{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RSRP6X5QOLOI3MOORM4S3OJ7EP","short_pith_number":"pith:RSRP6X5Q","canonical_record":{"source":{"id":"1008.4514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-26T14:01:29Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"120bb2b2f5806eae176257b4126ad2e3c4fd227f5ab81c52451c3d999b51887d","abstract_canon_sha256":"48510c09dfe596f4e4633f961ee8ee316a1ede85e6e061686bc2d7582965fea9"},"schema_version":"1.0"},"canonical_sha256":"8ca2ff5fb072dc8db1ce8b392db93f23f277f9cdd9f184893d5f9a5863ced700","source":{"kind":"arxiv","id":"1008.4514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4514","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4514v1","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4514","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"RSRP6X5QOLOI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RSRP6X5QOLOI3MOO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RSRP6X5Q","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RSRP6X5QOLOI3MOORM4S3OJ7EP","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-26T14:01:29Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"120bb2b2f5806eae176257b4126ad2e3c4fd227f5ab81c52451c3d999b51887d","abstract_canon_sha256":"48510c09dfe596f4e4633f961ee8ee316a1ede85e6e061686bc2d7582965fea9"},"schema_version":"1.0"},"canonical_sha256":"8ca2ff5fb072dc8db1ce8b392db93f23f277f9cdd9f184893d5f9a5863ced700","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:45.184064Z","signature_b64":"TIZomKDdplPx2bEivLlS9RREdjhDNqICv5IKCbk3GKfl5XlTxiGqxy5vKGXg42xcNIZ8bT/Pj5+xcuJq7p8iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ca2ff5fb072dc8db1ce8b392db93f23f277f9cdd9f184893d5f9a5863ced700","last_reissued_at":"2026-05-18T04:41:45.183643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:45.183643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4514","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":"2026-05-18T04:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h9TBUXTyqZiyImAnz8LDQhQ/mzpoL56VzoRGcuvq1ymWnRCgbBOsADyeUt7n2Ugl+OxlxyDQ5+IydBxinyslBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:52:13.387229Z"},"content_sha256":"9c1d8fbc3f307f8f53350a8e92946d0be2f516cb11b3e0f10acb61830d7c63cb","schema_version":"1.0","event_id":"sha256:9c1d8fbc3f307f8f53350a8e92946d0be2f516cb11b3e0f10acb61830d7c63cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RSRP6X5QOLOI3MOORM4S3OJ7EP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of small gap solitons in the nonlinear Dirac equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Atanas Stefanov, Dmitry E. Pelinovsky","submitted_at":"2010-08-26T14:01:29Z","abstract_excerpt":"We prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear Dirac equations with quintic and higher-order nonlinear terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4514","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":"2026-05-18T04:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JBCYUQ0oPOJPPexdowegR+gLTBQpdKKyVEpaX/6l0tLsRSmU2faFzNHu9onIJ7xxvddNdEckSl7TTF2nqWkDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:52:13.387920Z"},"content_sha256":"5f85a41b1c0817fc640a8873f6fea2bb67bade98df84c2cf6ef4ee291233ca6f","schema_version":"1.0","event_id":"sha256:5f85a41b1c0817fc640a8873f6fea2bb67bade98df84c2cf6ef4ee291233ca6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/bundle.json","state_url":"https://pith.science/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/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":"2026-05-28T18:52:13Z","links":{"resolver":"https://pith.science/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP","bundle":"https://pith.science/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/bundle.json","state":"https://pith.science/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSRP6X5QOLOI3MOORM4S3OJ7EP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RSRP6X5QOLOI3MOORM4S3OJ7EP","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":"48510c09dfe596f4e4633f961ee8ee316a1ede85e6e061686bc2d7582965fea9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-26T14:01:29Z","title_canon_sha256":"120bb2b2f5806eae176257b4126ad2e3c4fd227f5ab81c52451c3d999b51887d"},"schema_version":"1.0","source":{"id":"1008.4514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4514","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4514v1","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4514","created_at":"2026-05-18T04:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"RSRP6X5QOLOI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RSRP6X5QOLOI3MOO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RSRP6X5Q","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:5f85a41b1c0817fc640a8873f6fea2bb67bade98df84c2cf6ef4ee291233ca6f","target":"graph","created_at":"2026-05-18T04:41:45Z","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 prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear Dirac equations with quintic and higher-order nonlinear terms.","authors_text":"Atanas Stefanov, Dmitry E. Pelinovsky","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-26T14:01:29Z","title":"Asymptotic stability of small gap solitons in the nonlinear Dirac equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4514","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":"sha256:9c1d8fbc3f307f8f53350a8e92946d0be2f516cb11b3e0f10acb61830d7c63cb","target":"record","created_at":"2026-05-18T04:41:45Z","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":"48510c09dfe596f4e4633f961ee8ee316a1ede85e6e061686bc2d7582965fea9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-26T14:01:29Z","title_canon_sha256":"120bb2b2f5806eae176257b4126ad2e3c4fd227f5ab81c52451c3d999b51887d"},"schema_version":"1.0","source":{"id":"1008.4514","kind":"arxiv","version":1}},"canonical_sha256":"8ca2ff5fb072dc8db1ce8b392db93f23f277f9cdd9f184893d5f9a5863ced700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ca2ff5fb072dc8db1ce8b392db93f23f277f9cdd9f184893d5f9a5863ced700","first_computed_at":"2026-05-18T04:41:45.183643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:45.183643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIZomKDdplPx2bEivLlS9RREdjhDNqICv5IKCbk3GKfl5XlTxiGqxy5vKGXg42xcNIZ8bT/Pj5+xcuJq7p8iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:45.184064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c1d8fbc3f307f8f53350a8e92946d0be2f516cb11b3e0f10acb61830d7c63cb","sha256:5f85a41b1c0817fc640a8873f6fea2bb67bade98df84c2cf6ef4ee291233ca6f"],"state_sha256":"db9e5b74f0e1762d2ae7a10e463d38dc23a9075febaa93cf9c3dbdd22a68af48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJw8Rzj/Q8mBJb9LXGqsC8PYVY4TLwJeollOhrSvcoDTx261OgNLW9noTts+xMdsZ7zIIn7VBgOILETcNFmoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:52:13.391624Z","bundle_sha256":"5ed10268df96737e9164c30d4afbfdd3c51daf64dea141647ea193c87c263f1c"}}