{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:K5EVLZBPL2LZGLVSAQWSL2H77V","short_pith_number":"pith:K5EVLZBP","canonical_record":{"source":{"id":"2301.04690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-10-13T14:55:17Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"99a3a070089b2bcdb06b1dd6ad1564ff11a37fc57f38ac034da3e351649ca659","abstract_canon_sha256":"05b7c32fc036396bac81b0d325c008c0b7841fe51640a99f4ffa13c789abed29"},"schema_version":"1.0"},"canonical_sha256":"574955e42f5e97932eb2042d25e8fffd6fe975b8c3842c635d5083258e4656d1","source":{"kind":"arxiv","id":"2301.04690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04690","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04690v1","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04690","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"K5EVLZBPL2LZ","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_16","alias_value":"K5EVLZBPL2LZGLVS","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_8","alias_value":"K5EVLZBP","created_at":"2026-07-05T05:32:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:K5EVLZBPL2LZGLVSAQWSL2H77V","target":"record","payload":{"canonical_record":{"source":{"id":"2301.04690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-10-13T14:55:17Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"99a3a070089b2bcdb06b1dd6ad1564ff11a37fc57f38ac034da3e351649ca659","abstract_canon_sha256":"05b7c32fc036396bac81b0d325c008c0b7841fe51640a99f4ffa13c789abed29"},"schema_version":"1.0"},"canonical_sha256":"574955e42f5e97932eb2042d25e8fffd6fe975b8c3842c635d5083258e4656d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:32:34.892862Z","signature_b64":"42LZGnRWDHRgzb5vawLe6Bnik/G0YdtuSc99TDjbBIZCJlkPr1L4cm+aoRdUXRxK9D7svm8Dn5SY5/v6CWLqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"574955e42f5e97932eb2042d25e8fffd6fe975b8c3842c635d5083258e4656d1","last_reissued_at":"2026-07-05T05:32:34.892453Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:32:34.892453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.04690","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":"2026-07-05T05:32:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZMj4ie89XDy4rlSoOtdF1lgsVe+pe8ee+LFzdKCaqQZ2WUNlz0ROf3Qx9Se2NY26ZYUBzvev4Rz8TWOTD4sDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:49:53.547896Z"},"content_sha256":"bc45d4314e526e1b9db6df24b38ddcb54f8b6a82de088ea54915462e8710c7de","schema_version":"1.0","event_id":"sha256:bc45d4314e526e1b9db6df24b38ddcb54f8b6a82de088ea54915462e8710c7de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:K5EVLZBPL2LZGLVSAQWSL2H77V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Functorial Perspective on (Multi)computational Irreducibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Jonathan Gorard","submitted_at":"2022-10-13T14:55:17Z","abstract_excerpt":"This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding category of (1-dimensional) cobordisms. We proceed to demonstrate that, by equipping both categories with a symmetric monoidal structure and considering the case of higher-dimensional cobordism categories, we obtain a natural extension of this formalism that serves also to encompass non-deterministic or ``multiway'' computations, in which one quantifies not o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04690","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/2301.04690/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":"2026-07-05T05:32:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"abBYuWNAKM25fBR+uUk+51xiAXvX0TSygdCRu5QMmiccGi34bA9lm5auPCr2PpDDo20fFQm5o2Ou9vrp6embAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:49:53.548265Z"},"content_sha256":"16322988ea3aed881bffb571013dbdd8308b0c8febbe284486ff5132649aa50c","schema_version":"1.0","event_id":"sha256:16322988ea3aed881bffb571013dbdd8308b0c8febbe284486ff5132649aa50c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/bundle.json","state_url":"https://pith.science/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/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":"2026-07-06T15:49:53Z","links":{"resolver":"https://pith.science/pith/K5EVLZBPL2LZGLVSAQWSL2H77V","bundle":"https://pith.science/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/bundle.json","state":"https://pith.science/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5EVLZBPL2LZGLVSAQWSL2H77V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:K5EVLZBPL2LZGLVSAQWSL2H77V","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":"05b7c32fc036396bac81b0d325c008c0b7841fe51640a99f4ffa13c789abed29","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-10-13T14:55:17Z","title_canon_sha256":"99a3a070089b2bcdb06b1dd6ad1564ff11a37fc57f38ac034da3e351649ca659"},"schema_version":"1.0","source":{"id":"2301.04690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04690","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04690v1","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04690","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"K5EVLZBPL2LZ","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_16","alias_value":"K5EVLZBPL2LZGLVS","created_at":"2026-07-05T05:32:34Z"},{"alias_kind":"pith_short_8","alias_value":"K5EVLZBP","created_at":"2026-07-05T05:32:34Z"}],"graph_snapshots":[{"event_id":"sha256:16322988ea3aed881bffb571013dbdd8308b0c8febbe284486ff5132649aa50c","target":"graph","created_at":"2026-07-05T05:32:34Z","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/2301.04690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding category of (1-dimensional) cobordisms. We proceed to demonstrate that, by equipping both categories with a symmetric monoidal structure and considering the case of higher-dimensional cobordism categories, we obtain a natural extension of this formalism that serves also to encompass non-deterministic or ``multiway'' computations, in which one quantifies not o","authors_text":"Jonathan Gorard","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-10-13T14:55:17Z","title":"A Functorial Perspective on (Multi)computational Irreducibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04690","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:bc45d4314e526e1b9db6df24b38ddcb54f8b6a82de088ea54915462e8710c7de","target":"record","created_at":"2026-07-05T05:32:34Z","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":"05b7c32fc036396bac81b0d325c008c0b7841fe51640a99f4ffa13c789abed29","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-10-13T14:55:17Z","title_canon_sha256":"99a3a070089b2bcdb06b1dd6ad1564ff11a37fc57f38ac034da3e351649ca659"},"schema_version":"1.0","source":{"id":"2301.04690","kind":"arxiv","version":1}},"canonical_sha256":"574955e42f5e97932eb2042d25e8fffd6fe975b8c3842c635d5083258e4656d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"574955e42f5e97932eb2042d25e8fffd6fe975b8c3842c635d5083258e4656d1","first_computed_at":"2026-07-05T05:32:34.892453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:32:34.892453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42LZGnRWDHRgzb5vawLe6Bnik/G0YdtuSc99TDjbBIZCJlkPr1L4cm+aoRdUXRxK9D7svm8Dn5SY5/v6CWLqBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:32:34.892862Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.04690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc45d4314e526e1b9db6df24b38ddcb54f8b6a82de088ea54915462e8710c7de","sha256:16322988ea3aed881bffb571013dbdd8308b0c8febbe284486ff5132649aa50c"],"state_sha256":"25f253a8a4e9751e7cae27990de2bd1d4cbec176e66bd7ede1a7c2863d9c7dc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tkqt4mxX2/BlESRitIzYIO4WUIeen7PqeMzMCU6LWhKRmWZNNk8/B/9iG+SvTmUI3WlwXVwnFP0kjE2K3+1IDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:49:53.550250Z","bundle_sha256":"ad4d9089c1d5eb4ee3ae456c490abee7bfeb18ea436727569076bb020e25435a"}}