{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G4PSKK2B36X3MOKMIB2CAOAZBM","short_pith_number":"pith:G4PSKK2B","canonical_record":{"source":{"id":"1802.04823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-13T19:10:33Z","cross_cats_sorted":[],"title_canon_sha256":"2b6ef07d02a0be0335c7ee2fcfafc9e882c444511128800ebc4b7822d170da8e","abstract_canon_sha256":"136c2432d747f77b58c13ccdc7b58925c342d14c0707113ad9cbd7120e1e8607"},"schema_version":"1.0"},"canonical_sha256":"371f252b41dfafb6394c40742038190b216f531509dcde0f13c72e45f1a47934","source":{"kind":"arxiv","id":"1802.04823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04823","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04823v1","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04823","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"pith_short_12","alias_value":"G4PSKK2B36X3","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4PSKK2B36X3MOKM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4PSKK2B","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G4PSKK2B36X3MOKMIB2CAOAZBM","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-13T19:10:33Z","cross_cats_sorted":[],"title_canon_sha256":"2b6ef07d02a0be0335c7ee2fcfafc9e882c444511128800ebc4b7822d170da8e","abstract_canon_sha256":"136c2432d747f77b58c13ccdc7b58925c342d14c0707113ad9cbd7120e1e8607"},"schema_version":"1.0"},"canonical_sha256":"371f252b41dfafb6394c40742038190b216f531509dcde0f13c72e45f1a47934","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:57.388792Z","signature_b64":"C0B5a9s6LpbVGt2KDAkT/a0MD4zPtH1hGQUIMMiZuRh4aO3XJhj+9bMKjWS8G6GAzBxCNQkhwAwKUd1XM88sCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"371f252b41dfafb6394c40742038190b216f531509dcde0f13c72e45f1a47934","last_reissued_at":"2026-05-18T00:00:57.388383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:57.388383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04823","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":"2026-05-18T00:00:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o011KgZg4MrqQKIH4/Plzpy2SUAMjtpk0yswrc+9dexGcZE1wtbPd3s78TrAF2/DkjnhN7eHa5sXIPfLRRnYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T05:56:49.399263Z"},"content_sha256":"3daeddbf53e9322e75afc0f5d1ce06a5cd1e3c1637c476ab5816374278853a6a","schema_version":"1.0","event_id":"sha256:3daeddbf53e9322e75afc0f5d1ce06a5cd1e3c1637c476ab5816374278853a6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G4PSKK2B36X3MOKMIB2CAOAZBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mark Groves, Mats Ehrnstr\\\"om","submitted_at":"2018-02-13T19:10:33Z","abstract_excerpt":"The KP-I equation \\[ (u_t-2uu_x+\\tfrac{1}{2}(\\beta-\\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \\] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\\beta>1/3$). This equation admits --- as an explicit solution --- a `fully localised' or `lump' solitary wave which decays to zero in all spatial directions. Recently there has been interest in the \\emph{full-dispersion KP-I equation} \\[u_t + m({\\mathrm D}) u_x + 2 u u_x = 0,\\] where $m({\\mathrm D})$ is the Fourier multiplier with symbol \\[ m(k) = \\left( 1 + \\beta |k|^2|\\right)^{\\frac{1}{2}} \\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04823","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":"2026-05-18T00:00:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xlf4T5FMKuxQnRclbSoJItNyVpUcZ6zAEExhY2OI/jqr2sDagT5j0VFBFuV5v14XBpGRXK9yJRTdUnUBRSHzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T05:56:49.399626Z"},"content_sha256":"530ece8ebbce063a10086af9e9ee7f2337f464fb7fd338e2ddf340961f6b3b14","schema_version":"1.0","event_id":"sha256:530ece8ebbce063a10086af9e9ee7f2337f464fb7fd338e2ddf340961f6b3b14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/bundle.json","state_url":"https://pith.science/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/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":"2026-07-03T05:56:49Z","links":{"resolver":"https://pith.science/pith/G4PSKK2B36X3MOKMIB2CAOAZBM","bundle":"https://pith.science/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/bundle.json","state":"https://pith.science/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4PSKK2B36X3MOKMIB2CAOAZBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4PSKK2B36X3MOKMIB2CAOAZBM","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":"136c2432d747f77b58c13ccdc7b58925c342d14c0707113ad9cbd7120e1e8607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-13T19:10:33Z","title_canon_sha256":"2b6ef07d02a0be0335c7ee2fcfafc9e882c444511128800ebc4b7822d170da8e"},"schema_version":"1.0","source":{"id":"1802.04823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04823","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04823v1","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04823","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"pith_short_12","alias_value":"G4PSKK2B36X3","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4PSKK2B36X3MOKM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4PSKK2B","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:530ece8ebbce063a10086af9e9ee7f2337f464fb7fd338e2ddf340961f6b3b14","target":"graph","created_at":"2026-05-18T00:00:57Z","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":"The KP-I equation \\[ (u_t-2uu_x+\\tfrac{1}{2}(\\beta-\\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \\] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\\beta>1/3$). This equation admits --- as an explicit solution --- a `fully localised' or `lump' solitary wave which decays to zero in all spatial directions. Recently there has been interest in the \\emph{full-dispersion KP-I equation} \\[u_t + m({\\mathrm D}) u_x + 2 u u_x = 0,\\] where $m({\\mathrm D})$ is the Fourier multiplier with symbol \\[ m(k) = \\left( 1 + \\beta |k|^2|\\right)^{\\frac{1}{2}} \\le","authors_text":"Mark Groves, Mats Ehrnstr\\\"om","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-13T19:10:33Z","title":"Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04823","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":"sha256:3daeddbf53e9322e75afc0f5d1ce06a5cd1e3c1637c476ab5816374278853a6a","target":"record","created_at":"2026-05-18T00:00:57Z","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":"136c2432d747f77b58c13ccdc7b58925c342d14c0707113ad9cbd7120e1e8607","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-13T19:10:33Z","title_canon_sha256":"2b6ef07d02a0be0335c7ee2fcfafc9e882c444511128800ebc4b7822d170da8e"},"schema_version":"1.0","source":{"id":"1802.04823","kind":"arxiv","version":1}},"canonical_sha256":"371f252b41dfafb6394c40742038190b216f531509dcde0f13c72e45f1a47934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"371f252b41dfafb6394c40742038190b216f531509dcde0f13c72e45f1a47934","first_computed_at":"2026-05-18T00:00:57.388383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:57.388383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C0B5a9s6LpbVGt2KDAkT/a0MD4zPtH1hGQUIMMiZuRh4aO3XJhj+9bMKjWS8G6GAzBxCNQkhwAwKUd1XM88sCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:57.388792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3daeddbf53e9322e75afc0f5d1ce06a5cd1e3c1637c476ab5816374278853a6a","sha256:530ece8ebbce063a10086af9e9ee7f2337f464fb7fd338e2ddf340961f6b3b14"],"state_sha256":"82b2fa2014cb40bf94b62c177d740213dec6845f01da83852080200903dacb12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIuYynFINnemABd/vzaRSapYvCkBYlYAu/QGhJS5/y3j0VVQOEyBR6XyT0uBq/Q6tVtLCp9tXStD2i4IQR3/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T05:56:49.401417Z","bundle_sha256":"5d5ec31116b923db255f29ff6554caeb61957b9ca1fe90b11675d74cc020aa44"}}