{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:A3L4VPZY34O3R3OK6U37P67QOH","short_pith_number":"pith:A3L4VPZY","canonical_record":{"source":{"id":"1405.7909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T16:38:55Z","cross_cats_sorted":[],"title_canon_sha256":"debaf8ad7dfeda42fe4295a824622e5e512e39e561a4ff5554143aa35d5015d5","abstract_canon_sha256":"8fb72fa7402fe9ff2744d5c6f5ea0b118c6c30d1db85636eebfe6cc1eff09aa5"},"schema_version":"1.0"},"canonical_sha256":"06d7cabf38df1db8edcaf537f7fbf071c2cb03f4ff51c0f69c9934b6fd800c4d","source":{"kind":"arxiv","id":"1405.7909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7909","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7909v1","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7909","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"A3L4VPZY34O3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A3L4VPZY34O3R3OK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A3L4VPZY","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:A3L4VPZY34O3R3OK6U37P67QOH","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T16:38:55Z","cross_cats_sorted":[],"title_canon_sha256":"debaf8ad7dfeda42fe4295a824622e5e512e39e561a4ff5554143aa35d5015d5","abstract_canon_sha256":"8fb72fa7402fe9ff2744d5c6f5ea0b118c6c30d1db85636eebfe6cc1eff09aa5"},"schema_version":"1.0"},"canonical_sha256":"06d7cabf38df1db8edcaf537f7fbf071c2cb03f4ff51c0f69c9934b6fd800c4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:43.730172Z","signature_b64":"K39CbBmLoLSzOTzTRhnYZahkKYRrN3YTaAL2qbIcGbaukLSfbyDp/T73uwSXvQRI5delBxl3f5sqjiyUP3/bDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06d7cabf38df1db8edcaf537f7fbf071c2cb03f4ff51c0f69c9934b6fd800c4d","last_reissued_at":"2026-05-18T02:50:43.729565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:43.729565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7909","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":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwByueNH2cSGSJVbn/MFAVNreegZeeGdq0hNM0zc/L4kIbK8EzORhvvLsSXz2suG/o5u6+OQ1P8gOPk47bGCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:38:16.158514Z"},"content_sha256":"30b1d86a6c08180d6bf309274c553095dd65275d08f27f98e56043f9e293ec15","schema_version":"1.0","event_id":"sha256:30b1d86a6c08180d6bf309274c553095dd65275d08f27f98e56043f9e293ec15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:A3L4VPZY34O3R3OK6U37P67QOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On persistence properties in fractional weighted spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Linares, G. Fonseca, G. Ponce","submitted_at":"2014-05-30T16:38:55Z","abstract_excerpt":"In this work we derive a point-wise formula that will allows us to study the well-posedness of initial value problem associated to nonlinear dispersive equations in fractional weighted Sobolev spaces $H^s(\\R)\\cap L^2(|x|^{2r}dx)$, $s, r \\in \\R$. As an application of this formula we will study local and global well posedness of the $k$-generalized Korteweg-de Vries equation in these weighted Sobolev spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7909","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":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VvM8aQ4hALtPLNOoK8LhoQUipepPNxDHc+irpbL0SpEmdwYlSxXmpmWe8XRdgi5AOxm4GoP8obFI8KW5KuhTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:38:16.159218Z"},"content_sha256":"d338ef6eeff6323969f9dbd7dac2f76209e31485119ab6831efbb90a0d9810f5","schema_version":"1.0","event_id":"sha256:d338ef6eeff6323969f9dbd7dac2f76209e31485119ab6831efbb90a0d9810f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3L4VPZY34O3R3OK6U37P67QOH/bundle.json","state_url":"https://pith.science/pith/A3L4VPZY34O3R3OK6U37P67QOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3L4VPZY34O3R3OK6U37P67QOH/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":"2026-06-07T13:38:16Z","links":{"resolver":"https://pith.science/pith/A3L4VPZY34O3R3OK6U37P67QOH","bundle":"https://pith.science/pith/A3L4VPZY34O3R3OK6U37P67QOH/bundle.json","state":"https://pith.science/pith/A3L4VPZY34O3R3OK6U37P67QOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3L4VPZY34O3R3OK6U37P67QOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A3L4VPZY34O3R3OK6U37P67QOH","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":"8fb72fa7402fe9ff2744d5c6f5ea0b118c6c30d1db85636eebfe6cc1eff09aa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T16:38:55Z","title_canon_sha256":"debaf8ad7dfeda42fe4295a824622e5e512e39e561a4ff5554143aa35d5015d5"},"schema_version":"1.0","source":{"id":"1405.7909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7909","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7909v1","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7909","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"A3L4VPZY34O3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A3L4VPZY34O3R3OK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A3L4VPZY","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d338ef6eeff6323969f9dbd7dac2f76209e31485119ab6831efbb90a0d9810f5","target":"graph","created_at":"2026-05-18T02:50:43Z","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 derive a point-wise formula that will allows us to study the well-posedness of initial value problem associated to nonlinear dispersive equations in fractional weighted Sobolev spaces $H^s(\\R)\\cap L^2(|x|^{2r}dx)$, $s, r \\in \\R$. As an application of this formula we will study local and global well posedness of the $k$-generalized Korteweg-de Vries equation in these weighted Sobolev spaces.","authors_text":"F. Linares, G. Fonseca, G. Ponce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T16:38:55Z","title":"On persistence properties in fractional weighted spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7909","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":"sha256:30b1d86a6c08180d6bf309274c553095dd65275d08f27f98e56043f9e293ec15","target":"record","created_at":"2026-05-18T02:50:43Z","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":"8fb72fa7402fe9ff2744d5c6f5ea0b118c6c30d1db85636eebfe6cc1eff09aa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-30T16:38:55Z","title_canon_sha256":"debaf8ad7dfeda42fe4295a824622e5e512e39e561a4ff5554143aa35d5015d5"},"schema_version":"1.0","source":{"id":"1405.7909","kind":"arxiv","version":1}},"canonical_sha256":"06d7cabf38df1db8edcaf537f7fbf071c2cb03f4ff51c0f69c9934b6fd800c4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06d7cabf38df1db8edcaf537f7fbf071c2cb03f4ff51c0f69c9934b6fd800c4d","first_computed_at":"2026-05-18T02:50:43.729565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:43.729565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K39CbBmLoLSzOTzTRhnYZahkKYRrN3YTaAL2qbIcGbaukLSfbyDp/T73uwSXvQRI5delBxl3f5sqjiyUP3/bDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:43.730172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30b1d86a6c08180d6bf309274c553095dd65275d08f27f98e56043f9e293ec15","sha256:d338ef6eeff6323969f9dbd7dac2f76209e31485119ab6831efbb90a0d9810f5"],"state_sha256":"6fec34dcd50eab3b14cf6133de11d7e42357054faf4bf1efedaf7807a17dd492"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Jnwirpp12bintyZ4pL9bm4sBARI0MtT4CE5IQ0/5majC4A6wnmhP9ZM9U/JxYgFNELlr4299ZQVkH5pJMfaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T13:38:16.162594Z","bundle_sha256":"49d1ebbe086f8485babb52995783e90d4db98cd2c005c96a6267063eb2fe718c"}}