{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NPBJZBXOF5RKI7XU65ABVN2W4N","short_pith_number":"pith:NPBJZBXO","canonical_record":{"source":{"id":"2208.02235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-03T17:41:11Z","cross_cats_sorted":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"title_canon_sha256":"d3087d4a1e7212a195f3135a4fd368152794a92f672d24011af68bb7e6713297","abstract_canon_sha256":"55f3e8501d3437101f31328f8c69f11fbaace5ad6e47884fece645de9641aea5"},"schema_version":"1.0"},"canonical_sha256":"6bc29c86ee2f62a47ef4f7401ab756e3736c0d557a702e64328593a89295e861","source":{"kind":"arxiv","id":"2208.02235","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.02235","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"2208.02235v2","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.02235","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"NPBJZBXOF5RK","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"NPBJZBXOF5RKI7XU","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"NPBJZBXO","created_at":"2026-07-05T04:47:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NPBJZBXOF5RKI7XU65ABVN2W4N","target":"record","payload":{"canonical_record":{"source":{"id":"2208.02235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-03T17:41:11Z","cross_cats_sorted":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"title_canon_sha256":"d3087d4a1e7212a195f3135a4fd368152794a92f672d24011af68bb7e6713297","abstract_canon_sha256":"55f3e8501d3437101f31328f8c69f11fbaace5ad6e47884fece645de9641aea5"},"schema_version":"1.0"},"canonical_sha256":"6bc29c86ee2f62a47ef4f7401ab756e3736c0d557a702e64328593a89295e861","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:47:29.494278Z","signature_b64":"iWFjdkihDeE2F80Grs7Zb47rCsuDPpNWDkf5xUOGvBU5c822Ymj01TAC0lXuJh/yu7ZgwSRaTiMiMeHQb51UAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bc29c86ee2f62a47ef4f7401ab756e3736c0d557a702e64328593a89295e861","last_reissued_at":"2026-07-05T04:47:29.493833Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:47:29.493833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.02235","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHdSmiTaZMACHl/iDB+ixL+fMhUi1RXX6F3kfnvnNmrEHkQZI+01l3s4SsFERHi09kvOldszX8kGX+JY7vNhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-21T12:26:09.375169Z"},"content_sha256":"d906e3095e8e49a3f150c1e8796fa5e834827d5364c46dd84fb984c263edc65d","schema_version":"1.0","event_id":"sha256:d906e3095e8e49a3f150c1e8796fa5e834827d5364c46dd84fb984c263edc65d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NPBJZBXOF5RKI7XU65ABVN2W4N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum-Inspired Tensor Neural Networks for Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"primary_cat":"cs.LG","authors_text":"Chia-Wei Hsing, Chi-Guhn Lee, Christophe Michel, Mustafa Abid, Pierre Castellani, Raj Patel, Roman Orus, Saeed S. Jahromi, Samuel Mugel, Samuel Palmer, Serkan Sahin, Shivam Sharma, Stephane Aubert, Vincent Porte","submitted_at":"2022-08-03T17:41:11Z","abstract_excerpt":"Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of dimensionality in new ways. However, deep learning methods are constrained by training time and memory. To tackle these shortcomings, we implement Tensor Neural Networks (TNN), a quantum-inspired neural network architecture that leverages Tensor Network ideas to improve upon deep learning approaches. We demonstrate that TNN provide significant parameter savings while att"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.02235","kind":"arxiv","version":2},"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/2208.02235/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":"2026-07-05T04:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uL7cIVK7M++pNvREV2xoFHYsLvKgQkNev0Szh0Vjpi1qDU3mnEYHKGf/p/19CimzwNQX7hW5Ujbhf7bfSFCSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-21T12:26:09.375565Z"},"content_sha256":"f16aa6e278809a6759860ca3ba4ece6c36c17b0dcbf0a7b72e95824c004dfe6f","schema_version":"1.0","event_id":"sha256:f16aa6e278809a6759860ca3ba4ece6c36c17b0dcbf0a7b72e95824c004dfe6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/bundle.json","state_url":"https://pith.science/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/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":"2026-07-21T12:26:09Z","links":{"resolver":"https://pith.science/pith/NPBJZBXOF5RKI7XU65ABVN2W4N","bundle":"https://pith.science/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/bundle.json","state":"https://pith.science/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPBJZBXOF5RKI7XU65ABVN2W4N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NPBJZBXOF5RKI7XU65ABVN2W4N","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":"55f3e8501d3437101f31328f8c69f11fbaace5ad6e47884fece645de9641aea5","cross_cats_sorted":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-03T17:41:11Z","title_canon_sha256":"d3087d4a1e7212a195f3135a4fd368152794a92f672d24011af68bb7e6713297"},"schema_version":"1.0","source":{"id":"2208.02235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.02235","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"2208.02235v2","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.02235","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"NPBJZBXOF5RK","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"NPBJZBXOF5RKI7XU","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"NPBJZBXO","created_at":"2026-07-05T04:47:29Z"}],"graph_snapshots":[{"event_id":"sha256:f16aa6e278809a6759860ca3ba4ece6c36c17b0dcbf0a7b72e95824c004dfe6f","target":"graph","created_at":"2026-07-05T04:47:29Z","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/2208.02235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of dimensionality in new ways. However, deep learning methods are constrained by training time and memory. To tackle these shortcomings, we implement Tensor Neural Networks (TNN), a quantum-inspired neural network architecture that leverages Tensor Network ideas to improve upon deep learning approaches. We demonstrate that TNN provide significant parameter savings while att","authors_text":"Chia-Wei Hsing, Chi-Guhn Lee, Christophe Michel, Mustafa Abid, Pierre Castellani, Raj Patel, Roman Orus, Saeed S. Jahromi, Samuel Mugel, Samuel Palmer, Serkan Sahin, Shivam Sharma, Stephane Aubert, Vincent Porte","cross_cats":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-03T17:41:11Z","title":"Quantum-Inspired Tensor Neural Networks for Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.02235","kind":"arxiv","version":2},"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:d906e3095e8e49a3f150c1e8796fa5e834827d5364c46dd84fb984c263edc65d","target":"record","created_at":"2026-07-05T04:47:29Z","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":"55f3e8501d3437101f31328f8c69f11fbaace5ad6e47884fece645de9641aea5","cross_cats_sorted":["cond-mat.str-el","cs.AI","physics.comp-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-03T17:41:11Z","title_canon_sha256":"d3087d4a1e7212a195f3135a4fd368152794a92f672d24011af68bb7e6713297"},"schema_version":"1.0","source":{"id":"2208.02235","kind":"arxiv","version":2}},"canonical_sha256":"6bc29c86ee2f62a47ef4f7401ab756e3736c0d557a702e64328593a89295e861","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bc29c86ee2f62a47ef4f7401ab756e3736c0d557a702e64328593a89295e861","first_computed_at":"2026-07-05T04:47:29.493833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:29.493833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iWFjdkihDeE2F80Grs7Zb47rCsuDPpNWDkf5xUOGvBU5c822Ymj01TAC0lXuJh/yu7ZgwSRaTiMiMeHQb51UAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:29.494278Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.02235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d906e3095e8e49a3f150c1e8796fa5e834827d5364c46dd84fb984c263edc65d","sha256:f16aa6e278809a6759860ca3ba4ece6c36c17b0dcbf0a7b72e95824c004dfe6f"],"state_sha256":"8ce8b5ffd04a7c7e4b75dace1a98252bc1c4246acdb5e2fc106f59a15a1fd9d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgeTgyzjdF6wBPOk4K1SCGsE0kKGyv+C4eR9N4WzxogHMBsvE6yzZKvXy7NBKB1ijExMiK33s1d0GkWlBWNQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-21T12:26:09.378198Z","bundle_sha256":"8679477a0f933bc6f7b62fdfcefa6108d80b62787a9995824b2080a5d01ab7b9"}}