{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:BORC7QEGEUAOPRDH7YINPDQYUH","short_pith_number":"pith:BORC7QEG","canonical_record":{"source":{"id":"0704.2088","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2007-04-17T02:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"431b0b3b79b8ae6d2452e0a8b84102f9ad53712cf0c525812d551ca2758d518a","abstract_canon_sha256":"efcb2c6ca406c70cc4b7d9d2ded22aa1872e4cab916594f0c1052878000b9ed9"},"schema_version":"1.0"},"canonical_sha256":"0ba22fc0862500e7c467fe10d78e18a1c6bb69c5a47aef0006cca14f2d68f361","source":{"kind":"arxiv","id":"0704.2088","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.2088","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"0704.2088v3","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2088","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"BORC7QEGEUAO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BORC7QEGEUAOPRDH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BORC7QEG","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:BORC7QEGEUAOPRDH7YINPDQYUH","target":"record","payload":{"canonical_record":{"source":{"id":"0704.2088","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2007-04-17T02:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"431b0b3b79b8ae6d2452e0a8b84102f9ad53712cf0c525812d551ca2758d518a","abstract_canon_sha256":"efcb2c6ca406c70cc4b7d9d2ded22aa1872e4cab916594f0c1052878000b9ed9"},"schema_version":"1.0"},"canonical_sha256":"0ba22fc0862500e7c467fe10d78e18a1c6bb69c5a47aef0006cca14f2d68f361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:24.122411Z","signature_b64":"fAmWjkE3euaQnlmVOqndtUGglWCta0lHy4rqELLruBYpMIvtE+hG5E/fkD1aDvgaP9D2f83KczTmx3hHB7VVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ba22fc0862500e7c467fe10d78e18a1c6bb69c5a47aef0006cca14f2d68f361","last_reissued_at":"2026-05-18T04:09:24.121915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:24.121915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.2088","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":"2026-05-18T04:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Br1ZN9lBWs0ipEi/fANig0Y6BTprF8FRSFnGCi9Fz4ljRqIN141Gh4Zru4AF1neOsxUNEv/bn/Q00kCEhzfPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:17:34.976423Z"},"content_sha256":"078fe0b68557d45dd2041292173fadfb3e546cac1acdb0e6372e161f5a5aac15","schema_version":"1.0","event_id":"sha256:078fe0b68557d45dd2041292173fadfb3e546cac1acdb0e6372e161f5a5aac15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:BORC7QEGEUAOPRDH7YINPDQYUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Shimul Akhanjee","submitted_at":"2007-04-17T02:39:42Z","abstract_excerpt":"We derive the exact longitudinal plasmon dispersion relations, $\\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb interactions. We make use of the polylogarithm function in order to evaluate the infinite lattice sums of the electrostatic force constants. From our exact results we recover the correct long-wavelength behavior of previous approximate methods. In 1D, $\\omega(k) \\sim | k |\\log ^{1/2} (1/k)$, validating the known RPA and bosonization form. In 2D $\\omega(k) \\sim \\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2088","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":"2026-05-18T04:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pl6aJV7oTTmQ0AUtRRXKT7Jl+QiEhKM5xydk5yK7Ng9Nrfla4PAtw8mFdEn7wIqAHc336sn6WVnJ6xox4HWgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:17:34.977075Z"},"content_sha256":"dbd7385c5a323f8dfc0e86a5b27f7f36bf64974de02337ebb9d0fc5fd5e5a301","schema_version":"1.0","event_id":"sha256:dbd7385c5a323f8dfc0e86a5b27f7f36bf64974de02337ebb9d0fc5fd5e5a301"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BORC7QEGEUAOPRDH7YINPDQYUH/bundle.json","state_url":"https://pith.science/pith/BORC7QEGEUAOPRDH7YINPDQYUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BORC7QEGEUAOPRDH7YINPDQYUH/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":"2026-06-01T00:17:34Z","links":{"resolver":"https://pith.science/pith/BORC7QEGEUAOPRDH7YINPDQYUH","bundle":"https://pith.science/pith/BORC7QEGEUAOPRDH7YINPDQYUH/bundle.json","state":"https://pith.science/pith/BORC7QEGEUAOPRDH7YINPDQYUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BORC7QEGEUAOPRDH7YINPDQYUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BORC7QEGEUAOPRDH7YINPDQYUH","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":"efcb2c6ca406c70cc4b7d9d2ded22aa1872e4cab916594f0c1052878000b9ed9","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2007-04-17T02:39:42Z","title_canon_sha256":"431b0b3b79b8ae6d2452e0a8b84102f9ad53712cf0c525812d551ca2758d518a"},"schema_version":"1.0","source":{"id":"0704.2088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.2088","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"0704.2088v3","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2088","created_at":"2026-05-18T04:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"BORC7QEGEUAO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BORC7QEGEUAOPRDH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BORC7QEG","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:dbd7385c5a323f8dfc0e86a5b27f7f36bf64974de02337ebb9d0fc5fd5e5a301","target":"graph","created_at":"2026-05-18T04:09:24Z","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":"We derive the exact longitudinal plasmon dispersion relations, $\\omega(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb interactions. We make use of the polylogarithm function in order to evaluate the infinite lattice sums of the electrostatic force constants. From our exact results we recover the correct long-wavelength behavior of previous approximate methods. In 1D, $\\omega(k) \\sim | k |\\log ^{1/2} (1/k)$, validating the known RPA and bosonization form. In 2D $\\omega(k) \\sim \\s","authors_text":"Shimul Akhanjee","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.str-el","submitted_at":"2007-04-17T02:39:42Z","title":"Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2088","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":"sha256:078fe0b68557d45dd2041292173fadfb3e546cac1acdb0e6372e161f5a5aac15","target":"record","created_at":"2026-05-18T04:09:24Z","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":"efcb2c6ca406c70cc4b7d9d2ded22aa1872e4cab916594f0c1052878000b9ed9","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2007-04-17T02:39:42Z","title_canon_sha256":"431b0b3b79b8ae6d2452e0a8b84102f9ad53712cf0c525812d551ca2758d518a"},"schema_version":"1.0","source":{"id":"0704.2088","kind":"arxiv","version":3}},"canonical_sha256":"0ba22fc0862500e7c467fe10d78e18a1c6bb69c5a47aef0006cca14f2d68f361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ba22fc0862500e7c467fe10d78e18a1c6bb69c5a47aef0006cca14f2d68f361","first_computed_at":"2026-05-18T04:09:24.121915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:24.121915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fAmWjkE3euaQnlmVOqndtUGglWCta0lHy4rqELLruBYpMIvtE+hG5E/fkD1aDvgaP9D2f83KczTmx3hHB7VVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:24.122411Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.2088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:078fe0b68557d45dd2041292173fadfb3e546cac1acdb0e6372e161f5a5aac15","sha256:dbd7385c5a323f8dfc0e86a5b27f7f36bf64974de02337ebb9d0fc5fd5e5a301"],"state_sha256":"d2c21975ed5102c82f5db30fbc6c894930f7395812159a10621a4d195ed43e6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQdjYlBwVhRjuHll1Cw/IYuxHeg0ZAmM6w/TCImcujAb5cH73cXSIjwY9zXpefDoLLJUURk/aH7Z1aREiN7/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:17:34.980094Z","bundle_sha256":"aeb7cc0592b907d37ce8b7656606ca8e05ebd9d29e869d352f6bb8ed5a6f9e1f"}}