{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7RZUTTNJUEIQIRPN7VOFWJAQJI","short_pith_number":"pith:7RZUTTNJ","canonical_record":{"source":{"id":"2506.23058","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.PL","submitted_at":"2025-06-29T02:10:25Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"4ddbff87c240884b79fd3bd516b8178e0a6cf1f3164eead9cef4de8e219b0024","abstract_canon_sha256":"81d739ca4ed5317da378fc9075e4dfb11c5150914852ba8ae4ca4d1528ec4d37"},"schema_version":"1.0"},"canonical_sha256":"fc7349cda9a1110445edfd5c5b24104a22cab9b23e3f2eac5c401004cc537de6","source":{"kind":"arxiv","id":"2506.23058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23058","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23058v1","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23058","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"7RZUTTNJUEIQ","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"7RZUTTNJUEIQIRPN","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"7RZUTTNJ","created_at":"2026-07-05T11:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7RZUTTNJUEIQIRPN7VOFWJAQJI","target":"record","payload":{"canonical_record":{"source":{"id":"2506.23058","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.PL","submitted_at":"2025-06-29T02:10:25Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"4ddbff87c240884b79fd3bd516b8178e0a6cf1f3164eead9cef4de8e219b0024","abstract_canon_sha256":"81d739ca4ed5317da378fc9075e4dfb11c5150914852ba8ae4ca4d1528ec4d37"},"schema_version":"1.0"},"canonical_sha256":"fc7349cda9a1110445edfd5c5b24104a22cab9b23e3f2eac5c401004cc537de6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:49.975607Z","signature_b64":"p8kAGUMXLkcgE7cNuQm8zqNV9nOT2eBx/lJnkcYeSV8OmqHe7RjVI5T3XdPTne2IZW8dBvSSYqLNum3UR7mpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc7349cda9a1110445edfd5c5b24104a22cab9b23e3f2eac5c401004cc537de6","last_reissued_at":"2026-07-05T11:28:49.974842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:49.974842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.23058","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":"2026-07-05T11:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mn97t+Kdtdk79dQY3GVKh15+aTwJRmhrjPrLrNRhBVXWUPpoX7ad71xH+Eog9KsB1nect6MeYwky4S+gyF1iBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:07:32.625018Z"},"content_sha256":"448c43c5fa3ab697c07ff376a534af3807c3dad2f52cae3108d14706013726e0","schema_version":"1.0","event_id":"sha256:448c43c5fa3ab697c07ff376a534af3807c3dad2f52cae3108d14706013726e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7RZUTTNJUEIQIRPN7VOFWJAQJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Verifying Properties of Index Arrays in a Purely-Functional Data-Parallel Language","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.PL","authors_text":"Cosmin E. Oancea, Nikolaj Hey Hinnerskov, Robert Schenck","submitted_at":"2025-06-29T02:10:25Z","abstract_excerpt":"This paper presents a novel approach to automatically verify properties of pure data-parallel programs with non-linear indexing -- expressed as pre- and post-conditions on functions. Programs consist of nests of second-order array combinators (e.g., map, scan, and scatter) and loops. The key idea is to represent arrays as index functions: programs are index function transformations over which properties are propagated and inferred. Our framework proves properties on index functions by distilling them into algebraic (in)equalities and discharging them to a Fourier-Motzkin-based solver. The fram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23058","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/2506.23058/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":"2026-07-05T11:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ExPwz6vReBgJElyDOcQVTryy4LAGGQgId50TElGV7b06Ato+aB9lmCVH6la7xDQSy25WlvcUTRfJDMuUD0FAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:07:32.625537Z"},"content_sha256":"605828abbc36c21e9fc0010477e0d768e3fe642e1c75be6c91d125fdbf3c4ad1","schema_version":"1.0","event_id":"sha256:605828abbc36c21e9fc0010477e0d768e3fe642e1c75be6c91d125fdbf3c4ad1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/bundle.json","state_url":"https://pith.science/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/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":"2026-08-19T21:07:32Z","links":{"resolver":"https://pith.science/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI","bundle":"https://pith.science/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/bundle.json","state":"https://pith.science/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RZUTTNJUEIQIRPN7VOFWJAQJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7RZUTTNJUEIQIRPN7VOFWJAQJI","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":"81d739ca4ed5317da378fc9075e4dfb11c5150914852ba8ae4ca4d1528ec4d37","cross_cats_sorted":["cs.DC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.PL","submitted_at":"2025-06-29T02:10:25Z","title_canon_sha256":"4ddbff87c240884b79fd3bd516b8178e0a6cf1f3164eead9cef4de8e219b0024"},"schema_version":"1.0","source":{"id":"2506.23058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23058","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23058v1","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23058","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"7RZUTTNJUEIQ","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"7RZUTTNJUEIQIRPN","created_at":"2026-07-05T11:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"7RZUTTNJ","created_at":"2026-07-05T11:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:605828abbc36c21e9fc0010477e0d768e3fe642e1c75be6c91d125fdbf3c4ad1","target":"graph","created_at":"2026-07-05T11:28:49Z","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/2506.23058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents a novel approach to automatically verify properties of pure data-parallel programs with non-linear indexing -- expressed as pre- and post-conditions on functions. Programs consist of nests of second-order array combinators (e.g., map, scan, and scatter) and loops. The key idea is to represent arrays as index functions: programs are index function transformations over which properties are propagated and inferred. Our framework proves properties on index functions by distilling them into algebraic (in)equalities and discharging them to a Fourier-Motzkin-based solver. The fram","authors_text":"Cosmin E. Oancea, Nikolaj Hey Hinnerskov, Robert Schenck","cross_cats":["cs.DC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.PL","submitted_at":"2025-06-29T02:10:25Z","title":"Verifying Properties of Index Arrays in a Purely-Functional Data-Parallel Language"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23058","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":"sha256:448c43c5fa3ab697c07ff376a534af3807c3dad2f52cae3108d14706013726e0","target":"record","created_at":"2026-07-05T11:28:49Z","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":"81d739ca4ed5317da378fc9075e4dfb11c5150914852ba8ae4ca4d1528ec4d37","cross_cats_sorted":["cs.DC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.PL","submitted_at":"2025-06-29T02:10:25Z","title_canon_sha256":"4ddbff87c240884b79fd3bd516b8178e0a6cf1f3164eead9cef4de8e219b0024"},"schema_version":"1.0","source":{"id":"2506.23058","kind":"arxiv","version":1}},"canonical_sha256":"fc7349cda9a1110445edfd5c5b24104a22cab9b23e3f2eac5c401004cc537de6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc7349cda9a1110445edfd5c5b24104a22cab9b23e3f2eac5c401004cc537de6","first_computed_at":"2026-07-05T11:28:49.974842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:49.974842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p8kAGUMXLkcgE7cNuQm8zqNV9nOT2eBx/lJnkcYeSV8OmqHe7RjVI5T3XdPTne2IZW8dBvSSYqLNum3UR7mpDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:49.975607Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.23058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:448c43c5fa3ab697c07ff376a534af3807c3dad2f52cae3108d14706013726e0","sha256:605828abbc36c21e9fc0010477e0d768e3fe642e1c75be6c91d125fdbf3c4ad1"],"state_sha256":"c747d1f68deacd4086b6a1d6bc2887daa9d5aab706267d5ae1fc76a9912f007f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pu9l8hMwcZwSDP6h7KNSJdVwlvsvp3kF1mGhxw9f2S20xCn2h51mwsrcyeYTzOGmU+UvRyMPkcPfSby4kddhAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T21:07:32.629912Z","bundle_sha256":"7d4c0d542bd8f71e3057a80872dc29c818002e1ff1ec9c281d4acc3f4f486d34"}}