{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:OGHQZMGZLHOGNI3TI4AFGAL7A2","short_pith_number":"pith:OGHQZMGZ","schema_version":"1.0","canonical_sha256":"718f0cb0d959dc66a373470053017f06a8310f4b7ed4ce1e2d0efd2e4866d8f1","source":{"kind":"arxiv","id":"0709.2727","version":1},"attestation_state":"computed","paper":{"title":"Does the complex deformation of the Riemann equation exhibit shocks?","license":"","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP","nlin.PS","physics.flu-dyn","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, Joshua Feinberg","submitted_at":"2007-09-17T21:40:50Z","abstract_excerpt":"The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is $\\cP\\cT$ symmetric. A one-parameter $\\cP\\cT$-invariant complex deformation of this equation, $u_t-iu(iu_x)^\\epsilon= 0$ ($\\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\\epsilon$ is an odd integer."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0709.2727","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-09-17T21:40:50Z","cross_cats_sorted":["cond-mat.other","math-ph","math.MP","nlin.PS","physics.flu-dyn","quant-ph"],"title_canon_sha256":"80b7eab75aad3808e768a46087a290b1187d6940d422fbb3f32e3b3e727a3ee1","abstract_canon_sha256":"60e8546e532e3386d0d024fd4b79ba8c4a431a0930b4488523dfd55aa2044069"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:14.024095Z","signature_b64":"ewF37FQE8lbyi3QyqEnK9I123tarIFxgOHHts51Rx9Sw14xdVwjOnMmka9upYQpCPwM4JzMnXIsQYM+51bWDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"718f0cb0d959dc66a373470053017f06a8310f4b7ed4ce1e2d0efd2e4866d8f1","last_reissued_at":"2026-05-18T01:05:14.023482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:14.023482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Does the complex deformation of the Riemann equation exhibit shocks?","license":"","headline":"","cross_cats":["cond-mat.other","math-ph","math.MP","nlin.PS","physics.flu-dyn","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, Joshua Feinberg","submitted_at":"2007-09-17T21:40:50Z","abstract_excerpt":"The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is $\\cP\\cT$ symmetric. A one-parameter $\\cP\\cT$-invariant complex deformation of this equation, $u_t-iu(iu_x)^\\epsilon= 0$ ($\\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\\epsilon$ is an odd integer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2727","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0709.2727","created_at":"2026-05-18T01:05:14.023581+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.2727v1","created_at":"2026-05-18T01:05:14.023581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2727","created_at":"2026-05-18T01:05:14.023581+00:00"},{"alias_kind":"pith_short_12","alias_value":"OGHQZMGZLHOG","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"OGHQZMGZLHOGNI3T","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"OGHQZMGZ","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2","json":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2.json","graph_json":"https://pith.science/api/pith-number/OGHQZMGZLHOGNI3TI4AFGAL7A2/graph.json","events_json":"https://pith.science/api/pith-number/OGHQZMGZLHOGNI3TI4AFGAL7A2/events.json","paper":"https://pith.science/paper/OGHQZMGZ"},"agent_actions":{"view_html":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2","download_json":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2.json","view_paper":"https://pith.science/paper/OGHQZMGZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.2727&json=true","fetch_graph":"https://pith.science/api/pith-number/OGHQZMGZLHOGNI3TI4AFGAL7A2/graph.json","fetch_events":"https://pith.science/api/pith-number/OGHQZMGZLHOGNI3TI4AFGAL7A2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2/action/storage_attestation","attest_author":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2/action/author_attestation","sign_citation":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2/action/citation_signature","submit_replication":"https://pith.science/pith/OGHQZMGZLHOGNI3TI4AFGAL7A2/action/replication_record"}},"created_at":"2026-05-18T01:05:14.023581+00:00","updated_at":"2026-05-18T01:05:14.023581+00:00"}