{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YCPMVRWOPG5ZB4UZ2JGMYBFIHB","short_pith_number":"pith:YCPMVRWO","canonical_record":{"source":{"id":"1501.07253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T19:47:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5fc5df77a59a2b3b3b619decd8e109e76400096b749b536cf5b38a7b5f426054","abstract_canon_sha256":"bf57aab4cb7976515b54fa1265d99f74dcc41531fa1c2fb388dadfc0a4ab2e1d"},"schema_version":"1.0"},"canonical_sha256":"c09ecac6ce79bb90f299d24ccc04a838669ce06f6d2bf4ed1c71dcb82fdf599b","source":{"kind":"arxiv","id":"1501.07253","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07253","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07253v1","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07253","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"YCPMVRWOPG5Z","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCPMVRWOPG5ZB4UZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCPMVRWO","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YCPMVRWOPG5ZB4UZ2JGMYBFIHB","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T19:47:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5fc5df77a59a2b3b3b619decd8e109e76400096b749b536cf5b38a7b5f426054","abstract_canon_sha256":"bf57aab4cb7976515b54fa1265d99f74dcc41531fa1c2fb388dadfc0a4ab2e1d"},"schema_version":"1.0"},"canonical_sha256":"c09ecac6ce79bb90f299d24ccc04a838669ce06f6d2bf4ed1c71dcb82fdf599b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:29.799343Z","signature_b64":"Gxs5t6rnErzMpW2mU4AoFbx44qVOog/z0wJNPH/re8TmW4eHXpRUIuOtNkqXIVyCONp4z5o92YVkwkRUBT6mCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c09ecac6ce79bb90f299d24ccc04a838669ce06f6d2bf4ed1c71dcb82fdf599b","last_reissued_at":"2026-05-18T02:28:29.798886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:29.798886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07253","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":"2026-05-18T02:28:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGN/2vyUeb7MS//RIW5pyqAINB8IYE2DDVE2DViuGGOLT8YgpaeuIridS8bqxZfo0zzE2k3+5GdVRE+GNLEPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:50:29.865374Z"},"content_sha256":"c758e675380f15f850ce734874bbb4dedcfff6b2e73336d7273526b32d1d005c","schema_version":"1.0","event_id":"sha256:c758e675380f15f850ce734874bbb4dedcfff6b2e73336d7273526b32d1d005c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YCPMVRWOPG5ZB4UZ2JGMYBFIHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric quotient stacks and Heisenberg actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Andreas Krug","submitted_at":"2015-01-28T19:47:20Z","abstract_excerpt":"For every smooth projective variety, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks which contains the Fock space as a subrepresentation. The action is induced by functors on the level of the derived categories which form a weak categorification of the action."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07253","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":""},"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":"2026-05-18T02:28:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fiKrurfv1XOHgIxpuamGdkmjDSEX3MyNV6CBqPFCzEL1iAhrcoLD2Uh7bAfuC5TUOINodGrUNX5zcBaS4U4ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:50:29.865935Z"},"content_sha256":"c8a4dac711ee33a943a69b1a9312931a715bb72a9a3e34467bf866e37000f449","schema_version":"1.0","event_id":"sha256:c8a4dac711ee33a943a69b1a9312931a715bb72a9a3e34467bf866e37000f449"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/bundle.json","state_url":"https://pith.science/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/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":"2026-05-26T20:50:29Z","links":{"resolver":"https://pith.science/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB","bundle":"https://pith.science/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/bundle.json","state":"https://pith.science/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCPMVRWOPG5ZB4UZ2JGMYBFIHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YCPMVRWOPG5ZB4UZ2JGMYBFIHB","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":"bf57aab4cb7976515b54fa1265d99f74dcc41531fa1c2fb388dadfc0a4ab2e1d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T19:47:20Z","title_canon_sha256":"5fc5df77a59a2b3b3b619decd8e109e76400096b749b536cf5b38a7b5f426054"},"schema_version":"1.0","source":{"id":"1501.07253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07253","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07253v1","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07253","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"YCPMVRWOPG5Z","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCPMVRWOPG5ZB4UZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCPMVRWO","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:c8a4dac711ee33a943a69b1a9312931a715bb72a9a3e34467bf866e37000f449","target":"graph","created_at":"2026-05-18T02:28:29Z","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":"For every smooth projective variety, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks which contains the Fock space as a subrepresentation. The action is induced by functors on the level of the derived categories which form a weak categorification of the action.","authors_text":"Andreas Krug","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T19:47:20Z","title":"Symmetric quotient stacks and Heisenberg actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07253","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:c758e675380f15f850ce734874bbb4dedcfff6b2e73336d7273526b32d1d005c","target":"record","created_at":"2026-05-18T02:28:29Z","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":"bf57aab4cb7976515b54fa1265d99f74dcc41531fa1c2fb388dadfc0a4ab2e1d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T19:47:20Z","title_canon_sha256":"5fc5df77a59a2b3b3b619decd8e109e76400096b749b536cf5b38a7b5f426054"},"schema_version":"1.0","source":{"id":"1501.07253","kind":"arxiv","version":1}},"canonical_sha256":"c09ecac6ce79bb90f299d24ccc04a838669ce06f6d2bf4ed1c71dcb82fdf599b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c09ecac6ce79bb90f299d24ccc04a838669ce06f6d2bf4ed1c71dcb82fdf599b","first_computed_at":"2026-05-18T02:28:29.798886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:29.798886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gxs5t6rnErzMpW2mU4AoFbx44qVOog/z0wJNPH/re8TmW4eHXpRUIuOtNkqXIVyCONp4z5o92YVkwkRUBT6mCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:29.799343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c758e675380f15f850ce734874bbb4dedcfff6b2e73336d7273526b32d1d005c","sha256:c8a4dac711ee33a943a69b1a9312931a715bb72a9a3e34467bf866e37000f449"],"state_sha256":"f193241fa948af07afb75b66189d1f273cb7c8edca477ee681ee347f364ffbcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUKfo8n+mPimhzlTVzX09N75CM6/0xThfUuLxakpOzx4OByABuRrBRIWltCvBH16NQIlhqzhbz9FsEuKi1wZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:50:29.868825Z","bundle_sha256":"f4596740c350a1e3441d718a2ef937a404ebf96d289bc49aa407cdb032dfa8b9"}}