{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5LTRN7RSUIDY5BK5SNLRSQAZBT","short_pith_number":"pith:5LTRN7RS","canonical_record":{"source":{"id":"1108.0351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-01T16:11:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"783c135798a8ece0464f75c49c15840486ee27e063f5a699616b8781620d409d","abstract_canon_sha256":"87b9268cb7e58c2c1d4b28ef487d4dfc5ad98b0d0a225b3e55e2876afd60c698"},"schema_version":"1.0"},"canonical_sha256":"eae716fe32a2078e855d93571940190ccc81dcb0be7648f79b98f62299d5b3dc","source":{"kind":"arxiv","id":"1108.0351","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0351","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0351v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0351","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"5LTRN7RSUIDY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5LTRN7RSUIDY5BK5","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5LTRN7RS","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5LTRN7RSUIDY5BK5SNLRSQAZBT","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-01T16:11:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"783c135798a8ece0464f75c49c15840486ee27e063f5a699616b8781620d409d","abstract_canon_sha256":"87b9268cb7e58c2c1d4b28ef487d4dfc5ad98b0d0a225b3e55e2876afd60c698"},"schema_version":"1.0"},"canonical_sha256":"eae716fe32a2078e855d93571940190ccc81dcb0be7648f79b98f62299d5b3dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:31.242059Z","signature_b64":"5JhoWzWgnyaVRNBNteNwt22sbRazSR2bhw/6OcrcM/g4H5XR3SE/Kr7o3rAGWZFTqAWFwGkZmM9MKfLVs/PQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eae716fe32a2078e855d93571940190ccc81dcb0be7648f79b98f62299d5b3dc","last_reissued_at":"2026-05-18T04:16:31.241678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:31.241678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0351","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":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oigjht7H8PN4LWZQJ1WHMde07nyajamn3aiiSyhzo+zxhFnCEUr5mlgoc6eSNFmkExGd8dFB1a1FGzNMabC/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:03:49.491510Z"},"content_sha256":"51843d7f588f6b4de387bcb2dff8785f9adc815a713a6d21eb517959d836fe71","schema_version":"1.0","event_id":"sha256:51843d7f588f6b4de387bcb2dff8785f9adc815a713a6d21eb517959d836fe71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5LTRN7RSUIDY5BK5SNLRSQAZBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The categorical Weil representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Ronny Hadani, Shamgar Gurevich","submitted_at":"2011-08-01T16:11:22Z","abstract_excerpt":"In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models of the Heisenberg representation. This defines a canonical vector space H(V) associated with a symplectic vector space V over k. In this paper we prove a general theorem about idempotents in categories, and we use it to solve the sign problem, formulated by Bernstein and Deligne, on the compatibility between the associativity constraint and the convolution st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0351","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":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cfYPiBdCsxwp8L8f3bgRmMK/OB7CjQlfeBKDtW0KxLY6iLN5empD+MKycLqhplg2dAwRclxzo75ofMPk2MeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:03:49.492130Z"},"content_sha256":"17ef9624da6bda7ebb1682be8ef349e8f083c476e224f42ab9e17c7f088cfbc9","schema_version":"1.0","event_id":"sha256:17ef9624da6bda7ebb1682be8ef349e8f083c476e224f42ab9e17c7f088cfbc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/bundle.json","state_url":"https://pith.science/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/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":"2026-05-30T05:03:49Z","links":{"resolver":"https://pith.science/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT","bundle":"https://pith.science/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/bundle.json","state":"https://pith.science/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5LTRN7RSUIDY5BK5SNLRSQAZBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5LTRN7RSUIDY5BK5SNLRSQAZBT","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":"87b9268cb7e58c2c1d4b28ef487d4dfc5ad98b0d0a225b3e55e2876afd60c698","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-01T16:11:22Z","title_canon_sha256":"783c135798a8ece0464f75c49c15840486ee27e063f5a699616b8781620d409d"},"schema_version":"1.0","source":{"id":"1108.0351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0351","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0351v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0351","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"5LTRN7RSUIDY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5LTRN7RSUIDY5BK5","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5LTRN7RS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:17ef9624da6bda7ebb1682be8ef349e8f083c476e224f42ab9e17c7f088cfbc9","target":"graph","created_at":"2026-05-18T04:16:31Z","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":"In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models of the Heisenberg representation. This defines a canonical vector space H(V) associated with a symplectic vector space V over k. In this paper we prove a general theorem about idempotents in categories, and we use it to solve the sign problem, formulated by Bernstein and Deligne, on the compatibility between the associativity constraint and the convolution st","authors_text":"Ronny Hadani, Shamgar Gurevich","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-01T16:11:22Z","title":"The categorical Weil representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0351","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":"sha256:51843d7f588f6b4de387bcb2dff8785f9adc815a713a6d21eb517959d836fe71","target":"record","created_at":"2026-05-18T04:16:31Z","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":"87b9268cb7e58c2c1d4b28ef487d4dfc5ad98b0d0a225b3e55e2876afd60c698","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-01T16:11:22Z","title_canon_sha256":"783c135798a8ece0464f75c49c15840486ee27e063f5a699616b8781620d409d"},"schema_version":"1.0","source":{"id":"1108.0351","kind":"arxiv","version":1}},"canonical_sha256":"eae716fe32a2078e855d93571940190ccc81dcb0be7648f79b98f62299d5b3dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eae716fe32a2078e855d93571940190ccc81dcb0be7648f79b98f62299d5b3dc","first_computed_at":"2026-05-18T04:16:31.241678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.241678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JhoWzWgnyaVRNBNteNwt22sbRazSR2bhw/6OcrcM/g4H5XR3SE/Kr7o3rAGWZFTqAWFwGkZmM9MKfLVs/PQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.242059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51843d7f588f6b4de387bcb2dff8785f9adc815a713a6d21eb517959d836fe71","sha256:17ef9624da6bda7ebb1682be8ef349e8f083c476e224f42ab9e17c7f088cfbc9"],"state_sha256":"2c08d92a8200f0eef51eb6a5843bcc794bc27124bcbdae708944af56010b9fb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8GYR5kXBUHzlYM+l6L0qflhRjMiFE+ZZm9sOK6sFJd2yL3woBZ/xUGar3toBOk2QTWn0RH+wl4ODrfTv+8ajBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:03:49.495464Z","bundle_sha256":"782a92fafc1e1be8f08047b5a59c005856a2d64e06015142b17fee014b5180fc"}}