{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HET42TE5SSFJNSRFOXV7LRIAAJ","short_pith_number":"pith:HET42TE5","canonical_record":{"source":{"id":"1708.09519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-31T01:14:03Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7b035bdb605d526e7403175ca2ab0e698835206a76afbd8d63db1f1703baefd7","abstract_canon_sha256":"822c5366b56d4ca59e0adbfcf0bb8d30567249904c8169a0d43545b9230f4bdd"},"schema_version":"1.0"},"canonical_sha256":"3927cd4c9d948a96ca2575ebf5c500026f7675659e3459b4857c5a353b9eecfb","source":{"kind":"arxiv","id":"1708.09519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09519","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09519v1","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09519","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"HET42TE5SSFJ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HET42TE5SSFJNSRF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HET42TE5","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HET42TE5SSFJNSRFOXV7LRIAAJ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.09519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-31T01:14:03Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7b035bdb605d526e7403175ca2ab0e698835206a76afbd8d63db1f1703baefd7","abstract_canon_sha256":"822c5366b56d4ca59e0adbfcf0bb8d30567249904c8169a0d43545b9230f4bdd"},"schema_version":"1.0"},"canonical_sha256":"3927cd4c9d948a96ca2575ebf5c500026f7675659e3459b4857c5a353b9eecfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:18.519989Z","signature_b64":"4oolavaTzatAgGW3TEMF99xh10khKUXR9ycu49R+I7HTQaMgGOhcqF3ICmAicjAj9N6JJXH78vbfDDlEaJKvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3927cd4c9d948a96ca2575ebf5c500026f7675659e3459b4857c5a353b9eecfb","last_reissued_at":"2026-05-18T00:36:18.519355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:18.519355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.09519","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":"2026-05-18T00:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2c1tXibtzeMV44JuE1tpvdF2/G0pcy36TgmOcoBfJwt42OXu0ylS+qjtiy7EuU5QZq+oeBoPQi3Tgzx459UwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:12:34.236887Z"},"content_sha256":"5d5de06bd1f9a2d5d2c218e315317a90207d1c369cf1b05ff8c6aaa3676d4428","schema_version":"1.0","event_id":"sha256:5d5de06bd1f9a2d5d2c218e315317a90207d1c369cf1b05ff8c6aaa3676d4428"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HET42TE5SSFJNSRFOXV7LRIAAJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Dissipative Nonlinear Evolutional Pseudo-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Mingjuan Chen, M. W. Wong, Shuxia Wang","submitted_at":"2017-08-31T01:14:03Z","abstract_excerpt":"First, using the uniform decomposition in both physical and frequency spaces, we obtain an equivalent norm on modulation spaces. Secondly, we consider the Cauchy problem for the dissipative evolutionary pseudo-differential equation \\partial_t u + A(x,D) u = F\\big((\\partial^\\alpha_x u)_{|\\alpha|\\leq \\kappa}\\big), \\ \\ u(0,x)= u_0(x), where $A(x,D)$ is a dissipative pseudo-differential operator and $F(z)$ is a multi-polynomial. We will develop the uniform decomposition techniques in both physical and frequency spaces to study its local well posedness in modulation spaces $M^s_{p,q}$ and in Sobole"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09519","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":"2026-05-18T00:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQLA1XgXB6hB25fVv3bqDKLDutk/yG/tRMD6Pt79+NG8skfaHwB1gOkh2AnTzKg4W49z+hYlMD111C+d3uzhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:12:34.237228Z"},"content_sha256":"c97905c378d6f1e2032221a139ceeedd35d59d9ce253ee6e1b44fd323da33e72","schema_version":"1.0","event_id":"sha256:c97905c378d6f1e2032221a139ceeedd35d59d9ce253ee6e1b44fd323da33e72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/bundle.json","state_url":"https://pith.science/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/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":"2026-06-03T08:12:34Z","links":{"resolver":"https://pith.science/pith/HET42TE5SSFJNSRFOXV7LRIAAJ","bundle":"https://pith.science/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/bundle.json","state":"https://pith.science/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HET42TE5SSFJNSRFOXV7LRIAAJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HET42TE5SSFJNSRFOXV7LRIAAJ","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":"822c5366b56d4ca59e0adbfcf0bb8d30567249904c8169a0d43545b9230f4bdd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-31T01:14:03Z","title_canon_sha256":"7b035bdb605d526e7403175ca2ab0e698835206a76afbd8d63db1f1703baefd7"},"schema_version":"1.0","source":{"id":"1708.09519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09519","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09519v1","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09519","created_at":"2026-05-18T00:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"HET42TE5SSFJ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HET42TE5SSFJNSRF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HET42TE5","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:c97905c378d6f1e2032221a139ceeedd35d59d9ce253ee6e1b44fd323da33e72","target":"graph","created_at":"2026-05-18T00:36:18Z","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":"First, using the uniform decomposition in both physical and frequency spaces, we obtain an equivalent norm on modulation spaces. Secondly, we consider the Cauchy problem for the dissipative evolutionary pseudo-differential equation \\partial_t u + A(x,D) u = F\\big((\\partial^\\alpha_x u)_{|\\alpha|\\leq \\kappa}\\big), \\ \\ u(0,x)= u_0(x), where $A(x,D)$ is a dissipative pseudo-differential operator and $F(z)$ is a multi-polynomial. We will develop the uniform decomposition techniques in both physical and frequency spaces to study its local well posedness in modulation spaces $M^s_{p,q}$ and in Sobole","authors_text":"Baoxiang Wang, Mingjuan Chen, M. W. Wong, Shuxia Wang","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-31T01:14:03Z","title":"On Dissipative Nonlinear Evolutional Pseudo-Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09519","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":"sha256:5d5de06bd1f9a2d5d2c218e315317a90207d1c369cf1b05ff8c6aaa3676d4428","target":"record","created_at":"2026-05-18T00:36:18Z","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":"822c5366b56d4ca59e0adbfcf0bb8d30567249904c8169a0d43545b9230f4bdd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-31T01:14:03Z","title_canon_sha256":"7b035bdb605d526e7403175ca2ab0e698835206a76afbd8d63db1f1703baefd7"},"schema_version":"1.0","source":{"id":"1708.09519","kind":"arxiv","version":1}},"canonical_sha256":"3927cd4c9d948a96ca2575ebf5c500026f7675659e3459b4857c5a353b9eecfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3927cd4c9d948a96ca2575ebf5c500026f7675659e3459b4857c5a353b9eecfb","first_computed_at":"2026-05-18T00:36:18.519355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:18.519355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4oolavaTzatAgGW3TEMF99xh10khKUXR9ycu49R+I7HTQaMgGOhcqF3ICmAicjAj9N6JJXH78vbfDDlEaJKvCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:18.519989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d5de06bd1f9a2d5d2c218e315317a90207d1c369cf1b05ff8c6aaa3676d4428","sha256:c97905c378d6f1e2032221a139ceeedd35d59d9ce253ee6e1b44fd323da33e72"],"state_sha256":"6e4c43fc365d939e8e7f7bc66f800d1bc8e5015d6ccdcf8c3911cd68c602add8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"haC5XUAtWQJjf4dTLW1852A28mGDPOJBsDiatBPF1qnrsENDkVxigx5EEHJmbIYxBSSUZPOawXL7xRyVnt4SCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:12:34.239215Z","bundle_sha256":"43b92f75eef75e20cc9b5ec7e753718fdb63020b625514be75b11e88f63cef09"}}