{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6FRWSJJFLDKTLLQYWB4KCAO33A","short_pith_number":"pith:6FRWSJJF","canonical_record":{"source":{"id":"1508.02011","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-08-09T11:21:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a1f154c868b0d9021ad21c4f9f2d00432a5fd6e77cbc8b25a35ffa1ff22e1061","abstract_canon_sha256":"f13a1bcb7a76fa215956fd39a9e158a15f8502e089173c1a9a11dcd7d1af6c7f"},"schema_version":"1.0"},"canonical_sha256":"f16369252558d535ae18b078a101dbd836969fb9d57c89d96978b26adeddfc48","source":{"kind":"arxiv","id":"1508.02011","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02011","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02011v4","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02011","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"6FRWSJJFLDKT","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FRWSJJFLDKTLLQY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FRWSJJF","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6FRWSJJFLDKTLLQYWB4KCAO33A","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02011","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-08-09T11:21:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a1f154c868b0d9021ad21c4f9f2d00432a5fd6e77cbc8b25a35ffa1ff22e1061","abstract_canon_sha256":"f13a1bcb7a76fa215956fd39a9e158a15f8502e089173c1a9a11dcd7d1af6c7f"},"schema_version":"1.0"},"canonical_sha256":"f16369252558d535ae18b078a101dbd836969fb9d57c89d96978b26adeddfc48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:45.551680Z","signature_b64":"X3O2Ku5G+hcQn1eBHjOYUFDviPqlr+tbT6Um1lNRpVD5H7P0jo/Xg2yTdDIQmKdIcS4xPlm6GiXEn5G3UzoRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f16369252558d535ae18b078a101dbd836969fb9d57c89d96978b26adeddfc48","last_reissued_at":"2026-05-18T01:20:45.551273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:45.551273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02011","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1bMztzDd24S9YTo9GCQSa59GIzTAIGDK4LygBbdy+my0I/fi6xGsCO/zAisasBAGVrbwL4v5TM5RNnXJP+NBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:10:38.052952Z"},"content_sha256":"536200bbd51f0ec40567dec2f3031a40084fda7f1921244e9f4c83b7f722c9d7","schema_version":"1.0","event_id":"sha256:536200bbd51f0ec40567dec2f3031a40084fda7f1921244e9f4c83b7f722c9d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6FRWSJJFLDKTLLQYWB4KCAO33A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized Lieb-Liniger model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.quant-gas","authors_text":"Hagar Veksler, Shmuel Fishman","submitted_at":"2015-08-09T11:21:25Z","abstract_excerpt":"In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive \\delta-potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of three \\delta-functions, one of them is repulsive and the other two are attractive, modeling some aspects of the interaction between atoms, and present an approximate solution for a dilute gas. In this limit, for low energy states, the results are found to be reduced to the ones of an effective Lieb Liniger model with an effective \\delta-function of strength $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02011","kind":"arxiv","version":4},"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":"2026-05-18T01:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwX7ywbgoVQenVIHH1YuEWP+7PjjvAvwGtP0srIxAx7O3PRmd9/HhCEj0rmxxPtqTtJ5bUBzvxjMR/UbhVDhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:10:38.053383Z"},"content_sha256":"71e996c99dd1d50808d8f7fd4f07f8376491993f45169e5ad14f836708ab0560","schema_version":"1.0","event_id":"sha256:71e996c99dd1d50808d8f7fd4f07f8376491993f45169e5ad14f836708ab0560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/bundle.json","state_url":"https://pith.science/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/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":"2026-05-23T19:10:38Z","links":{"resolver":"https://pith.science/pith/6FRWSJJFLDKTLLQYWB4KCAO33A","bundle":"https://pith.science/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/bundle.json","state":"https://pith.science/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FRWSJJFLDKTLLQYWB4KCAO33A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6FRWSJJFLDKTLLQYWB4KCAO33A","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":"f13a1bcb7a76fa215956fd39a9e158a15f8502e089173c1a9a11dcd7d1af6c7f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-08-09T11:21:25Z","title_canon_sha256":"a1f154c868b0d9021ad21c4f9f2d00432a5fd6e77cbc8b25a35ffa1ff22e1061"},"schema_version":"1.0","source":{"id":"1508.02011","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02011","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02011v4","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02011","created_at":"2026-05-18T01:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"6FRWSJJFLDKT","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FRWSJJFLDKTLLQY","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FRWSJJF","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:71e996c99dd1d50808d8f7fd4f07f8376491993f45169e5ad14f836708ab0560","target":"graph","created_at":"2026-05-18T01:20:45Z","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":"In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive \\delta-potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of three \\delta-functions, one of them is repulsive and the other two are attractive, modeling some aspects of the interaction between atoms, and present an approximate solution for a dilute gas. In this limit, for low energy states, the results are found to be reduced to the ones of an effective Lieb Liniger model with an effective \\delta-function of strength $","authors_text":"Hagar Veksler, Shmuel Fishman","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-08-09T11:21:25Z","title":"A generalized Lieb-Liniger model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02011","kind":"arxiv","version":4},"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":"sha256:536200bbd51f0ec40567dec2f3031a40084fda7f1921244e9f4c83b7f722c9d7","target":"record","created_at":"2026-05-18T01:20:45Z","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":"f13a1bcb7a76fa215956fd39a9e158a15f8502e089173c1a9a11dcd7d1af6c7f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-08-09T11:21:25Z","title_canon_sha256":"a1f154c868b0d9021ad21c4f9f2d00432a5fd6e77cbc8b25a35ffa1ff22e1061"},"schema_version":"1.0","source":{"id":"1508.02011","kind":"arxiv","version":4}},"canonical_sha256":"f16369252558d535ae18b078a101dbd836969fb9d57c89d96978b26adeddfc48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f16369252558d535ae18b078a101dbd836969fb9d57c89d96978b26adeddfc48","first_computed_at":"2026-05-18T01:20:45.551273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:45.551273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X3O2Ku5G+hcQn1eBHjOYUFDviPqlr+tbT6Um1lNRpVD5H7P0jo/Xg2yTdDIQmKdIcS4xPlm6GiXEn5G3UzoRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:45.551680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02011","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:536200bbd51f0ec40567dec2f3031a40084fda7f1921244e9f4c83b7f722c9d7","sha256:71e996c99dd1d50808d8f7fd4f07f8376491993f45169e5ad14f836708ab0560"],"state_sha256":"42fd9258e368ee8af2951e5925956ceb345826732d470dd2a71aa0a6b66f7ee1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enMiy8v7QiHwlMrGHhlPo+vZdBsXdNvp5fe6wy+41Sx4wunl2Ml4jnm9AlM9mwGRiud5DJi5VJ8EVp2u0/A2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T19:10:38.055744Z","bundle_sha256":"1c95fbbf9d7bd6d78115685cb4d2c66827e17c382396a45291f7ba77a2e85caf"}}