{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZBQ2W7NS3MDX565ZIDPZTYQDD4","short_pith_number":"pith:ZBQ2W7NS","canonical_record":{"source":{"id":"1410.6873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T02:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"e687ad7ef74514ee1ea51aa83b405099868221f5b38b23cf6bcab33b19277c70","abstract_canon_sha256":"71826b6bd563388a79a2eb329b26da22b00dcb5ab6f6e1a32ec54962a3e74c9a"},"schema_version":"1.0"},"canonical_sha256":"c861ab7db2db077efbb940df99e2031f0f2623089bbdde9bc9b55422e7e04c2b","source":{"kind":"arxiv","id":"1410.6873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6873","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6873v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6873","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZBQ2W7NS3MDX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZBQ2W7NS3MDX565Z","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZBQ2W7NS","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZBQ2W7NS3MDX565ZIDPZTYQDD4","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T02:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"e687ad7ef74514ee1ea51aa83b405099868221f5b38b23cf6bcab33b19277c70","abstract_canon_sha256":"71826b6bd563388a79a2eb329b26da22b00dcb5ab6f6e1a32ec54962a3e74c9a"},"schema_version":"1.0"},"canonical_sha256":"c861ab7db2db077efbb940df99e2031f0f2623089bbdde9bc9b55422e7e04c2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:18.416558Z","signature_b64":"d4sGhsNkqOuS4AVOUKViNfBxEr3u5kecRf4MijAF5AG5RbF6JV+oxhbmmL9uKpfffXsmscYK9d2wm3tAI81cDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c861ab7db2db077efbb940df99e2031f0f2623089bbdde9bc9b55422e7e04c2b","last_reissued_at":"2026-05-18T02:39:18.416181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:18.416181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6873","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrsAsC1sGtcdVE5TmE+ItJancxBfzzpPGe7n+FaXi/Y4jJMaQZVHwCdNzfxB5q6W0WCq08VLOXpOdXR8Vy9RAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:31:32.016443Z"},"content_sha256":"19022f3366c670a9b0448c0d21ca9ba904810b1e3d612ddd80c044005a6e0577","schema_version":"1.0","event_id":"sha256:19022f3366c670a9b0448c0d21ca9ba904810b1e3d612ddd80c044005a6e0577"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZBQ2W7NS3MDX565ZIDPZTYQDD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Stability for KdV Solitons in Weighted $H^s$ Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Brian Pigott, Sarah Raynor","submitted_at":"2014-10-25T02:52:25Z","abstract_excerpt":"In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restriction is due to a lack of global control of the unweighted perturbation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6873","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaqAlej+pPy5o57N/dcvo7kkFbLja72XCxWN+EiHlCcWD3dqZ9RRvKihSGAEbqZOnqyTbq0KyeJ6nkJjT9PvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:31:32.017087Z"},"content_sha256":"6b2b637d160e0bbf3e5d599b8d7dcc7f99999509493d2f38df687c96656983ba","schema_version":"1.0","event_id":"sha256:6b2b637d160e0bbf3e5d599b8d7dcc7f99999509493d2f38df687c96656983ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/bundle.json","state_url":"https://pith.science/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/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":"2026-06-01T01:31:32Z","links":{"resolver":"https://pith.science/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4","bundle":"https://pith.science/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/bundle.json","state":"https://pith.science/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBQ2W7NS3MDX565ZIDPZTYQDD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZBQ2W7NS3MDX565ZIDPZTYQDD4","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":"71826b6bd563388a79a2eb329b26da22b00dcb5ab6f6e1a32ec54962a3e74c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T02:52:25Z","title_canon_sha256":"e687ad7ef74514ee1ea51aa83b405099868221f5b38b23cf6bcab33b19277c70"},"schema_version":"1.0","source":{"id":"1410.6873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6873","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6873v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6873","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZBQ2W7NS3MDX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZBQ2W7NS3MDX565Z","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZBQ2W7NS","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:6b2b637d160e0bbf3e5d599b8d7dcc7f99999509493d2f38df687c96656983ba","target":"graph","created_at":"2026-05-18T02:39:18Z","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 this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restriction is due to a lack of global control of the unweighted perturbation.","authors_text":"Brian Pigott, Sarah Raynor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T02:52:25Z","title":"Asymptotic Stability for KdV Solitons in Weighted $H^s$ Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6873","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":"sha256:19022f3366c670a9b0448c0d21ca9ba904810b1e3d612ddd80c044005a6e0577","target":"record","created_at":"2026-05-18T02:39:18Z","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":"71826b6bd563388a79a2eb329b26da22b00dcb5ab6f6e1a32ec54962a3e74c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T02:52:25Z","title_canon_sha256":"e687ad7ef74514ee1ea51aa83b405099868221f5b38b23cf6bcab33b19277c70"},"schema_version":"1.0","source":{"id":"1410.6873","kind":"arxiv","version":1}},"canonical_sha256":"c861ab7db2db077efbb940df99e2031f0f2623089bbdde9bc9b55422e7e04c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c861ab7db2db077efbb940df99e2031f0f2623089bbdde9bc9b55422e7e04c2b","first_computed_at":"2026-05-18T02:39:18.416181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:18.416181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4sGhsNkqOuS4AVOUKViNfBxEr3u5kecRf4MijAF5AG5RbF6JV+oxhbmmL9uKpfffXsmscYK9d2wm3tAI81cDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:18.416558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19022f3366c670a9b0448c0d21ca9ba904810b1e3d612ddd80c044005a6e0577","sha256:6b2b637d160e0bbf3e5d599b8d7dcc7f99999509493d2f38df687c96656983ba"],"state_sha256":"3e368ad89f331e49e646e84c6155f0df9a01210c05b9681f5f39569b8f3cacab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3bb8oz9nwOeO7oPFTQsIYgxcc7mJ7uv+N5vfYosCkl1+M3HfKVb/wBDhet6SXsIjZ8WGnXMAXa54oVe8/0qAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:31:32.021001Z","bundle_sha256":"219b4a99ced28fd242bfc7c7864f7857ba52eed3086e25aa19cde00eff063513"}}