{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:T7GJUIQHKKWOSJX42URUOM4XZ7","short_pith_number":"pith:T7GJUIQH","canonical_record":{"source":{"id":"2206.15008","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-06-30T04:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"35f95c11f26d180035bc586f5cc6a81d29717271aaf6a53e561de29fefecfe74","abstract_canon_sha256":"329b1240cf922858e2874ee9fffb20c719b4474637ae0fc116a6cc431823a60f"},"schema_version":"1.0"},"canonical_sha256":"9fcc9a220752ace926fcd523473397cfffee26672fa72e78f911f34db5387574","source":{"kind":"arxiv","id":"2206.15008","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.15008","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"arxiv_version","alias_value":"2206.15008v2","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.15008","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_12","alias_value":"T7GJUIQHKKWO","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_16","alias_value":"T7GJUIQHKKWOSJX4","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_8","alias_value":"T7GJUIQH","created_at":"2026-07-05T09:16:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:T7GJUIQHKKWOSJX42URUOM4XZ7","target":"record","payload":{"canonical_record":{"source":{"id":"2206.15008","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-06-30T04:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"35f95c11f26d180035bc586f5cc6a81d29717271aaf6a53e561de29fefecfe74","abstract_canon_sha256":"329b1240cf922858e2874ee9fffb20c719b4474637ae0fc116a6cc431823a60f"},"schema_version":"1.0"},"canonical_sha256":"9fcc9a220752ace926fcd523473397cfffee26672fa72e78f911f34db5387574","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:16:43.157741Z","signature_b64":"xFbnGpkcVrD4P1od9IOlNqqGQWn+Jhq40y4jioM9E3/pfMZlNzRq+a0Cd/74kydrXo3ahWYnou9yQkTCJvh2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fcc9a220752ace926fcd523473397cfffee26672fa72e78f911f34db5387574","last_reissued_at":"2026-07-05T09:16:43.157276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:16:43.157276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.15008","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:16:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sirJNEQCijJ5c0GZmIBEMppMHXVBW+1elqoj64shE/qcLAWvS3MObsJMdwQRxW6eR+bbya1LJewyyuDp62d6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:40:10.708779Z"},"content_sha256":"707011825eb1a9b72af9330c6c87b80f49141fcaa42cd71503a39089a8dc68a8","schema_version":"1.0","event_id":"sha256:707011825eb1a9b72af9330c6c87b80f49141fcaa42cd71503a39089a8dc68a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:T7GJUIQHKKWOSJX42URUOM4XZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability near the soliton for quartic Klein-Gordon in 1D","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adilbek Kairzhan, Fabio Pusateri","submitted_at":"2022-06-30T04:19:31Z","abstract_excerpt":"We consider the nonlinear focusing Klein-Gordon equation in $1 + 1$ dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof of optimal decay, and local decay, for even perturbations of the static soliton originating from well-prepared initial data belonging to a subset of the stable manifold constructed in Bates-Jones (Dynamics reported, 1989) and Kowalczyk-Martel-Mu\\~noz (J. Eur. Math. Soc., 2021). Our results complement those of Kowalczyk-Martel-Mu\\~noz (J. Eur. Math. Soc., 2021) and confirm numerical results of Bizon-Chmaj-Szpak (J. M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15008","kind":"arxiv","version":2},"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/2206.15008/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":"2026-07-05T09:16:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttO844C+XIRU6TDeqG0OYJCLxptKpnG99oXiqKkrlKzHIAHG1Klf6aE/oJZwTXCxdPafPjOP8dCoDe+5ENW/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:40:10.709098Z"},"content_sha256":"612342c2f2a91027b5bd7abf10a2b332637df1a61e38f32b487acafce854f7e4","schema_version":"1.0","event_id":"sha256:612342c2f2a91027b5bd7abf10a2b332637df1a61e38f32b487acafce854f7e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/bundle.json","state_url":"https://pith.science/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/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":"2026-08-11T12:40:10Z","links":{"resolver":"https://pith.science/pith/T7GJUIQHKKWOSJX42URUOM4XZ7","bundle":"https://pith.science/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/bundle.json","state":"https://pith.science/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7GJUIQHKKWOSJX42URUOM4XZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:T7GJUIQHKKWOSJX42URUOM4XZ7","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":"329b1240cf922858e2874ee9fffb20c719b4474637ae0fc116a6cc431823a60f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-06-30T04:19:31Z","title_canon_sha256":"35f95c11f26d180035bc586f5cc6a81d29717271aaf6a53e561de29fefecfe74"},"schema_version":"1.0","source":{"id":"2206.15008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.15008","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"arxiv_version","alias_value":"2206.15008v2","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.15008","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_12","alias_value":"T7GJUIQHKKWO","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_16","alias_value":"T7GJUIQHKKWOSJX4","created_at":"2026-07-05T09:16:43Z"},{"alias_kind":"pith_short_8","alias_value":"T7GJUIQH","created_at":"2026-07-05T09:16:43Z"}],"graph_snapshots":[{"event_id":"sha256:612342c2f2a91027b5bd7abf10a2b332637df1a61e38f32b487acafce854f7e4","target":"graph","created_at":"2026-07-05T09:16:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.15008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the nonlinear focusing Klein-Gordon equation in $1 + 1$ dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof of optimal decay, and local decay, for even perturbations of the static soliton originating from well-prepared initial data belonging to a subset of the stable manifold constructed in Bates-Jones (Dynamics reported, 1989) and Kowalczyk-Martel-Mu\\~noz (J. Eur. Math. Soc., 2021). Our results complement those of Kowalczyk-Martel-Mu\\~noz (J. Eur. Math. Soc., 2021) and confirm numerical results of Bizon-Chmaj-Szpak (J. M","authors_text":"Adilbek Kairzhan, Fabio Pusateri","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-06-30T04:19:31Z","title":"Asymptotic stability near the soliton for quartic Klein-Gordon in 1D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15008","kind":"arxiv","version":2},"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":"sha256:707011825eb1a9b72af9330c6c87b80f49141fcaa42cd71503a39089a8dc68a8","target":"record","created_at":"2026-07-05T09:16:43Z","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":"329b1240cf922858e2874ee9fffb20c719b4474637ae0fc116a6cc431823a60f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-06-30T04:19:31Z","title_canon_sha256":"35f95c11f26d180035bc586f5cc6a81d29717271aaf6a53e561de29fefecfe74"},"schema_version":"1.0","source":{"id":"2206.15008","kind":"arxiv","version":2}},"canonical_sha256":"9fcc9a220752ace926fcd523473397cfffee26672fa72e78f911f34db5387574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fcc9a220752ace926fcd523473397cfffee26672fa72e78f911f34db5387574","first_computed_at":"2026-07-05T09:16:43.157276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:16:43.157276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xFbnGpkcVrD4P1od9IOlNqqGQWn+Jhq40y4jioM9E3/pfMZlNzRq+a0Cd/74kydrXo3ahWYnou9yQkTCJvh2DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:16:43.157741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.15008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:707011825eb1a9b72af9330c6c87b80f49141fcaa42cd71503a39089a8dc68a8","sha256:612342c2f2a91027b5bd7abf10a2b332637df1a61e38f32b487acafce854f7e4"],"state_sha256":"69df625a11c99ff1887b63c0a4d736925b6a4c30e698a79662fbc627cf4fa6d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OVVqUV5FW+zXT3tfrFMieplJmWR97/J59u+RTGvafqVuced3yizhRDxwnmcDDwzo8HDCdRHmObnhlkhGEqfRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:40:10.711858Z","bundle_sha256":"bc691bdb2da436b53f8508601f38bab13996a1f0578cde6e8c16ded4791101b2"}}