{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UWY3DGE3INY62LNC7JWJ2Q3FQY","short_pith_number":"pith:UWY3DGE3","canonical_record":{"source":{"id":"1011.2453","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-10T18:32:53Z","cross_cats_sorted":["cond-mat.stat-mech","nucl-th"],"title_canon_sha256":"c0b8c74dbd101fb7f0b30aa0dfba839554073d36fb12e3012f722a12a80d3a6f","abstract_canon_sha256":"a3a6101fec276c1b785dd0f48e2905dbe0bae52f779eda64f19b018e1b7cf4ca"},"schema_version":"1.0"},"canonical_sha256":"a5b1b1989b4371ed2da2fa6c9d4365860d1a7f1dedae35bc1d9cf2c450d8504c","source":{"kind":"arxiv","id":"1011.2453","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2453","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2453v3","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2453","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"UWY3DGE3INY6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UWY3DGE3INY62LNC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UWY3DGE3","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UWY3DGE3INY62LNC7JWJ2Q3FQY","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2453","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-10T18:32:53Z","cross_cats_sorted":["cond-mat.stat-mech","nucl-th"],"title_canon_sha256":"c0b8c74dbd101fb7f0b30aa0dfba839554073d36fb12e3012f722a12a80d3a6f","abstract_canon_sha256":"a3a6101fec276c1b785dd0f48e2905dbe0bae52f779eda64f19b018e1b7cf4ca"},"schema_version":"1.0"},"canonical_sha256":"a5b1b1989b4371ed2da2fa6c9d4365860d1a7f1dedae35bc1d9cf2c450d8504c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:37.615086Z","signature_b64":"zR61tJaDaF3ZZKHkZhurJD28HVbeSBMD9/sVJ31O9DQsAY8sydMhpL7Bv1NvSyBLeRtsEeJp0+yLUrb+vkYqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5b1b1989b4371ed2da2fa6c9d4365860d1a7f1dedae35bc1d9cf2c450d8504c","last_reissued_at":"2026-05-18T03:55:37.614370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:37.614370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2453","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":"2026-05-18T03:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qGmaC+SHpiswECifig8Mr8BNrb1sXkHPCK0hWOE5GlpplLh12p+ltmzlHqOW9MvUC7aMUMg8dRscRrks1xHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:23:05.783406Z"},"content_sha256":"fc8ef10b610a4e396cafe2a15d1aeb73115fa093c6bf16d6ce454b50c092b170","schema_version":"1.0","event_id":"sha256:fc8ef10b610a4e396cafe2a15d1aeb73115fa093c6bf16d6ce454b50c092b170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UWY3DGE3INY62LNC7JWJ2Q3FQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic Harmonic Approach to the N-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nucl-th"],"primary_cat":"cond-mat.quant-gas","authors_text":"A. S. Jensen, D. V. Fedorov, J. R. Armstrong, N. T. Zinner","submitted_at":"2010-11-10T18:32:53Z","abstract_excerpt":"We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions lik"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2453","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":"2026-05-18T03:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VXPBMXU14HHCCuhBmq0hy0RYiX+ggtmNh9tB6Pj7fDErlANzSO9JJdNKSpclvyJdtKq1BrLjKnn3aLHHGv4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:23:05.783837Z"},"content_sha256":"499ed45daf0ba42a7208287b76011233ee8d9127bcfc3f645431cc5c888a6a1a","schema_version":"1.0","event_id":"sha256:499ed45daf0ba42a7208287b76011233ee8d9127bcfc3f645431cc5c888a6a1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/bundle.json","state_url":"https://pith.science/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/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":"2026-06-05T22:23:05Z","links":{"resolver":"https://pith.science/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY","bundle":"https://pith.science/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/bundle.json","state":"https://pith.science/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWY3DGE3INY62LNC7JWJ2Q3FQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UWY3DGE3INY62LNC7JWJ2Q3FQY","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":"a3a6101fec276c1b785dd0f48e2905dbe0bae52f779eda64f19b018e1b7cf4ca","cross_cats_sorted":["cond-mat.stat-mech","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-10T18:32:53Z","title_canon_sha256":"c0b8c74dbd101fb7f0b30aa0dfba839554073d36fb12e3012f722a12a80d3a6f"},"schema_version":"1.0","source":{"id":"1011.2453","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2453","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2453v3","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2453","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"UWY3DGE3INY6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UWY3DGE3INY62LNC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UWY3DGE3","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:499ed45daf0ba42a7208287b76011233ee8d9127bcfc3f645431cc5c888a6a1a","target":"graph","created_at":"2026-05-18T03:55:37Z","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 consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions lik","authors_text":"A. S. Jensen, D. V. Fedorov, J. R. Armstrong, N. T. Zinner","cross_cats":["cond-mat.stat-mech","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-10T18:32:53Z","title":"Analytic Harmonic Approach to the N-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2453","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:fc8ef10b610a4e396cafe2a15d1aeb73115fa093c6bf16d6ce454b50c092b170","target":"record","created_at":"2026-05-18T03:55:37Z","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":"a3a6101fec276c1b785dd0f48e2905dbe0bae52f779eda64f19b018e1b7cf4ca","cross_cats_sorted":["cond-mat.stat-mech","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-10T18:32:53Z","title_canon_sha256":"c0b8c74dbd101fb7f0b30aa0dfba839554073d36fb12e3012f722a12a80d3a6f"},"schema_version":"1.0","source":{"id":"1011.2453","kind":"arxiv","version":3}},"canonical_sha256":"a5b1b1989b4371ed2da2fa6c9d4365860d1a7f1dedae35bc1d9cf2c450d8504c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5b1b1989b4371ed2da2fa6c9d4365860d1a7f1dedae35bc1d9cf2c450d8504c","first_computed_at":"2026-05-18T03:55:37.614370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:37.614370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zR61tJaDaF3ZZKHkZhurJD28HVbeSBMD9/sVJ31O9DQsAY8sydMhpL7Bv1NvSyBLeRtsEeJp0+yLUrb+vkYqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:37.615086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2453","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc8ef10b610a4e396cafe2a15d1aeb73115fa093c6bf16d6ce454b50c092b170","sha256:499ed45daf0ba42a7208287b76011233ee8d9127bcfc3f645431cc5c888a6a1a"],"state_sha256":"024e872995ccc7c6ee5a1f8b911d4e52b403581a2a969a8ab37c1011a656c5fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOQyuFUqJSBJ0rFGGPLw8RO16CiMusdJjUQHdaAia7cOOOdo60RjYZGbTxp+skD6WZtrEnfpw9c+Kw29q7i6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:23:05.786134Z","bundle_sha256":"48c6bff11911fe44024291006c85f83ef6854bdedf9bfe2120c080065cc45465"}}