{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VQLI3GAK3APXYNXKNHCL44ESI4","short_pith_number":"pith:VQLI3GAK","canonical_record":{"source":{"id":"2403.18102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-26T21:01:39Z","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"title_canon_sha256":"fb3191963fbe8848b2709dedd9d40dd64717c6785e6231563cf0285f6026074c","abstract_canon_sha256":"50f9438eb9b3ecf058063c0b3ef590f834be2dc57468324486ad931e9ed1e4ab"},"schema_version":"1.0"},"canonical_sha256":"ac168d980ad81f7c36ea69c4be7092471fd976910ab60729376e2ba6c698ba5f","source":{"kind":"arxiv","id":"2403.18102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18102","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18102v1","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18102","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_12","alias_value":"VQLI3GAK3APX","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_16","alias_value":"VQLI3GAK3APXYNXK","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_8","alias_value":"VQLI3GAK","created_at":"2026-07-05T08:01:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VQLI3GAK3APXYNXKNHCL44ESI4","target":"record","payload":{"canonical_record":{"source":{"id":"2403.18102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-26T21:01:39Z","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"title_canon_sha256":"fb3191963fbe8848b2709dedd9d40dd64717c6785e6231563cf0285f6026074c","abstract_canon_sha256":"50f9438eb9b3ecf058063c0b3ef590f834be2dc57468324486ad931e9ed1e4ab"},"schema_version":"1.0"},"canonical_sha256":"ac168d980ad81f7c36ea69c4be7092471fd976910ab60729376e2ba6c698ba5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:01:04.810352Z","signature_b64":"CgIHsQfkpIjs59AxDqF/4Tri8S972Lp0lD/ZeTwDR1PXZSECV9ovYIBbZH6KtFaK6VYVvx3k5cKG8zH5/LfgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac168d980ad81f7c36ea69c4be7092471fd976910ab60729376e2ba6c698ba5f","last_reissued_at":"2026-07-05T08:01:04.809868Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:01:04.809868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.18102","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":"2026-07-05T08:01:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBzaiu38To6OufN5R8y2y9vJCG53MW46bAJc9xaymVnG6x/G2rpaPTgeXrnSuAZOc0PC9ahLm71/FB8joLFmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:33:42.134336Z"},"content_sha256":"0c3b66524234b206f7f6e9e1d6c2dc5dc363aa56d9a8c82d0bd105714be3e5f0","schema_version":"1.0","event_id":"sha256:0c3b66524234b206f7f6e9e1d6c2dc5dc363aa56d9a8c82d0bd105714be3e5f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VQLI3GAK3APXYNXKNHCL44ESI4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The operadic theory of convexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"math.CT","authors_text":"Cihan Okay, Redi Haderi, Walker H. Stern","submitted_at":"2024-03-26T21:01:39Z","abstract_excerpt":"In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\\scr{O}$-monoidal categories, we state and prove a Grothendieck construction for lax $\\scr{O}$-monoidal functors into convex sets. We apply this construction to the categorical characterization of entropy of Baez, Fritz, and Leinster, and to the study of quantum contextuality in the framework of simplicial distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18102","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/2403.18102/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":"2026-07-05T08:01:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7RsZ5d+KNwAlnnsAI/xR7A1F5wnNn/SnyBcwQyh4L1vkGdzybwwfRFS6R+D+yzDzWDof/5qPv+GATDGRa9sDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T11:33:42.135176Z"},"content_sha256":"00110e02fad6e3082f25c97fa7a9ed66356c89836396d21be2033382ca9a07df","schema_version":"1.0","event_id":"sha256:00110e02fad6e3082f25c97fa7a9ed66356c89836396d21be2033382ca9a07df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQLI3GAK3APXYNXKNHCL44ESI4/bundle.json","state_url":"https://pith.science/pith/VQLI3GAK3APXYNXKNHCL44ESI4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQLI3GAK3APXYNXKNHCL44ESI4/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":"2026-08-13T11:33:42Z","links":{"resolver":"https://pith.science/pith/VQLI3GAK3APXYNXKNHCL44ESI4","bundle":"https://pith.science/pith/VQLI3GAK3APXYNXKNHCL44ESI4/bundle.json","state":"https://pith.science/pith/VQLI3GAK3APXYNXKNHCL44ESI4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQLI3GAK3APXYNXKNHCL44ESI4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VQLI3GAK3APXYNXKNHCL44ESI4","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":"50f9438eb9b3ecf058063c0b3ef590f834be2dc57468324486ad931e9ed1e4ab","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-26T21:01:39Z","title_canon_sha256":"fb3191963fbe8848b2709dedd9d40dd64717c6785e6231563cf0285f6026074c"},"schema_version":"1.0","source":{"id":"2403.18102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18102","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18102v1","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18102","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_12","alias_value":"VQLI3GAK3APX","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_16","alias_value":"VQLI3GAK3APXYNXK","created_at":"2026-07-05T08:01:04Z"},{"alias_kind":"pith_short_8","alias_value":"VQLI3GAK","created_at":"2026-07-05T08:01:04Z"}],"graph_snapshots":[{"event_id":"sha256:00110e02fad6e3082f25c97fa7a9ed66356c89836396d21be2033382ca9a07df","target":"graph","created_at":"2026-07-05T08:01:04Z","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/2403.18102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\\scr{O}$-monoidal categories, we state and prove a Grothendieck construction for lax $\\scr{O}$-monoidal functors into convex sets. We apply this construction to the categorical characterization of entropy of Baez, Fritz, and Leinster, and to the study of quantum contextuality in the framework of simplicial distributions.","authors_text":"Cihan Okay, Redi Haderi, Walker H. Stern","cross_cats":["cs.IT","math.IT","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-26T21:01:39Z","title":"The operadic theory of convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18102","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":"sha256:0c3b66524234b206f7f6e9e1d6c2dc5dc363aa56d9a8c82d0bd105714be3e5f0","target":"record","created_at":"2026-07-05T08:01:04Z","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":"50f9438eb9b3ecf058063c0b3ef590f834be2dc57468324486ad931e9ed1e4ab","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-03-26T21:01:39Z","title_canon_sha256":"fb3191963fbe8848b2709dedd9d40dd64717c6785e6231563cf0285f6026074c"},"schema_version":"1.0","source":{"id":"2403.18102","kind":"arxiv","version":1}},"canonical_sha256":"ac168d980ad81f7c36ea69c4be7092471fd976910ab60729376e2ba6c698ba5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac168d980ad81f7c36ea69c4be7092471fd976910ab60729376e2ba6c698ba5f","first_computed_at":"2026-07-05T08:01:04.809868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:01:04.809868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CgIHsQfkpIjs59AxDqF/4Tri8S972Lp0lD/ZeTwDR1PXZSECV9ovYIBbZH6KtFaK6VYVvx3k5cKG8zH5/LfgBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:01:04.810352Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.18102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c3b66524234b206f7f6e9e1d6c2dc5dc363aa56d9a8c82d0bd105714be3e5f0","sha256:00110e02fad6e3082f25c97fa7a9ed66356c89836396d21be2033382ca9a07df"],"state_sha256":"99ebf0c7599d0ee847756cdf178b82b410e720e888008c1fbbb7886264500a6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wocox20Lpea+KCMwWqkwnwOh6FBHzq0ymB/9pzb7js6VEOSHuN3BC5MJhgXLOSasUEhiclokgbEhyvV+5lKABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T11:33:42.145726Z","bundle_sha256":"36e700a365e980ad70e163a4af0bdf511e33f7cd62aa13e859c4ed730aef147b"}}