{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:6Q4TPOPGYQPHJ75QA5KVPVD6QM","short_pith_number":"pith:6Q4TPOPG","canonical_record":{"source":{"id":"hep-th/9604122","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1996-04-19T05:15:37Z","cross_cats_sorted":["cond-mat","nlin.SI","solv-int"],"title_canon_sha256":"48b8c11f99c656e67decfac294d392f2f9942782411d86526dc1e2d964c06865","abstract_canon_sha256":"04df793648e8f96c837e743122f2b3756265bd454bc4545c10c3c6486982952a"},"schema_version":"1.0"},"canonical_sha256":"f43937b9e6c41e74ffb0075557d47e833fb479243b3f109561600b4f52d3411f","source":{"kind":"arxiv","id":"hep-th/9604122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9604122","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9604122v1","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9604122","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"6Q4TPOPGYQPH","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_16","alias_value":"6Q4TPOPGYQPHJ75Q","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_8","alias_value":"6Q4TPOPG","created_at":"2026-07-04T16:02:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:6Q4TPOPGYQPHJ75QA5KVPVD6QM","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9604122","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1996-04-19T05:15:37Z","cross_cats_sorted":["cond-mat","nlin.SI","solv-int"],"title_canon_sha256":"48b8c11f99c656e67decfac294d392f2f9942782411d86526dc1e2d964c06865","abstract_canon_sha256":"04df793648e8f96c837e743122f2b3756265bd454bc4545c10c3c6486982952a"},"schema_version":"1.0"},"canonical_sha256":"f43937b9e6c41e74ffb0075557d47e833fb479243b3f109561600b4f52d3411f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:02:07.482897Z","signature_b64":"eVFdtVHYmTl0irmhHDO6WHBTwQCQSdvDHWjxo/NikNUFxqWvyI9cugRLe8Y3RPCyGKvlIKNFRST7NScaGwCmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f43937b9e6c41e74ffb0075557d47e833fb479243b3f109561600b4f52d3411f","last_reissued_at":"2026-07-04T16:02:07.482532Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:02:07.482532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9604122","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":"2026-07-04T16:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"va1NsApF1e3uaHsYdzjH8JyumBvCgPg9WgxuEsy1SJo96uIOIyBtBmmEJxEmobeaqE1jxubbVOsbUGccQ98zBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:08:53.932473Z"},"content_sha256":"9c80f47eb9054c0aabc3981e97a5be87eefba19b758b2fbe9d1f1e55f1cb5f41","schema_version":"1.0","event_id":"sha256:9c80f47eb9054c0aabc3981e97a5be87eefba19b758b2fbe9d1f1e55f1cb5f41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:6Q4TPOPGYQPHJ75QA5KVPVD6QM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization","license":"","headline":"","cross_cats":["cond-mat","nlin.SI","solv-int"],"primary_cat":"hep-th","authors_text":"Avinash Khare C. Nagaraja Kumar, B. Dey","submitted_at":"1996-04-19T05:15:37Z","abstract_excerpt":"Exact stationary soliton solutions of the fifth order KdV type equation $$ u_t +\\alpha u^p u_x +\\beta u_{3x}+\\gamma u_{5x} = 0$$ are obtained for any p ($>0$) in case $\\alpha\\beta>0$, $D\\beta>0$, $\\beta\\gamma<0$ (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case $p\\geq 5$. Various properties of these solutions are discussed. In particular, it is shown that for any p, these solitons are lower and narrower than the corresponding $\\gamma = 0$ solitons. Finally, for p = 2 we obtain an exact stationary soliton solution ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9604122","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9604122/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMy3eAj9s4Pyn1UYOdhI+rbAv8FTPlAojnz4FI4Iyq8+NNuwBecEyhy61qun7flQSgBqVuz1LSK2QOfMr8duBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:08:53.933332Z"},"content_sha256":"4fd0faf92efd176577a7a79595e360aacc6dd08e35598eca903f1f128999e9f4","schema_version":"1.0","event_id":"sha256:4fd0faf92efd176577a7a79595e360aacc6dd08e35598eca903f1f128999e9f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/bundle.json","state_url":"https://pith.science/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/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":"2026-08-13T16:08:53Z","links":{"resolver":"https://pith.science/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM","bundle":"https://pith.science/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/bundle.json","state":"https://pith.science/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Q4TPOPGYQPHJ75QA5KVPVD6QM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:6Q4TPOPGYQPHJ75QA5KVPVD6QM","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":"04df793648e8f96c837e743122f2b3756265bd454bc4545c10c3c6486982952a","cross_cats_sorted":["cond-mat","nlin.SI","solv-int"],"license":"","primary_cat":"hep-th","submitted_at":"1996-04-19T05:15:37Z","title_canon_sha256":"48b8c11f99c656e67decfac294d392f2f9942782411d86526dc1e2d964c06865"},"schema_version":"1.0","source":{"id":"hep-th/9604122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9604122","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9604122v1","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9604122","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"6Q4TPOPGYQPH","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_16","alias_value":"6Q4TPOPGYQPHJ75Q","created_at":"2026-07-04T16:02:07Z"},{"alias_kind":"pith_short_8","alias_value":"6Q4TPOPG","created_at":"2026-07-04T16:02:07Z"}],"graph_snapshots":[{"event_id":"sha256:4fd0faf92efd176577a7a79595e360aacc6dd08e35598eca903f1f128999e9f4","target":"graph","created_at":"2026-07-04T16:02:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/9604122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Exact stationary soliton solutions of the fifth order KdV type equation $$ u_t +\\alpha u^p u_x +\\beta u_{3x}+\\gamma u_{5x} = 0$$ are obtained for any p ($>0$) in case $\\alpha\\beta>0$, $D\\beta>0$, $\\beta\\gamma<0$ (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case $p\\geq 5$. Various properties of these solutions are discussed. In particular, it is shown that for any p, these solitons are lower and narrower than the corresponding $\\gamma = 0$ solitons. Finally, for p = 2 we obtain an exact stationary soliton solution ev","authors_text":"Avinash Khare C. Nagaraja Kumar, B. Dey","cross_cats":["cond-mat","nlin.SI","solv-int"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1996-04-19T05:15:37Z","title":"Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9604122","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":"sha256:9c80f47eb9054c0aabc3981e97a5be87eefba19b758b2fbe9d1f1e55f1cb5f41","target":"record","created_at":"2026-07-04T16:02:07Z","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":"04df793648e8f96c837e743122f2b3756265bd454bc4545c10c3c6486982952a","cross_cats_sorted":["cond-mat","nlin.SI","solv-int"],"license":"","primary_cat":"hep-th","submitted_at":"1996-04-19T05:15:37Z","title_canon_sha256":"48b8c11f99c656e67decfac294d392f2f9942782411d86526dc1e2d964c06865"},"schema_version":"1.0","source":{"id":"hep-th/9604122","kind":"arxiv","version":1}},"canonical_sha256":"f43937b9e6c41e74ffb0075557d47e833fb479243b3f109561600b4f52d3411f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f43937b9e6c41e74ffb0075557d47e833fb479243b3f109561600b4f52d3411f","first_computed_at":"2026-07-04T16:02:07.482532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:02:07.482532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eVFdtVHYmTl0irmhHDO6WHBTwQCQSdvDHWjxo/NikNUFxqWvyI9cugRLe8Y3RPCyGKvlIKNFRST7NScaGwCmCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:02:07.482897Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9604122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c80f47eb9054c0aabc3981e97a5be87eefba19b758b2fbe9d1f1e55f1cb5f41","sha256:4fd0faf92efd176577a7a79595e360aacc6dd08e35598eca903f1f128999e9f4"],"state_sha256":"39f263e2b2fd4a6b57238629b04c2fb911413c76b3ff220ab20769a27ed78fb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ccfNxyV32beZFcuGREsTm02D/0S9qs2a2kf8/v9acq4lcFIYBS9YFMxSSGJn+Abkv5dcqnrVCaRUDh4YkN3lCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T16:08:53.940221Z","bundle_sha256":"39a95c98131a5dc0ea9d3e12fc7cb76dc73b659706a4d592a2352fb0c37c15f1"}}