{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XNZ6O4ARL7IV5VPQHKDLJ5VBP7","short_pith_number":"pith:XNZ6O4AR","canonical_record":{"source":{"id":"1904.05321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-10T17:29:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"38f0009ff9273a382acb5b793c5579891d0c83b72e009cc07893611ab86a818d","abstract_canon_sha256":"20106688af190b3a5c5272ca4f3695d1f4f8fbc57d4945fab134f23abd89be9f"},"schema_version":"1.0"},"canonical_sha256":"bb73e770115fd15ed5f03a86b4f6a17ffd41854a51063d1bee59dd64af7409af","source":{"kind":"arxiv","id":"1904.05321","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05321","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05321v2","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05321","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"XNZ6O4ARL7IV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XNZ6O4ARL7IV5VPQ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XNZ6O4AR","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XNZ6O4ARL7IV5VPQHKDLJ5VBP7","target":"record","payload":{"canonical_record":{"source":{"id":"1904.05321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-10T17:29:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"38f0009ff9273a382acb5b793c5579891d0c83b72e009cc07893611ab86a818d","abstract_canon_sha256":"20106688af190b3a5c5272ca4f3695d1f4f8fbc57d4945fab134f23abd89be9f"},"schema_version":"1.0"},"canonical_sha256":"bb73e770115fd15ed5f03a86b4f6a17ffd41854a51063d1bee59dd64af7409af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:15.521186Z","signature_b64":"Cqz8N53Vx4pgLe8tILSObGVN0oIjClC5yYt+nljSN6KHNkuIy5GffWpL53qjKimA3KXhHu1yzxG3Scdk6NCqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb73e770115fd15ed5f03a86b4f6a17ffd41854a51063d1bee59dd64af7409af","last_reissued_at":"2026-05-17T23:47:15.520647Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:15.520647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.05321","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":"2026-05-17T23:47:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+JaEdF0a+sifiuO62UsiFTOrJgXZJ4ikJNGn6qVjazdLi5RXa1dkuDxVuliUZ1Pk2gCZ6UDV+Wb/FugwF2QDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:08:18.921206Z"},"content_sha256":"dab07afa8d417e7dd69f822833a6931a949691b04db3446bfc1038f432f52520","schema_version":"1.0","event_id":"sha256:dab07afa8d417e7dd69f822833a6931a949691b04db3446bfc1038f432f52520"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XNZ6O4ARL7IV5VPQHKDLJ5VBP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ground States And Hyperuniformity Of The Hierarchical Coulomb Gas In All Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Shirshendu Ganguly, Sourav Sarkar","submitted_at":"2019-04-10T17:29:12Z","abstract_excerpt":"Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin, and Yalcin ('80,'83,'93), states that the variance of the number of points landing in a set should g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05321","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":"2026-05-17T23:47:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIhe3uUO87dHNKYq3bdAi33FvzfYfGQe+AYeAMzvZNCi6DEi8FiWHqMnRTurTUIewCwkgHJuYBFUO4vbHkJnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:08:18.921569Z"},"content_sha256":"5086eaecc7b114e381e3580a35f3cd09b5e508ff6be094b8b02f5efdb697bbfb","schema_version":"1.0","event_id":"sha256:5086eaecc7b114e381e3580a35f3cd09b5e508ff6be094b8b02f5efdb697bbfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/bundle.json","state_url":"https://pith.science/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/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":"2026-06-02T14:08:18Z","links":{"resolver":"https://pith.science/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7","bundle":"https://pith.science/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/bundle.json","state":"https://pith.science/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNZ6O4ARL7IV5VPQHKDLJ5VBP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XNZ6O4ARL7IV5VPQHKDLJ5VBP7","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":"20106688af190b3a5c5272ca4f3695d1f4f8fbc57d4945fab134f23abd89be9f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-10T17:29:12Z","title_canon_sha256":"38f0009ff9273a382acb5b793c5579891d0c83b72e009cc07893611ab86a818d"},"schema_version":"1.0","source":{"id":"1904.05321","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05321","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05321v2","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05321","created_at":"2026-05-17T23:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"XNZ6O4ARL7IV","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XNZ6O4ARL7IV5VPQ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XNZ6O4AR","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:5086eaecc7b114e381e3580a35f3cd09b5e508ff6be094b8b02f5efdb697bbfb","target":"graph","created_at":"2026-05-17T23:47:15Z","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":"Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin, and Yalcin ('80,'83,'93), states that the variance of the number of points landing in a set should g","authors_text":"Shirshendu Ganguly, Sourav Sarkar","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-10T17:29:12Z","title":"Ground States And Hyperuniformity Of The Hierarchical Coulomb Gas In All Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05321","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:dab07afa8d417e7dd69f822833a6931a949691b04db3446bfc1038f432f52520","target":"record","created_at":"2026-05-17T23:47:15Z","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":"20106688af190b3a5c5272ca4f3695d1f4f8fbc57d4945fab134f23abd89be9f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-10T17:29:12Z","title_canon_sha256":"38f0009ff9273a382acb5b793c5579891d0c83b72e009cc07893611ab86a818d"},"schema_version":"1.0","source":{"id":"1904.05321","kind":"arxiv","version":2}},"canonical_sha256":"bb73e770115fd15ed5f03a86b4f6a17ffd41854a51063d1bee59dd64af7409af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb73e770115fd15ed5f03a86b4f6a17ffd41854a51063d1bee59dd64af7409af","first_computed_at":"2026-05-17T23:47:15.520647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:15.520647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cqz8N53Vx4pgLe8tILSObGVN0oIjClC5yYt+nljSN6KHNkuIy5GffWpL53qjKimA3KXhHu1yzxG3Scdk6NCqCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:15.521186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05321","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dab07afa8d417e7dd69f822833a6931a949691b04db3446bfc1038f432f52520","sha256:5086eaecc7b114e381e3580a35f3cd09b5e508ff6be094b8b02f5efdb697bbfb"],"state_sha256":"60fdd0096894f225108cd0caa499e28f35631462bfeeae5da727437bba08a7cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5ZAmA6daE4tNULNb1xBSjF8lD4v0R9m9fvT0G+hrBDMoLcrJsSBIqcYkY1ExivgFNsKuRNxAGsu3fzVap1cBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:08:18.923621Z","bundle_sha256":"18874d2231b0d7ba31cda89d12cc78c88985ae2012a5b1b589f376eb8dd0f4f9"}}