4IQTYPMFYK7FQSDQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Solvable Two-Charge Ensemble on the Circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Christopher D. Sinclair, Christopher Shum","submitted_at":"2014-04-21T19:53:27Z","abstract_excerpt":"We introduce an ensemble consisting of logarithmically repelling charge one and charge two particles on the unit circle constrained so that the total charge of all particles equals $N$, but the proportion of each species of particle is allowed to vary according to a fugacity parameter. We identify the proper scaling of the fugacity with $N$ so that the proportion of each particle stays positive in the $N \\rightarrow \\infty$ limit. This ensemble forms a Pfaffian point process on the unit circle, and we derive the scaling limits of the matrix kernel(s) as a function of the interpolating paramete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5290","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7nPwjsgPqikyIVd8BURNLw70K8lf9Q7lIqDAqycnH8aX4aQ5vI+CBAceiGGaav1+PwBjxpdhLGofYLLXIJ/+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:47:20.127806Z"},"content_sha256":"3953ee0039a85fdfd24fc99cae11a5b5dc162152e230bcc1893a79b0bb627bc4","schema_version":"1.0","event_id":"sha256:3953ee0039a85fdfd24fc99cae11a5b5dc162152e230bcc1893a79b0bb627bc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/bundle.json","state_url":"https://pith.science/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/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":"2026-06-05T12:47:20Z","links":{"resolver":"https://pith.science/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF","bundle":"https://pith.science/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/bundle.json","state":"https://pith.science/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCNDZSHGV4IQTYPMFYK7FQSDQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCNDZSHGV4IQTYPMFYK7FQSDQF","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":"60e7f5eab5eb963ea41d582b6224a8108dec93e0f59888b5d9a27d63ac7dc304","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-21T19:53:27Z","title_canon_sha256":"84e49ffc1156f6409ccf2e7d89b915b359d89b1dd385936309cfa184ec8c2a29"},"schema_version":"1.0","source":{"id":"1404.5290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5290","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5290v2","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5290","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZCNDZSHGV4IQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCNDZSHGV4IQTYPM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCNDZSHG","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:3953ee0039a85fdfd24fc99cae11a5b5dc162152e230bcc1893a79b0bb627bc4","target":"graph","created_at":"2026-05-18T02:53:28Z","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 introduce an ensemble consisting of logarithmically repelling charge one and charge two particles on the unit circle constrained so that the total charge of all particles equals $N$, but the proportion of each species of particle is allowed to vary according to a fugacity parameter. We identify the proper scaling of the fugacity with $N$ so that the proportion of each particle stays positive in the $N \\rightarrow \\infty$ limit. This ensemble forms a Pfaffian point process on the unit circle, and we derive the scaling limits of the matrix kernel(s) as a function of the interpolating paramete","authors_text":"Christopher D. Sinclair, Christopher Shum","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-21T19:53:27Z","title":"A Solvable Two-Charge Ensemble on the Circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5290","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":"sha256:7129c9084a2a7f07de7c56fa05d6811c05e8e2dc49f1c35e539db004c6286dd3","target":"record","created_at":"2026-05-18T02:53:28Z","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":"60e7f5eab5eb963ea41d582b6224a8108dec93e0f59888b5d9a27d63ac7dc304","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-21T19:53:27Z","title_canon_sha256":"84e49ffc1156f6409ccf2e7d89b915b359d89b1dd385936309cfa184ec8c2a29"},"schema_version":"1.0","source":{"id":"1404.5290","kind":"arxiv","version":2}},"canonical_sha256":"c89a3cc8e6af1109e1ec2e15f2c24381646606fec46914b7ee7cb6181a0ca6ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89a3cc8e6af1109e1ec2e15f2c24381646606fec46914b7ee7cb6181a0ca6ed","first_computed_at":"2026-05-18T02:53:28.387682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:28.387682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QlXfR/B60ozgD1QL7s+XzHWLMtBVMahdZ4A8RSdHIgf6ZWGh4Y6VC7T7rbWwWM/VQ0FxWb2lr301E3PCpMUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:28.388442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7129c9084a2a7f07de7c56fa05d6811c05e8e2dc49f1c35e539db004c6286dd3","sha256:3953ee0039a85fdfd24fc99cae11a5b5dc162152e230bcc1893a79b0bb627bc4"],"state_sha256":"c14ccc987dccdc36b4dde84413e170dad131bad44cbd21a2451e6c1ce7f40d33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2q3qqattViAMIvyR6n9nL59iS2ZDgxhxARn425bfuePrDX590Rt0lfTtoBzA8g8z9UrjUsV8c4KR10VzP5cBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:47:20.129753Z","bundle_sha256":"8d5d0359e19b40c318ffa07694c469cf46672ee2b4daad66ec080b4c897cba37"}}