{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QQWQ6N3HXCIS6QVGWYOOVHB3X6","short_pith_number":"pith:QQWQ6N3H","canonical_record":{"source":{"id":"2509.05462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-09-05T19:35:08Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"9ded6d3f4fcfeb1df92f0618b8a0318a0fd6b660e3440736f4b2425b385cdc32","abstract_canon_sha256":"f251a85c3a1e9bfe37fdb416e66e191c0e18eccbd7734de1b070b2a0e3e60176"},"schema_version":"1.0"},"canonical_sha256":"842d0f3767b8912f42a6b61cea9c3bbfb37ef5481df559c33ed26c0a75bab6df","source":{"kind":"arxiv","id":"2509.05462","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05462","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05462v1","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05462","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"QQWQ6N3HXCIS","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"QQWQ6N3HXCIS6QVG","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"QQWQ6N3H","created_at":"2026-07-05T12:05:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QQWQ6N3HXCIS6QVGWYOOVHB3X6","target":"record","payload":{"canonical_record":{"source":{"id":"2509.05462","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-09-05T19:35:08Z","cross_cats_sorted":["cs.PL"],"title_canon_sha256":"9ded6d3f4fcfeb1df92f0618b8a0318a0fd6b660e3440736f4b2425b385cdc32","abstract_canon_sha256":"f251a85c3a1e9bfe37fdb416e66e191c0e18eccbd7734de1b070b2a0e3e60176"},"schema_version":"1.0"},"canonical_sha256":"842d0f3767b8912f42a6b61cea9c3bbfb37ef5481df559c33ed26c0a75bab6df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:05:48.135328Z","signature_b64":"1veP60bG5J9plytzfMrhywICPAdr6K/duY09nDw+aQQ/Gsp3JUk9Ibuypx1lwVi32Bx3SWk+M/NhWOvf8myLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"842d0f3767b8912f42a6b61cea9c3bbfb37ef5481df559c33ed26c0a75bab6df","last_reissued_at":"2026-07-05T12:05:48.134846Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:05:48.134846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.05462","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":"2026-07-05T12:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPP7TTcjaPR9w4pW23bFDRDL0SvomZ7MRz76GKFTP1MSaDfMJXJS+MHFiQ0Ve5AxJR2xmNAfNhkPJVGuTrQXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:24:27.425129Z"},"content_sha256":"60acb0618730917d47455dd4e6b0fcd576cdd4f340d62dbf9ca0686570c08a8c","schema_version":"1.0","event_id":"sha256:60acb0618730917d47455dd4e6b0fcd576cdd4f340d62dbf9ca0686570c08a8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QQWQ6N3HXCIS6QVGWYOOVHB3X6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The compact double category $\\mathbf{Int}(\\mathbf{Poly}_*)$ models control flow and data transformations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.PL"],"primary_cat":"math.CT","authors_text":"David I. Spivak, Grigory Kondyrev","submitted_at":"2025-09-05T19:35:08Z","abstract_excerpt":"Hasegawa showed that control flow in programming languages -- while loops and if-then-else statements -- can be modeled using traced cocartesian categories, such as the category $\\mathbf{Set}_*$ of pointed sets. In this paper we define an operad $\\mathscr{W}$ of wiring diagrams that provides syntax for categories whose control flow moreover includes data transformations, including deleting, duplicating, permuting, and applying pre-specified functions to variables. In the most basic version, the operad underlies $\\mathbf{Int}(\\mathbf{Poly}_*)$, where $\\mathbf{Int}(\\mathscr{T})$ denotes the free"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05462","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/2509.05462/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":"2026-07-05T12:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDiIPeGicyeNkABrmnOUGPDpFnLKGVRMnOcybE5zSC6YatGh28SNxwSjtMFAcZOWEgtIwRdTp8ORR9Sf7xcjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:24:27.425779Z"},"content_sha256":"be97521f7c50ddceb5421c29807bbf92804830bc1095556c6d7aadaaed65eefb","schema_version":"1.0","event_id":"sha256:be97521f7c50ddceb5421c29807bbf92804830bc1095556c6d7aadaaed65eefb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/bundle.json","state_url":"https://pith.science/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/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":"2026-08-17T02:24:27Z","links":{"resolver":"https://pith.science/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6","bundle":"https://pith.science/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/bundle.json","state":"https://pith.science/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQWQ6N3HXCIS6QVGWYOOVHB3X6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QQWQ6N3HXCIS6QVGWYOOVHB3X6","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":"f251a85c3a1e9bfe37fdb416e66e191c0e18eccbd7734de1b070b2a0e3e60176","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-09-05T19:35:08Z","title_canon_sha256":"9ded6d3f4fcfeb1df92f0618b8a0318a0fd6b660e3440736f4b2425b385cdc32"},"schema_version":"1.0","source":{"id":"2509.05462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05462","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05462v1","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05462","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"QQWQ6N3HXCIS","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"QQWQ6N3HXCIS6QVG","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"QQWQ6N3H","created_at":"2026-07-05T12:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:be97521f7c50ddceb5421c29807bbf92804830bc1095556c6d7aadaaed65eefb","target":"graph","created_at":"2026-07-05T12:05:48Z","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/2509.05462/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hasegawa showed that control flow in programming languages -- while loops and if-then-else statements -- can be modeled using traced cocartesian categories, such as the category $\\mathbf{Set}_*$ of pointed sets. In this paper we define an operad $\\mathscr{W}$ of wiring diagrams that provides syntax for categories whose control flow moreover includes data transformations, including deleting, duplicating, permuting, and applying pre-specified functions to variables. In the most basic version, the operad underlies $\\mathbf{Int}(\\mathbf{Poly}_*)$, where $\\mathbf{Int}(\\mathscr{T})$ denotes the free","authors_text":"David I. Spivak, Grigory Kondyrev","cross_cats":["cs.PL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-09-05T19:35:08Z","title":"The compact double category $\\mathbf{Int}(\\mathbf{Poly}_*)$ models control flow and data transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05462","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":"sha256:60acb0618730917d47455dd4e6b0fcd576cdd4f340d62dbf9ca0686570c08a8c","target":"record","created_at":"2026-07-05T12:05:48Z","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":"f251a85c3a1e9bfe37fdb416e66e191c0e18eccbd7734de1b070b2a0e3e60176","cross_cats_sorted":["cs.PL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-09-05T19:35:08Z","title_canon_sha256":"9ded6d3f4fcfeb1df92f0618b8a0318a0fd6b660e3440736f4b2425b385cdc32"},"schema_version":"1.0","source":{"id":"2509.05462","kind":"arxiv","version":1}},"canonical_sha256":"842d0f3767b8912f42a6b61cea9c3bbfb37ef5481df559c33ed26c0a75bab6df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842d0f3767b8912f42a6b61cea9c3bbfb37ef5481df559c33ed26c0a75bab6df","first_computed_at":"2026-07-05T12:05:48.134846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:48.134846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1veP60bG5J9plytzfMrhywICPAdr6K/duY09nDw+aQQ/Gsp3JUk9Ibuypx1lwVi32Bx3SWk+M/NhWOvf8myLBg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:48.135328Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60acb0618730917d47455dd4e6b0fcd576cdd4f340d62dbf9ca0686570c08a8c","sha256:be97521f7c50ddceb5421c29807bbf92804830bc1095556c6d7aadaaed65eefb"],"state_sha256":"4cc1335e5391686a9447ddd216ae40d89a16adadd5487620f9274b0eca40aa61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNm6PHLQvzePYmdM6ADSylOKV3YU3EOzw3Fl2jQUU/j0CaVkyXzzFG7z2CyWGgRoT1gagDfWol5U0gvRoYs+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:24:27.430081Z","bundle_sha256":"e596dcb5f1f6192e7eef073f9ee300dc2c1f95ff7f35a615f9069fb65b245406"}}