{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6P3WWUPGXBNJSRAVK2DPHKCK6G","short_pith_number":"pith:6P3WWUPG","canonical_record":{"source":{"id":"0912.3906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-12-19T17:10:54Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.other"],"title_canon_sha256":"eb73d6056c4e908853a0867c0564a94e7deb91485e9c77bd894a71d579e4354b","abstract_canon_sha256":"ce09efc81f2042ca7076b477656ff6ede34e5731e9d7512281c50095dea707a6"},"schema_version":"1.0"},"canonical_sha256":"f3f76b51e6b85a9944155686f3a84af1870802d335546df3e7b81cebdc892fda","source":{"kind":"arxiv","id":"0912.3906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3906","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3906v1","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3906","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"6P3WWUPGXBNJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6P3WWUPGXBNJSRAV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6P3WWUPG","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6P3WWUPGXBNJSRAVK2DPHKCK6G","target":"record","payload":{"canonical_record":{"source":{"id":"0912.3906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-12-19T17:10:54Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.other"],"title_canon_sha256":"eb73d6056c4e908853a0867c0564a94e7deb91485e9c77bd894a71d579e4354b","abstract_canon_sha256":"ce09efc81f2042ca7076b477656ff6ede34e5731e9d7512281c50095dea707a6"},"schema_version":"1.0"},"canonical_sha256":"f3f76b51e6b85a9944155686f3a84af1870802d335546df3e7b81cebdc892fda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:41.301718Z","signature_b64":"CPSre5txyxPZ+4RWgGI2eK4qi6lNnsim3DjwSQiEkdCTHMENRhi4liwfFMuUa64/fCg17m9jJfDkanz7OhumCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3f76b51e6b85a9944155686f3a84af1870802d335546df3e7b81cebdc892fda","last_reissued_at":"2026-05-18T03:14:41.300975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:41.300975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.3906","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJbGLBo6W+DhdXNDgogoUe2Mj/7gVnaT+q0jqNg0WHpvOd07vomC+OIKeWnL0gof5Yd0Y3ugT/hrX5qnDgXxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T09:41:05.755681Z"},"content_sha256":"272be2e9611bb40a15d7e09c35a453bce106708777c3fd703938818e13b978e3","schema_version":"1.0","event_id":"sha256:272be2e9611bb40a15d7e09c35a453bce106708777c3fd703938818e13b978e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6P3WWUPGXBNJSRAVK2DPHKCK6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical and symbolical approximation of the Nonlinear Anderson Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.other"],"primary_cat":"cond-mat.mes-hall","authors_text":"Avy Soffer, Shmuel Fishman, Yevgeny Krivolapov","submitted_at":"2009-12-19T17:10:54Z","abstract_excerpt":"A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we obtain error estimates. This approach can be useful for the solution of other nonlinear differential equations of physical relevance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3906","kind":"arxiv","version":1},"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":"2026-05-18T03:14:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnLCMtub9G0rgZwovxjiRFzAYnKHp9v4Vq3e/T9I26QP5Tp/QB9qKLrB9bTXYTLep632wNYQLjP2Nk5Ax/I+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T09:41:05.756438Z"},"content_sha256":"adb5dac38144a47272f3c6a347c51bad59da979277f6bfd3795240c5c0cdd350","schema_version":"1.0","event_id":"sha256:adb5dac38144a47272f3c6a347c51bad59da979277f6bfd3795240c5c0cdd350"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/bundle.json","state_url":"https://pith.science/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/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":"2026-05-23T09:41:05Z","links":{"resolver":"https://pith.science/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G","bundle":"https://pith.science/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/bundle.json","state":"https://pith.science/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6P3WWUPGXBNJSRAVK2DPHKCK6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6P3WWUPGXBNJSRAVK2DPHKCK6G","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":"ce09efc81f2042ca7076b477656ff6ede34e5731e9d7512281c50095dea707a6","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-12-19T17:10:54Z","title_canon_sha256":"eb73d6056c4e908853a0867c0564a94e7deb91485e9c77bd894a71d579e4354b"},"schema_version":"1.0","source":{"id":"0912.3906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3906","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3906v1","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3906","created_at":"2026-05-18T03:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"6P3WWUPGXBNJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6P3WWUPGXBNJSRAV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6P3WWUPG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:adb5dac38144a47272f3c6a347c51bad59da979277f6bfd3795240c5c0cdd350","target":"graph","created_at":"2026-05-18T03:14:41Z","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":"A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we obtain error estimates. This approach can be useful for the solution of other nonlinear differential equations of physical relevance.","authors_text":"Avy Soffer, Shmuel Fishman, Yevgeny Krivolapov","cross_cats":["cond-mat.dis-nn","cond-mat.other"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-12-19T17:10:54Z","title":"A numerical and symbolical approximation of the Nonlinear Anderson Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3906","kind":"arxiv","version":1},"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":"sha256:272be2e9611bb40a15d7e09c35a453bce106708777c3fd703938818e13b978e3","target":"record","created_at":"2026-05-18T03:14:41Z","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":"ce09efc81f2042ca7076b477656ff6ede34e5731e9d7512281c50095dea707a6","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-12-19T17:10:54Z","title_canon_sha256":"eb73d6056c4e908853a0867c0564a94e7deb91485e9c77bd894a71d579e4354b"},"schema_version":"1.0","source":{"id":"0912.3906","kind":"arxiv","version":1}},"canonical_sha256":"f3f76b51e6b85a9944155686f3a84af1870802d335546df3e7b81cebdc892fda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3f76b51e6b85a9944155686f3a84af1870802d335546df3e7b81cebdc892fda","first_computed_at":"2026-05-18T03:14:41.300975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:41.300975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CPSre5txyxPZ+4RWgGI2eK4qi6lNnsim3DjwSQiEkdCTHMENRhi4liwfFMuUa64/fCg17m9jJfDkanz7OhumCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:41.301718Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:272be2e9611bb40a15d7e09c35a453bce106708777c3fd703938818e13b978e3","sha256:adb5dac38144a47272f3c6a347c51bad59da979277f6bfd3795240c5c0cdd350"],"state_sha256":"b114afe369409619fb1ad83740fdcc105dbd93ba28e471fd6d850c87ff69d9ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFPJo2OvoeyXkhkYdyJOS9O5PVjakl25Wj/0BUrD7jezkzacdbft0moPIo89Wr+PDYk6dcvrZfAhCSp+tYKRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T09:41:05.760209Z","bundle_sha256":"29d243a9f3400437d695bb05fbbd2d853ec7ed35bed4d4e30fadfba3c18eee92"}}