{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5L4FWBGSAXIJKJSJVVX7M64VKF","short_pith_number":"pith:5L4FWBGS","canonical_record":{"source":{"id":"2605.17968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T07:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"88b0f3a4cee88ef72b906ea5f939bb8299261c1f633ac2a33f6b09b2d726c762","abstract_canon_sha256":"d723c2ae5ffdc439e805101de3a65cd942094276b08f6a476f6899c06acb9fbe"},"schema_version":"1.0"},"canonical_sha256":"eaf85b04d205d0952649ad6ff67b955144913cd05123f154261db0306213bb89","source":{"kind":"arxiv","id":"2605.17968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17968","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17968v1","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17968","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"5L4FWBGSAXIJ","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"5L4FWBGSAXIJKJSJ","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"5L4FWBGS","created_at":"2026-05-20T00:05:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5L4FWBGSAXIJKJSJVVX7M64VKF","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T07:25:14Z","cross_cats_sorted":[],"title_canon_sha256":"88b0f3a4cee88ef72b906ea5f939bb8299261c1f633ac2a33f6b09b2d726c762","abstract_canon_sha256":"d723c2ae5ffdc439e805101de3a65cd942094276b08f6a476f6899c06acb9fbe"},"schema_version":"1.0"},"canonical_sha256":"eaf85b04d205d0952649ad6ff67b955144913cd05123f154261db0306213bb89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:08.616727Z","signature_b64":"HumbtXezydCVJKJ4sqzDMG4OtZxaa3vl+wbGVtRUsH7bjOnAlNpOdb+EbTaayy+VXGzFou5h0K5k/tqqsr66Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaf85b04d205d0952649ad6ff67b955144913cd05123f154261db0306213bb89","last_reissued_at":"2026-05-20T00:05:08.615886Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:08.615886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17968","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":"2026-05-20T00:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aC7/LJe3m+3/B4SL3WuDC3U0ITgS3izHjMpQRkBiUcOFvUjpEWJBKbSgYHpB3NvcFWLsiRdaOxW7bV4TSeRABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:57:56.240183Z"},"content_sha256":"73bdcaf9e5020d83eba385d121ad349ac6bb368da663c836d4631d4b7c710f52","schema_version":"1.0","event_id":"sha256:73bdcaf9e5020d83eba385d121ad349ac6bb368da663c836d4631d4b7c710f52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5L4FWBGSAXIJKJSJVVX7M64VKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Function graph transformers universally approximate operators between function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"David Mis, Ivan Dokmani\\'c, Maarten V. de Hoop, Matti Lassas, Takashi Furuya","submitted_at":"2026-05-18T07:25:14Z","abstract_excerpt":"We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function $h$ is represented by its graph measure $\\gamma_h$, with finite tokens $\\{(x_j,h(x_j))\\}_{j=1}^N$ being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17968","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/2605.17968/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.578581Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8c19e717ba1c74ec971f3ce48874ed3ea386229f99090879be448234b7b459aa"},"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":"2026-05-20T00:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O41JYweK+8LwGQMcJ1K6u3+S5hYFHEPGlra1O/wLA6oGv3kAVPB8a2w9Qz7jjayeqM0lMxQNOVBKhJl3nixcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:57:56.240933Z"},"content_sha256":"c1f4add4b00a0280c82b4c43789e52c87500d753d65c75d1f427ca8afc476c19","schema_version":"1.0","event_id":"sha256:c1f4add4b00a0280c82b4c43789e52c87500d753d65c75d1f427ca8afc476c19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/bundle.json","state_url":"https://pith.science/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/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":"2026-05-27T09:57:56Z","links":{"resolver":"https://pith.science/pith/5L4FWBGSAXIJKJSJVVX7M64VKF","bundle":"https://pith.science/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/bundle.json","state":"https://pith.science/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5L4FWBGSAXIJKJSJVVX7M64VKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5L4FWBGSAXIJKJSJVVX7M64VKF","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":"d723c2ae5ffdc439e805101de3a65cd942094276b08f6a476f6899c06acb9fbe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T07:25:14Z","title_canon_sha256":"88b0f3a4cee88ef72b906ea5f939bb8299261c1f633ac2a33f6b09b2d726c762"},"schema_version":"1.0","source":{"id":"2605.17968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17968","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17968v1","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17968","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"5L4FWBGSAXIJ","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"5L4FWBGSAXIJKJSJ","created_at":"2026-05-20T00:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"5L4FWBGS","created_at":"2026-05-20T00:05:08Z"}],"graph_snapshots":[{"event_id":"sha256:c1f4add4b00a0280c82b4c43789e52c87500d753d65c75d1f427ca8afc476c19","target":"graph","created_at":"2026-05-20T00:05:08Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.578581Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17968/integrity.json","findings":[],"snapshot_sha256":"8c19e717ba1c74ec971f3ce48874ed3ea386229f99090879be448234b7b459aa","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function $h$ is represented by its graph measure $\\gamma_h$, with finite tokens $\\{(x_j,h(x_j))\\}_{j=1}^N$ being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers,","authors_text":"David Mis, Ivan Dokmani\\'c, Maarten V. de Hoop, Matti Lassas, Takashi Furuya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T07:25:14Z","title":"Function graph transformers universally approximate operators between function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17968","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":"sha256:73bdcaf9e5020d83eba385d121ad349ac6bb368da663c836d4631d4b7c710f52","target":"record","created_at":"2026-05-20T00:05:08Z","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":"d723c2ae5ffdc439e805101de3a65cd942094276b08f6a476f6899c06acb9fbe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T07:25:14Z","title_canon_sha256":"88b0f3a4cee88ef72b906ea5f939bb8299261c1f633ac2a33f6b09b2d726c762"},"schema_version":"1.0","source":{"id":"2605.17968","kind":"arxiv","version":1}},"canonical_sha256":"eaf85b04d205d0952649ad6ff67b955144913cd05123f154261db0306213bb89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaf85b04d205d0952649ad6ff67b955144913cd05123f154261db0306213bb89","first_computed_at":"2026-05-20T00:05:08.615886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:08.615886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HumbtXezydCVJKJ4sqzDMG4OtZxaa3vl+wbGVtRUsH7bjOnAlNpOdb+EbTaayy+VXGzFou5h0K5k/tqqsr66Bg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:08.616727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73bdcaf9e5020d83eba385d121ad349ac6bb368da663c836d4631d4b7c710f52","sha256:c1f4add4b00a0280c82b4c43789e52c87500d753d65c75d1f427ca8afc476c19"],"state_sha256":"0e23e9d44051498d3567b03cdc26255acbe661352460554ea49fd7fa071482c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stwntFGQM7mvAnyEqs0+B+YtK01P6Eu3J5/b8UnCnpc7yMX0waSAeUv+1mrGtuD6/yzrJrnGgUEzsS1y25aJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:57:56.244909Z","bundle_sha256":"8952f80c5f32522e8736fe2a75c1417e736682ca0498ae885001b6f12f062917"}}