{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:A5DQX2LIJUQEZIJVHZIT6ZM666","short_pith_number":"pith:A5DQX2LI","canonical_record":{"source":{"id":"2306.03043","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-05T17:06:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d63de6147e56aa281acb05f6a80bb4ae2dded25363fb070d60b5df9f33bb5a76","abstract_canon_sha256":"1f1f05fc06b07f1d6b66670b2012e35c8e58727a1d8cc52ce0b4a990be42985c"},"schema_version":"1.0"},"canonical_sha256":"07470be9684d204ca1353e513f659ef7a535035eb6816e5ee3ed01a28ac03bea","source":{"kind":"arxiv","id":"2306.03043","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.03043","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"2306.03043v2","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.03043","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"A5DQX2LIJUQE","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_16","alias_value":"A5DQX2LIJUQEZIJV","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_8","alias_value":"A5DQX2LI","created_at":"2026-07-05T07:31:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:A5DQX2LIJUQEZIJVHZIT6ZM666","target":"record","payload":{"canonical_record":{"source":{"id":"2306.03043","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-05T17:06:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d63de6147e56aa281acb05f6a80bb4ae2dded25363fb070d60b5df9f33bb5a76","abstract_canon_sha256":"1f1f05fc06b07f1d6b66670b2012e35c8e58727a1d8cc52ce0b4a990be42985c"},"schema_version":"1.0"},"canonical_sha256":"07470be9684d204ca1353e513f659ef7a535035eb6816e5ee3ed01a28ac03bea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:31:52.711199Z","signature_b64":"TaV5h0Anbgw+oquRHbwCCMLWR6thQb9jviLcO7YsgjlS6LBBzbKFR9BNQE4X9lVg97S3EVEfvgQ4zF4JJgGJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07470be9684d204ca1353e513f659ef7a535035eb6816e5ee3ed01a28ac03bea","last_reissued_at":"2026-07-05T07:31:52.710765Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:31:52.710765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.03043","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":"2026-07-05T07:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kMie1nnGsZle5GlCMkmJg64yxbnRY0Tauh4++9QWKyN6+FdkW4R5oJQfm0HI0a0Xa+hbmXRSKF7U+03xCh8ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T00:28:44.366170Z"},"content_sha256":"33ba78f14864fe9ab8953c00968a9159feaecb9930c4914dd225172e69293eca","schema_version":"1.0","event_id":"sha256:33ba78f14864fe9ab8953c00968a9159feaecb9930c4914dd225172e69293eca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:A5DQX2LIJUQEZIJVHZIT6ZM666","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ind-geometric stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Harold Williams, Sabin Cautis","submitted_at":"2023-06-05T17:06:54Z","abstract_excerpt":"We develop the theory of ind-geometric stacks, in particular their coherent and ind-coherent sheaf theory. This provides a convenient framework for working with equivariant sheaves on ind-schemes, especially in derived settings. Motivating examples include the coherent Satake category, the double affine Hecke category, and related categories in the theory of Coulomb branches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03043","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/2306.03043/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":"2026-07-05T07:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xa1lHB3QPw4tf4+M0hNafXoBa7maWudfVb9OkuH6+6FhZHWIwTVTzuk1W2mI3Hba6afoPmJyb8qley/GaKSmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T00:28:44.366735Z"},"content_sha256":"f99731f50d49559f07c33c4bdcd2ea9d49faff34406f6af8448b746de147bfed","schema_version":"1.0","event_id":"sha256:f99731f50d49559f07c33c4bdcd2ea9d49faff34406f6af8448b746de147bfed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/bundle.json","state_url":"https://pith.science/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/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":"2026-08-22T00:28:44Z","links":{"resolver":"https://pith.science/pith/A5DQX2LIJUQEZIJVHZIT6ZM666","bundle":"https://pith.science/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/bundle.json","state":"https://pith.science/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5DQX2LIJUQEZIJVHZIT6ZM666/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:A5DQX2LIJUQEZIJVHZIT6ZM666","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":"1f1f05fc06b07f1d6b66670b2012e35c8e58727a1d8cc52ce0b4a990be42985c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-05T17:06:54Z","title_canon_sha256":"d63de6147e56aa281acb05f6a80bb4ae2dded25363fb070d60b5df9f33bb5a76"},"schema_version":"1.0","source":{"id":"2306.03043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.03043","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"2306.03043v2","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.03043","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"A5DQX2LIJUQE","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_16","alias_value":"A5DQX2LIJUQEZIJV","created_at":"2026-07-05T07:31:52Z"},{"alias_kind":"pith_short_8","alias_value":"A5DQX2LI","created_at":"2026-07-05T07:31:52Z"}],"graph_snapshots":[{"event_id":"sha256:f99731f50d49559f07c33c4bdcd2ea9d49faff34406f6af8448b746de147bfed","target":"graph","created_at":"2026-07-05T07:31:52Z","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/2306.03043/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the theory of ind-geometric stacks, in particular their coherent and ind-coherent sheaf theory. This provides a convenient framework for working with equivariant sheaves on ind-schemes, especially in derived settings. Motivating examples include the coherent Satake category, the double affine Hecke category, and related categories in the theory of Coulomb branches.","authors_text":"Harold Williams, Sabin Cautis","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-05T17:06:54Z","title":"Ind-geometric stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03043","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":"sha256:33ba78f14864fe9ab8953c00968a9159feaecb9930c4914dd225172e69293eca","target":"record","created_at":"2026-07-05T07:31:52Z","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":"1f1f05fc06b07f1d6b66670b2012e35c8e58727a1d8cc52ce0b4a990be42985c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-05T17:06:54Z","title_canon_sha256":"d63de6147e56aa281acb05f6a80bb4ae2dded25363fb070d60b5df9f33bb5a76"},"schema_version":"1.0","source":{"id":"2306.03043","kind":"arxiv","version":2}},"canonical_sha256":"07470be9684d204ca1353e513f659ef7a535035eb6816e5ee3ed01a28ac03bea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07470be9684d204ca1353e513f659ef7a535035eb6816e5ee3ed01a28ac03bea","first_computed_at":"2026-07-05T07:31:52.710765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:31:52.710765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TaV5h0Anbgw+oquRHbwCCMLWR6thQb9jviLcO7YsgjlS6LBBzbKFR9BNQE4X9lVg97S3EVEfvgQ4zF4JJgGJAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:31:52.711199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.03043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ba78f14864fe9ab8953c00968a9159feaecb9930c4914dd225172e69293eca","sha256:f99731f50d49559f07c33c4bdcd2ea9d49faff34406f6af8448b746de147bfed"],"state_sha256":"02f94f96f32b187fdd62b9a793539b078044cb528850c2d1adf4308e1b0c8c2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DHxTXqUblOlhUFWczWNn5HTSAD7FM4c8RGJxpMtuEUgh46I23jMkcQsOToZpgpNJfHagWGeBtjzh0dVHdyloCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T00:28:44.373052Z","bundle_sha256":"8e825de9f0c5056070e60fdd8080d771fc133ac541e236419f34d6a0b53c4b05"}}