{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WCTQOYYG7U6WPGJZ2RRBNPAU4M","short_pith_number":"pith:WCTQOYYG","canonical_record":{"source":{"id":"1701.09064","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-31T14:45:06Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"title_canon_sha256":"4b213acbddceffefd33ea966514cfde1e4c1dffa09e738c2b4317ea92451ffac","abstract_canon_sha256":"3d8042b07127cdb3d94c746a7e0eb995741f0a06ca24501627faebcc367bddc8"},"schema_version":"1.0"},"canonical_sha256":"b0a7076306fd3d679939d46216bc14e3344f43627e3442e848e76fed3b5764b5","source":{"kind":"arxiv","id":"1701.09064","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.09064","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1701.09064v3","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.09064","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"WCTQOYYG7U6W","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WCTQOYYG7U6WPGJZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WCTQOYYG","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WCTQOYYG7U6WPGJZ2RRBNPAU4M","target":"record","payload":{"canonical_record":{"source":{"id":"1701.09064","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-31T14:45:06Z","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"title_canon_sha256":"4b213acbddceffefd33ea966514cfde1e4c1dffa09e738c2b4317ea92451ffac","abstract_canon_sha256":"3d8042b07127cdb3d94c746a7e0eb995741f0a06ca24501627faebcc367bddc8"},"schema_version":"1.0"},"canonical_sha256":"b0a7076306fd3d679939d46216bc14e3344f43627e3442e848e76fed3b5764b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.432284Z","signature_b64":"UsNWkYd3gs8QbQp84WTgYarH8d0kb+3nljIFolCvRbSJZdvlDecu27mXBw5jhM0L7xQHUHo80wLlG7Evrvj6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0a7076306fd3d679939d46216bc14e3344f43627e3442e848e76fed3b5764b5","last_reissued_at":"2026-05-18T00:09:31.431581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.431581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.09064","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":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hd90SdMqTYVhoP20ai+UkQkKUVH/BvCt+HqRK3IPzgALmScf30Qj7UY83FG2vJChRSBll6CuUeu1HjmTNjRGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:41.148818Z"},"content_sha256":"8612f7fd65c85c5541a0904f96f8f58ed88adf95a0a925ce61d6dd80df4b21af","schema_version":"1.0","event_id":"sha256:8612f7fd65c85c5541a0904f96f8f58ed88adf95a0a925ce61d6dd80df4b21af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WCTQOYYG7U6WPGJZ2RRBNPAU4M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local incompressibility estimates for the Laughlin phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"primary_cat":"math-ph","authors_text":"Elliott Lieb, Jakob Yngvason, Nicolas Rougerie (LPMMC)","submitted_at":"2017-01-31T14:45:06Z","abstract_excerpt":"We prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof. Our method is new, based on an auxiliary Thomas-Fermi-like variational model. Moreover, we deduce density upper bounds for the related low-temperature Gibbs states. Our motivation comes from fractional quantum Hall physics, more precisely, the perturbation of the Laughlin state by external potentials or impurities. These give rise to a class of many-body wave-functions that have the form of a product of the Laughlin state and an analytic function of ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09064","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":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+dk9ThzvDx2SNh4Cxattazm7jMccR6rRznoHvxe9eLETWUEST7c0Hgc7TccPdc0lMQQBSNtkjqR4eJGEOsTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:41.149172Z"},"content_sha256":"1c9c012e807844995e92716f20dfd34981f09a159fa6b1cf7c60dc305bf6f714","schema_version":"1.0","event_id":"sha256:1c9c012e807844995e92716f20dfd34981f09a159fa6b1cf7c60dc305bf6f714"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/bundle.json","state_url":"https://pith.science/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/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":"2026-05-28T11:09:41Z","links":{"resolver":"https://pith.science/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M","bundle":"https://pith.science/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/bundle.json","state":"https://pith.science/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCTQOYYG7U6WPGJZ2RRBNPAU4M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WCTQOYYG7U6WPGJZ2RRBNPAU4M","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":"3d8042b07127cdb3d94c746a7e0eb995741f0a06ca24501627faebcc367bddc8","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-31T14:45:06Z","title_canon_sha256":"4b213acbddceffefd33ea966514cfde1e4c1dffa09e738c2b4317ea92451ffac"},"schema_version":"1.0","source":{"id":"1701.09064","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.09064","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1701.09064v3","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.09064","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"WCTQOYYG7U6W","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WCTQOYYG7U6WPGJZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WCTQOYYG","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:1c9c012e807844995e92716f20dfd34981f09a159fa6b1cf7c60dc305bf6f714","target":"graph","created_at":"2026-05-18T00:09:31Z","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 prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof. Our method is new, based on an auxiliary Thomas-Fermi-like variational model. Moreover, we deduce density upper bounds for the related low-temperature Gibbs states. Our motivation comes from fractional quantum Hall physics, more precisely, the perturbation of the Laughlin state by external potentials or impurities. These give rise to a class of many-body wave-functions that have the form of a product of the Laughlin state and an analytic function of ma","authors_text":"Elliott Lieb, Jakob Yngvason, Nicolas Rougerie (LPMMC)","cross_cats":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-31T14:45:06Z","title":"Local incompressibility estimates for the Laughlin phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09064","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":"sha256:8612f7fd65c85c5541a0904f96f8f58ed88adf95a0a925ce61d6dd80df4b21af","target":"record","created_at":"2026-05-18T00:09:31Z","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":"3d8042b07127cdb3d94c746a7e0eb995741f0a06ca24501627faebcc367bddc8","cross_cats_sorted":["cond-mat.mes-hall","cond-mat.quant-gas","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-31T14:45:06Z","title_canon_sha256":"4b213acbddceffefd33ea966514cfde1e4c1dffa09e738c2b4317ea92451ffac"},"schema_version":"1.0","source":{"id":"1701.09064","kind":"arxiv","version":3}},"canonical_sha256":"b0a7076306fd3d679939d46216bc14e3344f43627e3442e848e76fed3b5764b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0a7076306fd3d679939d46216bc14e3344f43627e3442e848e76fed3b5764b5","first_computed_at":"2026-05-18T00:09:31.431581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:31.431581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UsNWkYd3gs8QbQp84WTgYarH8d0kb+3nljIFolCvRbSJZdvlDecu27mXBw5jhM0L7xQHUHo80wLlG7Evrvj6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:31.432284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.09064","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8612f7fd65c85c5541a0904f96f8f58ed88adf95a0a925ce61d6dd80df4b21af","sha256:1c9c012e807844995e92716f20dfd34981f09a159fa6b1cf7c60dc305bf6f714"],"state_sha256":"3770a14ca98323da713f424617a6aacccc716312c4d765033184e8e800209e53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0slyzBVYnYyRWaLTEOGon4RFJHjRUYZ1LnFMPxCj4Z9chsTMfOJkeBBAbs/hh+TCiw1ZCqVfY3HjX2AtSmUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:09:41.151236Z","bundle_sha256":"790533208b51914f3bb963eb45e7714a6bfec42376ef464cc74c00b14a7bdaad"}}