{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DGW5WWTECOU5BJCKMEMHNAFEDD","short_pith_number":"pith:DGW5WWTE","canonical_record":{"source":{"id":"2606.20326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:03:43Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"58425cc72d2de1ba96278661f2187865f1146049c0880c714374e2c9913cc5b8","abstract_canon_sha256":"6f17bbc6c3096465b07f476130d84fd8062b0f51cfa38e24d1f0388d7f112709"},"schema_version":"1.0"},"canonical_sha256":"19addb5a6413a9d0a44a61187680a418e4295e7d732d7c1951fa97dfe7ae443b","source":{"kind":"arxiv","id":"2606.20326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20326","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20326v1","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20326","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"DGW5WWTECOU5","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_16","alias_value":"DGW5WWTECOU5BJCK","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_8","alias_value":"DGW5WWTE","created_at":"2026-06-19T16:13:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DGW5WWTECOU5BJCKMEMHNAFEDD","target":"record","payload":{"canonical_record":{"source":{"id":"2606.20326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:03:43Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"58425cc72d2de1ba96278661f2187865f1146049c0880c714374e2c9913cc5b8","abstract_canon_sha256":"6f17bbc6c3096465b07f476130d84fd8062b0f51cfa38e24d1f0388d7f112709"},"schema_version":"1.0"},"canonical_sha256":"19addb5a6413a9d0a44a61187680a418e4295e7d732d7c1951fa97dfe7ae443b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:13:08.987719Z","signature_b64":"yRyg/WdOpUJxBl1FMcndfhOirpVUrxjt7jPvf504wx/BRmPbR7GfjvpfvWSZv1wwKTFwF0r0DvkVT4jfRGplAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19addb5a6413a9d0a44a61187680a418e4295e7d732d7c1951fa97dfe7ae443b","last_reissued_at":"2026-06-19T16:13:08.987347Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:13:08.987347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.20326","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":"2026-06-19T16:13:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e//sRLYEFxIEB95OTcH+tOHvaeospg1HVoV39pbHI05kRh4IPiEzcZXEO6dV3ZxAhbleEmOyI3NjUSh52+a0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:30:25.214506Z"},"content_sha256":"2bc4071b01502be8b4664b750e53adb5c6337943be45187e08344c10ab37372d","schema_version":"1.0","event_id":"sha256:2bc4071b01502be8b4664b750e53adb5c6337943be45187e08344c10ab37372d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DGW5WWTECOU5BJCKMEMHNAFEDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Xiang Rao, Yuxuan Shen","submitted_at":"2026-06-18T15:03:43Z","abstract_excerpt":"We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20326","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/2606.20326/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":"2026-06-19T16:13:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2CxwmErgwwdXVTysju3+ES6X7L/ceApW5DJ2Ad3mvzkq33832qEtTv9e1xPGKt4b2s/Arvkx9W0uB9tB47IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:30:25.214879Z"},"content_sha256":"33b16f1bb1bb87b1bc042be07ace36f98967cd192f5a84c4efeca945073d8be5","schema_version":"1.0","event_id":"sha256:33b16f1bb1bb87b1bc042be07ace36f98967cd192f5a84c4efeca945073d8be5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/bundle.json","state_url":"https://pith.science/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/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":"2026-06-27T03:30:25Z","links":{"resolver":"https://pith.science/pith/DGW5WWTECOU5BJCKMEMHNAFEDD","bundle":"https://pith.science/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/bundle.json","state":"https://pith.science/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGW5WWTECOU5BJCKMEMHNAFEDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DGW5WWTECOU5BJCKMEMHNAFEDD","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":"6f17bbc6c3096465b07f476130d84fd8062b0f51cfa38e24d1f0388d7f112709","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:03:43Z","title_canon_sha256":"58425cc72d2de1ba96278661f2187865f1146049c0880c714374e2c9913cc5b8"},"schema_version":"1.0","source":{"id":"2606.20326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20326","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20326v1","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20326","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"DGW5WWTECOU5","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_16","alias_value":"DGW5WWTECOU5BJCK","created_at":"2026-06-19T16:13:08Z"},{"alias_kind":"pith_short_8","alias_value":"DGW5WWTE","created_at":"2026-06-19T16:13:08Z"}],"graph_snapshots":[{"event_id":"sha256:33b16f1bb1bb87b1bc042be07ace36f98967cd192f5a84c4efeca945073d8be5","target":"graph","created_at":"2026-06-19T16:13:08Z","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/2606.20326/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios","authors_text":"Xiang Rao, Yuxuan Shen","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:03:43Z","title":"Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20326","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":"sha256:2bc4071b01502be8b4664b750e53adb5c6337943be45187e08344c10ab37372d","target":"record","created_at":"2026-06-19T16:13:08Z","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":"6f17bbc6c3096465b07f476130d84fd8062b0f51cfa38e24d1f0388d7f112709","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:03:43Z","title_canon_sha256":"58425cc72d2de1ba96278661f2187865f1146049c0880c714374e2c9913cc5b8"},"schema_version":"1.0","source":{"id":"2606.20326","kind":"arxiv","version":1}},"canonical_sha256":"19addb5a6413a9d0a44a61187680a418e4295e7d732d7c1951fa97dfe7ae443b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19addb5a6413a9d0a44a61187680a418e4295e7d732d7c1951fa97dfe7ae443b","first_computed_at":"2026-06-19T16:13:08.987347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:08.987347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yRyg/WdOpUJxBl1FMcndfhOirpVUrxjt7jPvf504wx/BRmPbR7GfjvpfvWSZv1wwKTFwF0r0DvkVT4jfRGplAA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:08.987719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bc4071b01502be8b4664b750e53adb5c6337943be45187e08344c10ab37372d","sha256:33b16f1bb1bb87b1bc042be07ace36f98967cd192f5a84c4efeca945073d8be5"],"state_sha256":"f7ec24ee3185b11d0ae2e1be1620a5b421054c778634936560e40f325fbbf11d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpI5xeV5ihKjMvKeK/E6Eto1ZtgwvxaT3RthS53H/itv1o9Xya/NzIwJ0bzLRn1xjVMBtq/CxhYsbd4izUvVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:30:25.216921Z","bundle_sha256":"9e23b479d633d5dd06a69da86fd6d8888c7ce85af66518df633bd4ee35c1b7e9"}}