{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DMO4YNQ6PED5N7GF6DIQSNJCLV","short_pith_number":"pith:DMO4YNQ6","canonical_record":{"source":{"id":"2606.09687","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T16:05:03Z","cross_cats_sorted":[],"title_canon_sha256":"1ffefec43c85336a19b46dd40dbcdfd6edc00c8ead8c557d2548207c0fe51681","abstract_canon_sha256":"48c4dd5b6c6cf58288c4263617fedfac12543a2045fb627eee2b22ea6494d20f"},"schema_version":"1.0"},"canonical_sha256":"1b1dcc361e7907d6fcc5f0d10935225d45998489370f7cc1549686f1f84b5b9f","source":{"kind":"arxiv","id":"2606.09687","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09687","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09687v1","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09687","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"DMO4YNQ6PED5","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_16","alias_value":"DMO4YNQ6PED5N7GF","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_8","alias_value":"DMO4YNQ6","created_at":"2026-06-09T02:09:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DMO4YNQ6PED5N7GF6DIQSNJCLV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09687","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T16:05:03Z","cross_cats_sorted":[],"title_canon_sha256":"1ffefec43c85336a19b46dd40dbcdfd6edc00c8ead8c557d2548207c0fe51681","abstract_canon_sha256":"48c4dd5b6c6cf58288c4263617fedfac12543a2045fb627eee2b22ea6494d20f"},"schema_version":"1.0"},"canonical_sha256":"1b1dcc361e7907d6fcc5f0d10935225d45998489370f7cc1549686f1f84b5b9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:03.937498Z","signature_b64":"K9RA/0MftNT6Zo0qZqG5/l5z163/vmp2drUFFD+wZJJFB80g/n6D70UopDmQo9TV1SP8ZiCVmkXoom0bUUI6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b1dcc361e7907d6fcc5f0d10935225d45998489370f7cc1549686f1f84b5b9f","last_reissued_at":"2026-06-09T02:09:03.936667Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:03.936667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09687","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":"2026-06-09T02:09:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SemYDwV3u5iquapgI1/4x4Axfmp2L8V3sDVxgKJXKPIve9XSc/s+ECwYnqXYO8Patu1DUnuceCgw7c51Sgz9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:05:40.639077Z"},"content_sha256":"69f82871a796bda564f4f052ac08e4b1c62bf540cac82d9cdbb05d86e34efd10","schema_version":"1.0","event_id":"sha256:69f82871a796bda564f4f052ac08e4b1c62bf540cac82d9cdbb05d86e34efd10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DMO4YNQ6PED5N7GF6DIQSNJCLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Codifferential Calculi on Quantum Homogeneous Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Julius Benner","submitted_at":"2026-06-08T16:05:03Z","abstract_excerpt":"We develop the theory of first- and higher-order codifferential calculi over coalgebras $C$ over fields $k$ with characteristic $\\mathrm{char}(k)\\neq 2$. For a given first-order codifferential calculus, we introduce its maximal prolongation by means of an explicit construction that associates to it a differential graded coalgebra, satisfying a universal property. For module coalgebras over a Hopf algebra $U$, we introduce the notion of an equivariant codifferential calculus. If $C$ is of the form $U\\otimes_H k$ for a Hopf algebra $U$ and a right coideal subalgebra $H$ such that $U$ is faithful"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09687","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/2606.09687/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":"2026-06-09T02:09:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRBa/NpTmy1dcmq2H5jFbGdVrPFXDzeCUxnjWqBB3rbSxIFJLzGe5qyAE7W7D6I0kRfsvB6YL2x1dapXjB2nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:05:40.639464Z"},"content_sha256":"e1e81ae70aef0e31bfd31d56e2dba3d79d5debd565a93f79a1f216b00960f11f","schema_version":"1.0","event_id":"sha256:e1e81ae70aef0e31bfd31d56e2dba3d79d5debd565a93f79a1f216b00960f11f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/bundle.json","state_url":"https://pith.science/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/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":"2026-07-07T11:05:40Z","links":{"resolver":"https://pith.science/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV","bundle":"https://pith.science/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/bundle.json","state":"https://pith.science/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMO4YNQ6PED5N7GF6DIQSNJCLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DMO4YNQ6PED5N7GF6DIQSNJCLV","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":"48c4dd5b6c6cf58288c4263617fedfac12543a2045fb627eee2b22ea6494d20f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T16:05:03Z","title_canon_sha256":"1ffefec43c85336a19b46dd40dbcdfd6edc00c8ead8c557d2548207c0fe51681"},"schema_version":"1.0","source":{"id":"2606.09687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09687","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09687v1","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09687","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"DMO4YNQ6PED5","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_16","alias_value":"DMO4YNQ6PED5N7GF","created_at":"2026-06-09T02:09:03Z"},{"alias_kind":"pith_short_8","alias_value":"DMO4YNQ6","created_at":"2026-06-09T02:09:03Z"}],"graph_snapshots":[{"event_id":"sha256:e1e81ae70aef0e31bfd31d56e2dba3d79d5debd565a93f79a1f216b00960f11f","target":"graph","created_at":"2026-06-09T02:09:03Z","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/2606.09687/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the theory of first- and higher-order codifferential calculi over coalgebras $C$ over fields $k$ with characteristic $\\mathrm{char}(k)\\neq 2$. For a given first-order codifferential calculus, we introduce its maximal prolongation by means of an explicit construction that associates to it a differential graded coalgebra, satisfying a universal property. For module coalgebras over a Hopf algebra $U$, we introduce the notion of an equivariant codifferential calculus. If $C$ is of the form $U\\otimes_H k$ for a Hopf algebra $U$ and a right coideal subalgebra $H$ such that $U$ is faithful","authors_text":"Julius Benner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T16:05:03Z","title":"Codifferential Calculi on Quantum Homogeneous Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09687","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":"sha256:69f82871a796bda564f4f052ac08e4b1c62bf540cac82d9cdbb05d86e34efd10","target":"record","created_at":"2026-06-09T02:09:03Z","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":"48c4dd5b6c6cf58288c4263617fedfac12543a2045fb627eee2b22ea6494d20f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-06-08T16:05:03Z","title_canon_sha256":"1ffefec43c85336a19b46dd40dbcdfd6edc00c8ead8c557d2548207c0fe51681"},"schema_version":"1.0","source":{"id":"2606.09687","kind":"arxiv","version":1}},"canonical_sha256":"1b1dcc361e7907d6fcc5f0d10935225d45998489370f7cc1549686f1f84b5b9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b1dcc361e7907d6fcc5f0d10935225d45998489370f7cc1549686f1f84b5b9f","first_computed_at":"2026-06-09T02:09:03.936667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:09:03.936667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K9RA/0MftNT6Zo0qZqG5/l5z163/vmp2drUFFD+wZJJFB80g/n6D70UopDmQo9TV1SP8ZiCVmkXoom0bUUI6DQ==","signature_status":"signed_v1","signed_at":"2026-06-09T02:09:03.937498Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69f82871a796bda564f4f052ac08e4b1c62bf540cac82d9cdbb05d86e34efd10","sha256:e1e81ae70aef0e31bfd31d56e2dba3d79d5debd565a93f79a1f216b00960f11f"],"state_sha256":"6057dfe619214e5c45d5617011c7554210f0e979a266d9eeaeea35e9244d516f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHlq95mDetDd/nmyEL5Ujgvf3bFBXT8jx0QtHkxBlVM6VTsMACVzkoA+6f8y6Klwhfhk9s1y9CwgC3d+kcvQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:05:40.641504Z","bundle_sha256":"862cd486de8b9112b3027f894ad4947f100ef31dd2c42cace564ad8fd98b914d"}}