{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GFCNWAEVL73HUZSB3CL4SH7TLJ","short_pith_number":"pith:GFCNWAEV","canonical_record":{"source":{"id":"1412.4394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-14T18:54:41Z","cross_cats_sorted":[],"title_canon_sha256":"1bf12a134718841b63f0fe6e8d295a35cafdc0da77c3e1852150e0ce6fce73ee","abstract_canon_sha256":"affe0201e0a18603a07302bb4f7a38e6df8184b93176ab42adb065039e8ef81f"},"schema_version":"1.0"},"canonical_sha256":"3144db00955ff67a6641d897c91ff35a78ed7080ddc34c325710d80994eb00f9","source":{"kind":"arxiv","id":"1412.4394","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4394","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4394v3","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4394","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"pith_short_12","alias_value":"GFCNWAEVL73H","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFCNWAEVL73HUZSB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFCNWAEV","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GFCNWAEVL73HUZSB3CL4SH7TLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-14T18:54:41Z","cross_cats_sorted":[],"title_canon_sha256":"1bf12a134718841b63f0fe6e8d295a35cafdc0da77c3e1852150e0ce6fce73ee","abstract_canon_sha256":"affe0201e0a18603a07302bb4f7a38e6df8184b93176ab42adb065039e8ef81f"},"schema_version":"1.0"},"canonical_sha256":"3144db00955ff67a6641d897c91ff35a78ed7080ddc34c325710d80994eb00f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:59.044253Z","signature_b64":"zw38pk1dN4Xphm/alDUUy1rdJcx6MXtqHGuDakZNOnuPYBCa74xM2TC1L8FwxIJCrt6GgNulhDX4Q+D34X2IDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3144db00955ff67a6641d897c91ff35a78ed7080ddc34c325710d80994eb00f9","last_reissued_at":"2026-05-18T00:45:59.043809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:59.043809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4394","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52RThbMIlMdhXcx07hUdXVIFuxXerDk9jogfn5/MqyTlWWLq79Y5rPO2V40CJ1RYi2nEYM+Y7BbOLuO+2iLpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:10:22.376944Z"},"content_sha256":"2dd1520fc98e8c603aa23171a1d598e5049c2961f2decabbe19eedb88ed814b7","schema_version":"1.0","event_id":"sha256:2dd1520fc98e8c603aa23171a1d598e5049c2961f2decabbe19eedb88ed814b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GFCNWAEVL73HUZSB3CL4SH7TLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The category of singularities as a crystal and global Springer fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Arinkin, D. Gaitsgory","submitted_at":"2014-12-14T18:54:41Z","abstract_excerpt":"We prove the \"Gluing Conjecture\" on the spectral side of the categorical geometric Langlands correspondence. The key tool is the structure of crystal on the category of singularities, which allows to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4394","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:45:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWBcAK5megYe+slpCDLn8eltNzToaaa6EOYZdHvV+3IQ8tIQzIeyEw7ublv3fhOj4L6P1Cfc3wLklxS1fM1bCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:10:22.377588Z"},"content_sha256":"74dade1a27432dc9c496c9733c15a757add2d07eced53bbf6d6beea6cdfe97d1","schema_version":"1.0","event_id":"sha256:74dade1a27432dc9c496c9733c15a757add2d07eced53bbf6d6beea6cdfe97d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/bundle.json","state_url":"https://pith.science/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/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":"2026-05-26T14:10:22Z","links":{"resolver":"https://pith.science/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ","bundle":"https://pith.science/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/bundle.json","state":"https://pith.science/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFCNWAEVL73HUZSB3CL4SH7TLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GFCNWAEVL73HUZSB3CL4SH7TLJ","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":"affe0201e0a18603a07302bb4f7a38e6df8184b93176ab42adb065039e8ef81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-14T18:54:41Z","title_canon_sha256":"1bf12a134718841b63f0fe6e8d295a35cafdc0da77c3e1852150e0ce6fce73ee"},"schema_version":"1.0","source":{"id":"1412.4394","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4394","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4394v3","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4394","created_at":"2026-05-18T00:45:59Z"},{"alias_kind":"pith_short_12","alias_value":"GFCNWAEVL73H","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GFCNWAEVL73HUZSB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GFCNWAEV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:74dade1a27432dc9c496c9733c15a757add2d07eced53bbf6d6beea6cdfe97d1","target":"graph","created_at":"2026-05-18T00:45:59Z","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"},"paper":{"abstract_excerpt":"We prove the \"Gluing Conjecture\" on the spectral side of the categorical geometric Langlands correspondence. The key tool is the structure of crystal on the category of singularities, which allows to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.","authors_text":"D. Arinkin, D. Gaitsgory","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-14T18:54:41Z","title":"The category of singularities as a crystal and global Springer fibers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4394","kind":"arxiv","version":3},"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":"sha256:2dd1520fc98e8c603aa23171a1d598e5049c2961f2decabbe19eedb88ed814b7","target":"record","created_at":"2026-05-18T00:45:59Z","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":"affe0201e0a18603a07302bb4f7a38e6df8184b93176ab42adb065039e8ef81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-14T18:54:41Z","title_canon_sha256":"1bf12a134718841b63f0fe6e8d295a35cafdc0da77c3e1852150e0ce6fce73ee"},"schema_version":"1.0","source":{"id":"1412.4394","kind":"arxiv","version":3}},"canonical_sha256":"3144db00955ff67a6641d897c91ff35a78ed7080ddc34c325710d80994eb00f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3144db00955ff67a6641d897c91ff35a78ed7080ddc34c325710d80994eb00f9","first_computed_at":"2026-05-18T00:45:59.043809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:59.043809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zw38pk1dN4Xphm/alDUUy1rdJcx6MXtqHGuDakZNOnuPYBCa74xM2TC1L8FwxIJCrt6GgNulhDX4Q+D34X2IDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:59.044253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4394","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd1520fc98e8c603aa23171a1d598e5049c2961f2decabbe19eedb88ed814b7","sha256:74dade1a27432dc9c496c9733c15a757add2d07eced53bbf6d6beea6cdfe97d1"],"state_sha256":"a3ff5b11c61ae2c33c1996f81c7b235f6c23335cfe6b42623c16540a8d9208ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNd548POjtV0opiSJCRnZc/YTleWweVFt4n6C5v8Hc7boqzyYj1z0Q7ltuPM9y1NLCnGgIXe/jTAG+pTJaduCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:10:22.380751Z","bundle_sha256":"f5f6febc705dda66e493ffeb5e57872d3abba5c7c18844bc890808c90897b0a7"}}