{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KBCXTBLUGMXHN73CZ67OJIJW5I","short_pith_number":"pith:KBCXTBLU","canonical_record":{"source":{"id":"1302.6661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-27T04:43:19Z","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"title_canon_sha256":"5cec7d73196b3eea665d0b0dde648ffc821d6fad3baf9684f4c3a56718a563af","abstract_canon_sha256":"b301fbd27476726bdc2fc3be41dca635aba4ba6590da6f3de2d15f247e3d1aed"},"schema_version":"1.0"},"canonical_sha256":"5045798574332e76ff62cfbee4a136ea34e9cd98c85d41bf83513e18322b2002","source":{"kind":"arxiv","id":"1302.6661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6661","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6661v2","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6661","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"KBCXTBLUGMXH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KBCXTBLUGMXHN73C","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KBCXTBLU","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KBCXTBLUGMXHN73CZ67OJIJW5I","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-27T04:43:19Z","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"title_canon_sha256":"5cec7d73196b3eea665d0b0dde648ffc821d6fad3baf9684f4c3a56718a563af","abstract_canon_sha256":"b301fbd27476726bdc2fc3be41dca635aba4ba6590da6f3de2d15f247e3d1aed"},"schema_version":"1.0"},"canonical_sha256":"5045798574332e76ff62cfbee4a136ea34e9cd98c85d41bf83513e18322b2002","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:45.170019Z","signature_b64":"VAqXuaIHWwv8LKtKgqq3LKUE920xFykrxGrGTjrXfzs3SQI8Ld8yQ8HbMiuc2Vu18fEcE54Jnvsp0ZvNQvEaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5045798574332e76ff62cfbee4a136ea34e9cd98c85d41bf83513e18322b2002","last_reissued_at":"2026-05-18T03:15:45.169348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:45.169348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6661","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":"2026-05-18T03:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dxHJugV3ils48DTREsLu20O3DSE88SJwSI0KaLCq4fihzyUb70WsBQLBnEvBW9NdpS6vSsk0XEniLZrfzpZPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:42:38.231626Z"},"content_sha256":"4fdb2dcfeb38971279e7f1541d58cfe0cd1a20bc0e7cafca0692ba0d2d7de514","schema_version":"1.0","event_id":"sha256:4fdb2dcfeb38971279e7f1541d58cfe0cd1a20bc0e7cafca0692ba0d2d7de514"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KBCXTBLUGMXHN73CZ67OJIJW5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform electron gases. I. Electrons on a ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","physics.chem-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","submitted_at":"2013-02-27T04:43:19Z","abstract_excerpt":"We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\\\"odinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e. per electron) energy can be expanded as $\\eps(r_s,n) = \\eps_0(n) r_s^{-2} + \\eps_1(n) r_s^{-1} + \\eps_2(n) +\\eps_3(n) r_s + \\ldots$, where $r_s$ is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as $\\eps(r_s,n) = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6661","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":"2026-05-18T03:15:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rw2iFP4gKEn7BLks7teInPmFiX27d0w/WFHVVO/QSU/Y2Zz/k0Fh31uvSP8rqVn9aoPyk385KxWg2H/aqsvKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:42:38.232339Z"},"content_sha256":"f1efbaeab204d61955ff935c19923d0b0d1fd1a480a066b8d54049b8b56e83a8","schema_version":"1.0","event_id":"sha256:f1efbaeab204d61955ff935c19923d0b0d1fd1a480a066b8d54049b8b56e83a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/bundle.json","state_url":"https://pith.science/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/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":"2026-06-10T07:42:38Z","links":{"resolver":"https://pith.science/pith/KBCXTBLUGMXHN73CZ67OJIJW5I","bundle":"https://pith.science/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/bundle.json","state":"https://pith.science/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBCXTBLUGMXHN73CZ67OJIJW5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KBCXTBLUGMXHN73CZ67OJIJW5I","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":"b301fbd27476726bdc2fc3be41dca635aba4ba6590da6f3de2d15f247e3d1aed","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-27T04:43:19Z","title_canon_sha256":"5cec7d73196b3eea665d0b0dde648ffc821d6fad3baf9684f4c3a56718a563af"},"schema_version":"1.0","source":{"id":"1302.6661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6661","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6661v2","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6661","created_at":"2026-05-18T03:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"KBCXTBLUGMXH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KBCXTBLUGMXHN73C","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KBCXTBLU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:f1efbaeab204d61955ff935c19923d0b0d1fd1a480a066b8d54049b8b56e83a8","target":"graph","created_at":"2026-05-18T03:15:45Z","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 a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\\\"odinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e. per electron) energy can be expanded as $\\eps(r_s,n) = \\eps_0(n) r_s^{-2} + \\eps_1(n) r_s^{-1} + \\eps_2(n) +\\eps_3(n) r_s + \\ldots$, where $r_s$ is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as $\\eps(r_s,n) = ","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","cross_cats":["cond-mat.other","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-27T04:43:19Z","title":"Uniform electron gases. I. Electrons on a ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6661","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":"sha256:4fdb2dcfeb38971279e7f1541d58cfe0cd1a20bc0e7cafca0692ba0d2d7de514","target":"record","created_at":"2026-05-18T03:15:45Z","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":"b301fbd27476726bdc2fc3be41dca635aba4ba6590da6f3de2d15f247e3d1aed","cross_cats_sorted":["cond-mat.other","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-27T04:43:19Z","title_canon_sha256":"5cec7d73196b3eea665d0b0dde648ffc821d6fad3baf9684f4c3a56718a563af"},"schema_version":"1.0","source":{"id":"1302.6661","kind":"arxiv","version":2}},"canonical_sha256":"5045798574332e76ff62cfbee4a136ea34e9cd98c85d41bf83513e18322b2002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5045798574332e76ff62cfbee4a136ea34e9cd98c85d41bf83513e18322b2002","first_computed_at":"2026-05-18T03:15:45.169348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:45.169348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAqXuaIHWwv8LKtKgqq3LKUE920xFykrxGrGTjrXfzs3SQI8Ld8yQ8HbMiuc2Vu18fEcE54Jnvsp0ZvNQvEaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:45.170019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fdb2dcfeb38971279e7f1541d58cfe0cd1a20bc0e7cafca0692ba0d2d7de514","sha256:f1efbaeab204d61955ff935c19923d0b0d1fd1a480a066b8d54049b8b56e83a8"],"state_sha256":"c4ac6c5e949e37f4604fef17e77169e1c9aa2e8b858fb945c13b13ba88c7aea9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1Lv90bbxACQ4ovKnFCg/Gu6dkhhHxZeKLnSUeuBPrxuZimWqZ+UKodPJn58nBKjJ2V1vLdGXHqxEr0AGtWMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:42:38.236242Z","bundle_sha256":"ceb01cc83af7a79e5eafd61c9b935be12cf51faa97deceed688783cb2e33138b"}}