{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QRZQIWKGZOOXFQYTSSSAWEFUV3","short_pith_number":"pith:QRZQIWKG","canonical_record":{"source":{"id":"2506.07867","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-09T15:34:30Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"d88f15033971183488ff6f4594a96418f8d4e3bf93d0becc596500b4ff8be1e0","abstract_canon_sha256":"0e56b7211bc01e5aa70c25a70e9b861bbd32c806191b794cac6945a1dc6a60bc"},"schema_version":"1.0"},"canonical_sha256":"8473045946cb9d72c31394a40b10b4aee4cc6692244713f2b53d47a4730bc8f9","source":{"kind":"arxiv","id":"2506.07867","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07867","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07867v2","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07867","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"QRZQIWKGZOOX","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_16","alias_value":"QRZQIWKGZOOXFQYT","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_8","alias_value":"QRZQIWKG","created_at":"2026-07-05T11:19:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QRZQIWKGZOOXFQYTSSSAWEFUV3","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07867","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-09T15:34:30Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"d88f15033971183488ff6f4594a96418f8d4e3bf93d0becc596500b4ff8be1e0","abstract_canon_sha256":"0e56b7211bc01e5aa70c25a70e9b861bbd32c806191b794cac6945a1dc6a60bc"},"schema_version":"1.0"},"canonical_sha256":"8473045946cb9d72c31394a40b10b4aee4cc6692244713f2b53d47a4730bc8f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:08.407450Z","signature_b64":"ozyjFRafQX7RsW/S3EN3eXRd1No+XW4huIJoSQD6Cc+XPWZF1m7vr5BEO+IlOupSS8RgSN/IqP7e7+evstA2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8473045946cb9d72c31394a40b10b4aee4cc6692244713f2b53d47a4730bc8f9","last_reissued_at":"2026-07-05T11:19:08.406972Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:08.406972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07867","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":"2026-07-05T11:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMraiIDpiG2EDAdcoDYbDZcwkxla3iHDqAWP4UUdeeHE9Rv4A9gnZFhjQ+hLtkN9Z6Eh9WbPOY3sxPzigXEhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:18:39.898842Z"},"content_sha256":"64c1da0ca9058d83612b87c1fc07fbb46c4015f08ed7dba9b1f85096e285c51a","schema_version":"1.0","event_id":"sha256:64c1da0ca9058d83612b87c1fc07fbb46c4015f08ed7dba9b1f85096e285c51a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QRZQIWKGZOOXFQYTSSSAWEFUV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant $K$-theory of cellular toroidal embeddings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Alexis Tchoudjem, V. Uma","submitted_at":"2025-06-09T15:34:30Z","abstract_excerpt":"In this article we describe the\n  $G_{comp}\\times G_{comp}$-equivariant topological $K$-ring of a {\\em\n  cellular} toroidal embedding $\\mathbb{X}$ of a complex connected\n  reductive algebraic group $G$. In particular, our results extend the\n  results in \\cite{u1} and \\cite{u2} on the regular embeddings of $G$,\n  to the equivariant topological $K$-ring of a larger class of\n  (possibly singular) cellular toroidal embeddings. They are also a\n  topological analogue of the results in \\cite{gon} on the operational\n  equivariant algebraic $K$-ring, for cellular toroidal\n  embeddings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07867","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/2506.07867/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":"2026-07-05T11:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZfy5CRCZ/4pELNfxj1qcqaU9eO7E1Ozlic/ESdT1FxjInYu0K2+Gez7axP95GOhmaPfc2/pJ9gRxgvskjSrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:18:39.899336Z"},"content_sha256":"b59df0b2973614c59e45ea20d5d6d3eaf3de27d2618065c97b9180f559e4f8b6","schema_version":"1.0","event_id":"sha256:b59df0b2973614c59e45ea20d5d6d3eaf3de27d2618065c97b9180f559e4f8b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/bundle.json","state_url":"https://pith.science/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/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":"2026-08-10T04:18:39Z","links":{"resolver":"https://pith.science/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3","bundle":"https://pith.science/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/bundle.json","state":"https://pith.science/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QRZQIWKGZOOXFQYTSSSAWEFUV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QRZQIWKGZOOXFQYTSSSAWEFUV3","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":"0e56b7211bc01e5aa70c25a70e9b861bbd32c806191b794cac6945a1dc6a60bc","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-09T15:34:30Z","title_canon_sha256":"d88f15033971183488ff6f4594a96418f8d4e3bf93d0becc596500b4ff8be1e0"},"schema_version":"1.0","source":{"id":"2506.07867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07867","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07867v2","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07867","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"QRZQIWKGZOOX","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_16","alias_value":"QRZQIWKGZOOXFQYT","created_at":"2026-07-05T11:19:08Z"},{"alias_kind":"pith_short_8","alias_value":"QRZQIWKG","created_at":"2026-07-05T11:19:08Z"}],"graph_snapshots":[{"event_id":"sha256:b59df0b2973614c59e45ea20d5d6d3eaf3de27d2618065c97b9180f559e4f8b6","target":"graph","created_at":"2026-07-05T11:19:08Z","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/2506.07867/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we describe the\n  $G_{comp}\\times G_{comp}$-equivariant topological $K$-ring of a {\\em\n  cellular} toroidal embedding $\\mathbb{X}$ of a complex connected\n  reductive algebraic group $G$. In particular, our results extend the\n  results in \\cite{u1} and \\cite{u2} on the regular embeddings of $G$,\n  to the equivariant topological $K$-ring of a larger class of\n  (possibly singular) cellular toroidal embeddings. They are also a\n  topological analogue of the results in \\cite{gon} on the operational\n  equivariant algebraic $K$-ring, for cellular toroidal\n  embeddings.","authors_text":"Alexis Tchoudjem, V. Uma","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-09T15:34:30Z","title":"Equivariant $K$-theory of cellular toroidal embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07867","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":"sha256:64c1da0ca9058d83612b87c1fc07fbb46c4015f08ed7dba9b1f85096e285c51a","target":"record","created_at":"2026-07-05T11:19:08Z","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":"0e56b7211bc01e5aa70c25a70e9b861bbd32c806191b794cac6945a1dc6a60bc","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-09T15:34:30Z","title_canon_sha256":"d88f15033971183488ff6f4594a96418f8d4e3bf93d0becc596500b4ff8be1e0"},"schema_version":"1.0","source":{"id":"2506.07867","kind":"arxiv","version":2}},"canonical_sha256":"8473045946cb9d72c31394a40b10b4aee4cc6692244713f2b53d47a4730bc8f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8473045946cb9d72c31394a40b10b4aee4cc6692244713f2b53d47a4730bc8f9","first_computed_at":"2026-07-05T11:19:08.406972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:08.406972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ozyjFRafQX7RsW/S3EN3eXRd1No+XW4huIJoSQD6Cc+XPWZF1m7vr5BEO+IlOupSS8RgSN/IqP7e7+evstA2Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:08.407450Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64c1da0ca9058d83612b87c1fc07fbb46c4015f08ed7dba9b1f85096e285c51a","sha256:b59df0b2973614c59e45ea20d5d6d3eaf3de27d2618065c97b9180f559e4f8b6"],"state_sha256":"22fd96d75a249afd04f39a290e1a2c2e40154fcd2964ac7df6bcb5f26accf8fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cci+GI51O7WuWFvEc1n/g1hieQPPhm/oI2/h6na60VLoUoVzg/j333qgSOYb1/Cx29coTmIF7ecenWuMyykRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T04:18:39.904725Z","bundle_sha256":"a70793258a0f2ee25b27335d3caa232a8468a425b5168eaf86fa37e2503e7835"}}