{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:F7YV6W4NXKNAPELY3DWGL2XRCF","short_pith_number":"pith:F7YV6W4N","canonical_record":{"source":{"id":"2607.18113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T16:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"a280ca37cb8e130ab3496cd19fe80321e2ed8d15e2589e210f1d514d054826ee","abstract_canon_sha256":"752254d0f76095e093dbdb04a96a9e4d5e4f23da5bbf168b8780b4ea07697203"},"schema_version":"1.0"},"canonical_sha256":"2ff15f5b8dba9a079178d8ec65eaf1117e8a389ffbe3f2dd5225050b36b32e6f","source":{"kind":"arxiv","id":"2607.18113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18113","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18113v1","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18113","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"F7YV6W4NXKNA","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_16","alias_value":"F7YV6W4NXKNAPELY","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_8","alias_value":"F7YV6W4N","created_at":"2026-07-21T02:22:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:F7YV6W4NXKNAPELY3DWGL2XRCF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T16:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"a280ca37cb8e130ab3496cd19fe80321e2ed8d15e2589e210f1d514d054826ee","abstract_canon_sha256":"752254d0f76095e093dbdb04a96a9e4d5e4f23da5bbf168b8780b4ea07697203"},"schema_version":"1.0"},"canonical_sha256":"2ff15f5b8dba9a079178d8ec65eaf1117e8a389ffbe3f2dd5225050b36b32e6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T02:22:17.034047Z","signature_b64":"CI7RVemsBC2h0uktNbrDqn8I8E/JplrsEzSydMtconmgndkUI5vrP+352Xvz/psoKvgTUyQh8hfMibWrkktVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff15f5b8dba9a079178d8ec65eaf1117e8a389ffbe3f2dd5225050b36b32e6f","last_reissued_at":"2026-07-21T02:22:17.033050Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T02:22:17.033050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18113","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":"2026-07-21T02:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3UcLzb0nZrVl6zcjBDhK4+hDw3vju4r6wkse3grLxysUTET/K/02kMpmKLRZ2JSA5z3BglNshee/AFZng7MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T23:58:53.479470Z"},"content_sha256":"366572c2fb836de568ec9a37e38187bd4634991a56d06e57ab5a2e577f3800a9","schema_version":"1.0","event_id":"sha256:366572c2fb836de568ec9a37e38187bd4634991a56d06e57ab5a2e577f3800a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:F7YV6W4NXKNAPELY3DWGL2XRCF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Xiantao Li","submitted_at":"2026-07-20T16:09:24Z","abstract_excerpt":"Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial in $h^{-1}$, or equivalently in the number of spatial degrees of freedom $N_h=\\Theta(h^{-d})$. Direct quantum implementations of a parabolic semigroup still have coherent complexity $\\widetilde{\\mathcal O}(\\sqrt{T}/h)$, and gradient-dependent observables such as heat flux and dissipation introduce additional mesh dependence. Decay of the solution norm will further suppress the postselection probability for preparing a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18113","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.18113/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":"2026-07-21T02:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dsm2gdb3f2osqCOLZSWeMBadvNO0tqOmGat6Ls0uUPQfn1wPC8FmSGpYOldAbcEFIN71Z/i3P0ch+mahIVHaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T23:58:53.479955Z"},"content_sha256":"163c8b79103a31b95fac98830fba19c1d8be313a46df880ba21fff063ecd652b","schema_version":"1.0","event_id":"sha256:163c8b79103a31b95fac98830fba19c1d8be313a46df880ba21fff063ecd652b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/bundle.json","state_url":"https://pith.science/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/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":"2026-08-06T23:58:53Z","links":{"resolver":"https://pith.science/pith/F7YV6W4NXKNAPELY3DWGL2XRCF","bundle":"https://pith.science/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/bundle.json","state":"https://pith.science/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7YV6W4NXKNAPELY3DWGL2XRCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F7YV6W4NXKNAPELY3DWGL2XRCF","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":"752254d0f76095e093dbdb04a96a9e4d5e4f23da5bbf168b8780b4ea07697203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T16:09:24Z","title_canon_sha256":"a280ca37cb8e130ab3496cd19fe80321e2ed8d15e2589e210f1d514d054826ee"},"schema_version":"1.0","source":{"id":"2607.18113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18113","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18113v1","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18113","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"F7YV6W4NXKNA","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_16","alias_value":"F7YV6W4NXKNAPELY","created_at":"2026-07-21T02:22:17Z"},{"alias_kind":"pith_short_8","alias_value":"F7YV6W4N","created_at":"2026-07-21T02:22:17Z"}],"graph_snapshots":[{"event_id":"sha256:163c8b79103a31b95fac98830fba19c1d8be313a46df880ba21fff063ecd652b","target":"graph","created_at":"2026-07-21T02:22:17Z","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/2607.18113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial in $h^{-1}$, or equivalently in the number of spatial degrees of freedom $N_h=\\Theta(h^{-d})$. Direct quantum implementations of a parabolic semigroup still have coherent complexity $\\widetilde{\\mathcal O}(\\sqrt{T}/h)$, and gradient-dependent observables such as heat flux and dissipation introduce additional mesh dependence. Decay of the solution norm will further suppress the postselection probability for preparing a","authors_text":"Xiantao Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T16:09:24Z","title":"Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18113","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":"sha256:366572c2fb836de568ec9a37e38187bd4634991a56d06e57ab5a2e577f3800a9","target":"record","created_at":"2026-07-21T02:22:17Z","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":"752254d0f76095e093dbdb04a96a9e4d5e4f23da5bbf168b8780b4ea07697203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T16:09:24Z","title_canon_sha256":"a280ca37cb8e130ab3496cd19fe80321e2ed8d15e2589e210f1d514d054826ee"},"schema_version":"1.0","source":{"id":"2607.18113","kind":"arxiv","version":1}},"canonical_sha256":"2ff15f5b8dba9a079178d8ec65eaf1117e8a389ffbe3f2dd5225050b36b32e6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff15f5b8dba9a079178d8ec65eaf1117e8a389ffbe3f2dd5225050b36b32e6f","first_computed_at":"2026-07-21T02:22:17.033050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:22:17.033050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CI7RVemsBC2h0uktNbrDqn8I8E/JplrsEzSydMtconmgndkUI5vrP+352Xvz/psoKvgTUyQh8hfMibWrkktVCw==","signature_status":"signed_v1","signed_at":"2026-07-21T02:22:17.034047Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:366572c2fb836de568ec9a37e38187bd4634991a56d06e57ab5a2e577f3800a9","sha256:163c8b79103a31b95fac98830fba19c1d8be313a46df880ba21fff063ecd652b"],"state_sha256":"3f041638f692ea14e3762fc205e90009fa41c9bee594a11ba0b123f5d089427e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qlQ9mckvW4Q/R8j+0AXEs8m/2nANI+b/BtKPRHwk+Ma0rV9pN3luy+iz5RzSS7ZRrZpNBA9RiPTyCT/RV/NNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T23:58:53.483277Z","bundle_sha256":"688dd8a49b56477ba3fdf534bedae596e7b13893f28224bffc2d606e76ea1984"}}