{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5SBHME46EBHTIPICTYA7ZNZMAH","short_pith_number":"pith:5SBHME46","canonical_record":{"source":{"id":"2404.10653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2024-04-16T15:30:20Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"364d4c85265094266f5e36cd983bd01183abb3a32847c34957183b8ffee71c9a","abstract_canon_sha256":"49ac954a4eb670d1337605280ee3b863eb7ee2d4cd2e7be993fe6b7d686f8614"},"schema_version":"1.0"},"canonical_sha256":"ec8276139e204f343d029e01fcb72c01eedd2139daa63d5521b921643ab274c5","source":{"kind":"arxiv","id":"2404.10653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.10653","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2404.10653v1","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.10653","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"5SBHME46EBHT","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"5SBHME46EBHTIPIC","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"5SBHME46","created_at":"2026-07-05T08:08:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5SBHME46EBHTIPICTYA7ZNZMAH","target":"record","payload":{"canonical_record":{"source":{"id":"2404.10653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2024-04-16T15:30:20Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"364d4c85265094266f5e36cd983bd01183abb3a32847c34957183b8ffee71c9a","abstract_canon_sha256":"49ac954a4eb670d1337605280ee3b863eb7ee2d4cd2e7be993fe6b7d686f8614"},"schema_version":"1.0"},"canonical_sha256":"ec8276139e204f343d029e01fcb72c01eedd2139daa63d5521b921643ab274c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:08:43.197225Z","signature_b64":"hb0YDX4JjSYdvasJdIB3jop6CYwhYMPJr0lxjTScgtkwW4W64eDCizMh8O9Ke9cAvHQ7h9m6lBkwIzTv4JxSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec8276139e204f343d029e01fcb72c01eedd2139daa63d5521b921643ab274c5","last_reissued_at":"2026-07-05T08:08:43.196773Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:08:43.196773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.10653","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":"2026-07-05T08:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ag0w2cKwYpS69QIuITeWkvS18SQXsCdGypiM5cMeggU4Pm7hxhutR5bvMMzui2aYzcMx/3jREVIFVNdkBaQCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:27:53.365012Z"},"content_sha256":"90c854490734a6b64a7bdf8cd72ad074330560216bc51943b358b7bd55b7c25e","schema_version":"1.0","event_id":"sha256:90c854490734a6b64a7bdf8cd72ad074330560216bc51943b358b7bd55b7c25e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5SBHME46EBHTIPICTYA7ZNZMAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Context-Free Languages of String Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.FL","authors_text":"Mario Rom\\'an, Matt Earnshaw","submitted_at":"2024-04-16T15:30:20Z","abstract_excerpt":"We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include classical context-free languages of words, trees, and hypergraphs, when instantiated over appropriate monoidal categories. Using a contour-splicing adjunction, we prove a representation theorem for context-free languages of string diagrams: every such language arises as the image under a monoidal functor of a regular language of string diagrams."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.10653","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/2404.10653/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":"2026-07-05T08:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kehTBsm8a0b9yCwT8mIg4bWIQQB/9Glk+pqB1FjMeVk/LPU9nxlv6JRY+Yt2BxhIw2gp74yciy5jH+yOhcgBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:27:53.365561Z"},"content_sha256":"655cc1388d117ed40613bee8f88f365aefb03996d2e5d2567814f5120ad218ea","schema_version":"1.0","event_id":"sha256:655cc1388d117ed40613bee8f88f365aefb03996d2e5d2567814f5120ad218ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SBHME46EBHTIPICTYA7ZNZMAH/bundle.json","state_url":"https://pith.science/pith/5SBHME46EBHTIPICTYA7ZNZMAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SBHME46EBHTIPICTYA7ZNZMAH/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":"2026-08-05T04:27:53Z","links":{"resolver":"https://pith.science/pith/5SBHME46EBHTIPICTYA7ZNZMAH","bundle":"https://pith.science/pith/5SBHME46EBHTIPICTYA7ZNZMAH/bundle.json","state":"https://pith.science/pith/5SBHME46EBHTIPICTYA7ZNZMAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SBHME46EBHTIPICTYA7ZNZMAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5SBHME46EBHTIPICTYA7ZNZMAH","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":"49ac954a4eb670d1337605280ee3b863eb7ee2d4cd2e7be993fe6b7d686f8614","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2024-04-16T15:30:20Z","title_canon_sha256":"364d4c85265094266f5e36cd983bd01183abb3a32847c34957183b8ffee71c9a"},"schema_version":"1.0","source":{"id":"2404.10653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.10653","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2404.10653v1","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.10653","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"5SBHME46EBHT","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"5SBHME46EBHTIPIC","created_at":"2026-07-05T08:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"5SBHME46","created_at":"2026-07-05T08:08:43Z"}],"graph_snapshots":[{"event_id":"sha256:655cc1388d117ed40613bee8f88f365aefb03996d2e5d2567814f5120ad218ea","target":"graph","created_at":"2026-07-05T08:08:43Z","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/2404.10653/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include classical context-free languages of words, trees, and hypergraphs, when instantiated over appropriate monoidal categories. Using a contour-splicing adjunction, we prove a representation theorem for context-free languages of string diagrams: every such language arises as the image under a monoidal functor of a regular language of string diagrams.","authors_text":"Mario Rom\\'an, Matt Earnshaw","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2024-04-16T15:30:20Z","title":"Context-Free Languages of String Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.10653","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":"sha256:90c854490734a6b64a7bdf8cd72ad074330560216bc51943b358b7bd55b7c25e","target":"record","created_at":"2026-07-05T08:08:43Z","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":"49ac954a4eb670d1337605280ee3b863eb7ee2d4cd2e7be993fe6b7d686f8614","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2024-04-16T15:30:20Z","title_canon_sha256":"364d4c85265094266f5e36cd983bd01183abb3a32847c34957183b8ffee71c9a"},"schema_version":"1.0","source":{"id":"2404.10653","kind":"arxiv","version":1}},"canonical_sha256":"ec8276139e204f343d029e01fcb72c01eedd2139daa63d5521b921643ab274c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec8276139e204f343d029e01fcb72c01eedd2139daa63d5521b921643ab274c5","first_computed_at":"2026-07-05T08:08:43.196773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:08:43.196773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hb0YDX4JjSYdvasJdIB3jop6CYwhYMPJr0lxjTScgtkwW4W64eDCizMh8O9Ke9cAvHQ7h9m6lBkwIzTv4JxSDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:08:43.197225Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.10653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90c854490734a6b64a7bdf8cd72ad074330560216bc51943b358b7bd55b7c25e","sha256:655cc1388d117ed40613bee8f88f365aefb03996d2e5d2567814f5120ad218ea"],"state_sha256":"ca3c75fbd71d8bb097efa2c4d4da916488848901fcab73e0e7cea1c0ebe99689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AfVVWikRrqHTFbEgWhchcM0mGQUC3Kl6d7ts/+aANDiEQlbPRwD+2+uLSf+wkUEa+rSbjzgnGmMKC2T/CHDjAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:27:53.370463Z","bundle_sha256":"e25e4b02cd7b3bcbf13cc45c4ca8129c941bcbd67241a8ef9dc6eaf11b4d4a10"}}