{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7F7LFZSXDWXAQLKD3D4SAYMX2W","short_pith_number":"pith:7F7LFZSX","canonical_record":{"source":{"id":"1301.1585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"293555a0063992127c6def37321bce23db691a7d799c3707ba571553eedd2bcd","abstract_canon_sha256":"854d613e04ec1364a8079cc4f4dbe40066e68aee27fdc20ccecc4492ee097f5b"},"schema_version":"1.0"},"canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","source":{"kind":"arxiv","id":"1301.1585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1585","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1585v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1585","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"7F7LFZSXDWXA","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7F7LFZSXDWXAQLKD","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7F7LFZSX","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7F7LFZSXDWXAQLKD3D4SAYMX2W","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"293555a0063992127c6def37321bce23db691a7d799c3707ba571553eedd2bcd","abstract_canon_sha256":"854d613e04ec1364a8079cc4f4dbe40066e68aee27fdc20ccecc4492ee097f5b"},"schema_version":"1.0"},"canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:57.107720Z","signature_b64":"nrGKlmQghsH2gDUdYx1vnBpBrqmO3GJAbjIbHclc6/n6LgdN3Jm22X1NDPDzQv05oUKS94qpl8MKleMVasXjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","last_reissued_at":"2026-05-18T03:36:57.107243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:57.107243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1585","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":"2026-05-18T03:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/004Hpw878mZLEXENJs64DV+nP/9sbo3ISQeKTlX5VxcpKtG3A8ACPWy6nrp3s0x7Pqi4e9rqMOd2rMl3YRHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:00:16.688821Z"},"content_sha256":"63b273a857e8bf09a08c78338546c76c903ac0ce265e7530453a9fd65f38bb40","schema_version":"1.0","event_id":"sha256:63b273a857e8bf09a08c78338546c76c903ac0ce265e7530453a9fd65f38bb40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7F7LFZSXDWXAQLKD3D4SAYMX2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Averaging Theorem for Perturbed KdV Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guan Huang","submitted_at":"2013-01-08T16:31:46Z","abstract_excerpt":"We consider a perturbed KdV equation:\n  [\\dot{u}+u_{xxx} - 6uu_x = \\epsilon f(x,u(\\cdot)), \\quad x\\in \\mathbb{T}, \\quad\\int_\\mathbb{T} u dx=0.]\n  For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\\in\\mathbb{R}_+^{\\infty}$ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. Assuming that the perturbation $\\epsilon f(x,u(\\cdot))$ is a smoothing mapping (e.g. it is a smooth function $\\epsilon f(x)$, independent from $u$), and that solutions of the perturbed equation satisfy some mild a-priori assumptions, we prove that for solutions $u(t,x)$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1585","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":"2026-05-18T03:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEVbsyHlkWWQsKMhyczL3sC9IW55KhepW70ttqc/tK5d1WU904zmzbBM25UxVWn1PJRJZwB6yZY03EAafbBfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:00:16.689480Z"},"content_sha256":"40b900b2fa9812badcf1d881eebc05cf1141187a580af96753e518937b5c9275","schema_version":"1.0","event_id":"sha256:40b900b2fa9812badcf1d881eebc05cf1141187a580af96753e518937b5c9275"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/bundle.json","state_url":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/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":"2026-05-28T03:00:16Z","links":{"resolver":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W","bundle":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/bundle.json","state":"https://pith.science/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7F7LFZSXDWXAQLKD3D4SAYMX2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7F7LFZSXDWXAQLKD3D4SAYMX2W","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":"854d613e04ec1364a8079cc4f4dbe40066e68aee27fdc20ccecc4492ee097f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","title_canon_sha256":"293555a0063992127c6def37321bce23db691a7d799c3707ba571553eedd2bcd"},"schema_version":"1.0","source":{"id":"1301.1585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1585","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1585v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1585","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"7F7LFZSXDWXA","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7F7LFZSXDWXAQLKD","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7F7LFZSX","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:40b900b2fa9812badcf1d881eebc05cf1141187a580af96753e518937b5c9275","target":"graph","created_at":"2026-05-18T03:36:57Z","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 consider a perturbed KdV equation:\n  [\\dot{u}+u_{xxx} - 6uu_x = \\epsilon f(x,u(\\cdot)), \\quad x\\in \\mathbb{T}, \\quad\\int_\\mathbb{T} u dx=0.]\n  For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\\in\\mathbb{R}_+^{\\infty}$ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. Assuming that the perturbation $\\epsilon f(x,u(\\cdot))$ is a smoothing mapping (e.g. it is a smooth function $\\epsilon f(x)$, independent from $u$), and that solutions of the perturbed equation satisfy some mild a-priori assumptions, we prove that for solutions $u(t,x)$ wit","authors_text":"Guan Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","title":"An Averaging Theorem for Perturbed KdV Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1585","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":"sha256:63b273a857e8bf09a08c78338546c76c903ac0ce265e7530453a9fd65f38bb40","target":"record","created_at":"2026-05-18T03:36:57Z","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":"854d613e04ec1364a8079cc4f4dbe40066e68aee27fdc20ccecc4492ee097f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-08T16:31:46Z","title_canon_sha256":"293555a0063992127c6def37321bce23db691a7d799c3707ba571553eedd2bcd"},"schema_version":"1.0","source":{"id":"1301.1585","kind":"arxiv","version":1}},"canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f97eb2e6571dae082d43d8f9206197d59179d78327742ad0a8713d98606103ec","first_computed_at":"2026-05-18T03:36:57.107243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:57.107243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrGKlmQghsH2gDUdYx1vnBpBrqmO3GJAbjIbHclc6/n6LgdN3Jm22X1NDPDzQv05oUKS94qpl8MKleMVasXjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:57.107720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b273a857e8bf09a08c78338546c76c903ac0ce265e7530453a9fd65f38bb40","sha256:40b900b2fa9812badcf1d881eebc05cf1141187a580af96753e518937b5c9275"],"state_sha256":"4183004bd0dd065e459b27ff833cde1c8bc3d1e4b0f299ff754c0bc018af21a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ro1fBD3ji1kLwxifP6j+mfXSeSsbgNSjixHyWCHgnkfEdTZ5V1S6z0j1iRMlf2yKeEIdPfAcS5+o2lmaYPNhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:00:16.692865Z","bundle_sha256":"10d0ed1345e6cb318cfcb65f453852aa8e43a12edd025f82ec62acf141ebb58c"}}