{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WWNX55OBA5V66LBXCT54SJ5CP3","short_pith_number":"pith:WWNX55OB","canonical_record":{"source":{"id":"1806.06082","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-06-15T18:05:47Z","cross_cats_sorted":[],"title_canon_sha256":"3dd61858117824a83f9627f1b3058f583e66164a78f53d17cac40fe07ace3e0b","abstract_canon_sha256":"dd9a6bb508eb0916447b73b8b6390cc8e4e9cdb960ab12506df76a376989beed"},"schema_version":"1.0"},"canonical_sha256":"b59b7ef5c1076bef2c3714fbc927a27efb8c06a127623ed36546394ff744f754","source":{"kind":"arxiv","id":"1806.06082","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06082","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06082v2","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06082","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_12","alias_value":"WWNX55OBA5V6","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_16","alias_value":"WWNX55OBA5V66LBX","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_8","alias_value":"WWNX55OB","created_at":"2026-07-05T00:42:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WWNX55OBA5V66LBXCT54SJ5CP3","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06082","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-06-15T18:05:47Z","cross_cats_sorted":[],"title_canon_sha256":"3dd61858117824a83f9627f1b3058f583e66164a78f53d17cac40fe07ace3e0b","abstract_canon_sha256":"dd9a6bb508eb0916447b73b8b6390cc8e4e9cdb960ab12506df76a376989beed"},"schema_version":"1.0"},"canonical_sha256":"b59b7ef5c1076bef2c3714fbc927a27efb8c06a127623ed36546394ff744f754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:42:41.772874Z","signature_b64":"K265FvzrWudbl+D4o4vVBz1BsbLFd29MRT+gUg27SvMWTazY4jVsGOd7+SVgafk2xEB7mheVjazwzJeNVLNYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59b7ef5c1076bef2c3714fbc927a27efb8c06a127623ed36546394ff744f754","last_reissued_at":"2026-07-05T00:42:41.772402Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:42:41.772402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06082","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:42:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGTI+UoO/tcf868TxlFpw8oVhkXYra6wFwi3dmZoeDZCPKw2oBcVzxMKOj+hkpx/guSlTWMtoL3aMlUxU3/lAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:53:04.439164Z"},"content_sha256":"d48b3d4d7b7ecbc6e9c1ebdedc61f7e046f862c27905b3b219c5e2f93e219740","schema_version":"1.0","event_id":"sha256:d48b3d4d7b7ecbc6e9c1ebdedc61f7e046f862c27905b3b219c5e2f93e219740"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WWNX55OBA5V66LBXCT54SJ5CP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Michael Shulman","submitted_at":"2018-06-15T18:05:47Z","abstract_excerpt":"Cheng, Gurski, and Riehl constructed a cyclic double multicategory of multivariable adjunctions. We show that the same information is carried by a double polycategory, in which opposite categories are polycategorical duals. Moreover, this double polycategory is a full substructure of a double Chu construction, whose objects are a sort of polarized category, and which is a natural home for 2-categorical dualities.\n  We obtain the double Chu construction using a general \"Chu-Dialectica\" construction on polycategories, which includes both the Chu construction and the categorical Dialectica constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06082","kind":"arxiv","version":2},"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/1806.06082/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":"2026-07-05T00:42:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOrvDbPqGxHWvfX65A1woDg2xkfL5CKk0WKRLfjasOo48n0+36FKTbB6ggOzujn6+paCN6Ap8gfJiYwIlEUjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:53:04.439633Z"},"content_sha256":"572bda45dd9f90bf289588a229d3bc28176e49be3fc29dc5e3ec8619a1c938f1","schema_version":"1.0","event_id":"sha256:572bda45dd9f90bf289588a229d3bc28176e49be3fc29dc5e3ec8619a1c938f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWNX55OBA5V66LBXCT54SJ5CP3/bundle.json","state_url":"https://pith.science/pith/WWNX55OBA5V66LBXCT54SJ5CP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWNX55OBA5V66LBXCT54SJ5CP3/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":"2026-07-05T11:53:04Z","links":{"resolver":"https://pith.science/pith/WWNX55OBA5V66LBXCT54SJ5CP3","bundle":"https://pith.science/pith/WWNX55OBA5V66LBXCT54SJ5CP3/bundle.json","state":"https://pith.science/pith/WWNX55OBA5V66LBXCT54SJ5CP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWNX55OBA5V66LBXCT54SJ5CP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WWNX55OBA5V66LBXCT54SJ5CP3","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":"dd9a6bb508eb0916447b73b8b6390cc8e4e9cdb960ab12506df76a376989beed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-06-15T18:05:47Z","title_canon_sha256":"3dd61858117824a83f9627f1b3058f583e66164a78f53d17cac40fe07ace3e0b"},"schema_version":"1.0","source":{"id":"1806.06082","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06082","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06082v2","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06082","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_12","alias_value":"WWNX55OBA5V6","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_16","alias_value":"WWNX55OBA5V66LBX","created_at":"2026-07-05T00:42:41Z"},{"alias_kind":"pith_short_8","alias_value":"WWNX55OB","created_at":"2026-07-05T00:42:41Z"}],"graph_snapshots":[{"event_id":"sha256:572bda45dd9f90bf289588a229d3bc28176e49be3fc29dc5e3ec8619a1c938f1","target":"graph","created_at":"2026-07-05T00:42:41Z","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/1806.06082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Cheng, Gurski, and Riehl constructed a cyclic double multicategory of multivariable adjunctions. We show that the same information is carried by a double polycategory, in which opposite categories are polycategorical duals. Moreover, this double polycategory is a full substructure of a double Chu construction, whose objects are a sort of polarized category, and which is a natural home for 2-categorical dualities.\n  We obtain the double Chu construction using a general \"Chu-Dialectica\" construction on polycategories, which includes both the Chu construction and the categorical Dialectica constr","authors_text":"Michael Shulman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-06-15T18:05:47Z","title":"The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06082","kind":"arxiv","version":2},"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:d48b3d4d7b7ecbc6e9c1ebdedc61f7e046f862c27905b3b219c5e2f93e219740","target":"record","created_at":"2026-07-05T00:42:41Z","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":"dd9a6bb508eb0916447b73b8b6390cc8e4e9cdb960ab12506df76a376989beed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2018-06-15T18:05:47Z","title_canon_sha256":"3dd61858117824a83f9627f1b3058f583e66164a78f53d17cac40fe07ace3e0b"},"schema_version":"1.0","source":{"id":"1806.06082","kind":"arxiv","version":2}},"canonical_sha256":"b59b7ef5c1076bef2c3714fbc927a27efb8c06a127623ed36546394ff744f754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b59b7ef5c1076bef2c3714fbc927a27efb8c06a127623ed36546394ff744f754","first_computed_at":"2026-07-05T00:42:41.772402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:41.772402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K265FvzrWudbl+D4o4vVBz1BsbLFd29MRT+gUg27SvMWTazY4jVsGOd7+SVgafk2xEB7mheVjazwzJeNVLNYCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:41.772874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06082","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d48b3d4d7b7ecbc6e9c1ebdedc61f7e046f862c27905b3b219c5e2f93e219740","sha256:572bda45dd9f90bf289588a229d3bc28176e49be3fc29dc5e3ec8619a1c938f1"],"state_sha256":"015995e0ec750ce617c373099edf62cb12bb0aba7ef169a6c75bc40c09693130"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRerP6R6oQ9CuWr+tmuBUwb8thf+ihqO5ieeyJA7jt9rNOe1B09PWVMCzZbbWXRAuBCD836fIaIVD/2cIEpgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:53:04.442467Z","bundle_sha256":"2ca98679b71d353669bf1945dd31a20cdde5797f6545188ee3be88416f6bb7f4"}}