{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CW3DJJS3XVHHLVAJEF7JPGZRXT","short_pith_number":"pith:CW3DJJS3","canonical_record":{"source":{"id":"1902.00305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-01T12:36:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ca93a8ffdb8083f4d5186ca9a9022c3a14988abe0de71a9c5c68e555553e3aea","abstract_canon_sha256":"e0245d8f5b027151654caca3cf7661068db3a74b03fc1b8863c6bd68ba86b82d"},"schema_version":"1.0"},"canonical_sha256":"15b634a65bbd4e75d409217e979b31bcc6045bfa6db35593cbd36ea37e9b05fa","source":{"kind":"arxiv","id":"1902.00305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00305","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00305v2","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00305","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"CW3DJJS3XVHH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CW3DJJS3XVHHLVAJ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CW3DJJS3","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CW3DJJS3XVHHLVAJEF7JPGZRXT","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-01T12:36:28Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ca93a8ffdb8083f4d5186ca9a9022c3a14988abe0de71a9c5c68e555553e3aea","abstract_canon_sha256":"e0245d8f5b027151654caca3cf7661068db3a74b03fc1b8863c6bd68ba86b82d"},"schema_version":"1.0"},"canonical_sha256":"15b634a65bbd4e75d409217e979b31bcc6045bfa6db35593cbd36ea37e9b05fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:47.618057Z","signature_b64":"swQBJUgO3oRBNcb7VzfEGMiLnKcEAjZcvX0qhakes7N68UmBSTqoEl5tCgnsN2dFJMF8UlrZH8+RFWW8IJIrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b634a65bbd4e75d409217e979b31bcc6045bfa6db35593cbd36ea37e9b05fa","last_reissued_at":"2026-05-17T23:44:47.617532Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:47.617532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00305","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":"2026-05-17T23:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7FCpwfICT5sxJtCp0YL+6ADnR0fTOvemgjCsbosOChDrkbjNkQZLRgW9dzP5cMuVBh5XEP5t2IceFOog5FXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:39:59.263958Z"},"content_sha256":"12d8d884e42f0b1eed0d43c8c89a693d6d0341d571c454178f37d3f53ca24b7d","schema_version":"1.0","event_id":"sha256:12d8d884e42f0b1eed0d43c8c89a693d6d0341d571c454178f37d3f53ca24b7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CW3DJJS3XVHHLVAJEF7JPGZRXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-Jones-Wenzl idempotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Gaston Burrull, Nicolas Libedinsky, Paolo Sentinelli","submitted_at":"2019-02-01T12:36:28Z","abstract_excerpt":"For a prime number $p$ and any natural number $n$ we introduce, by giving an explicit recursive formula, the $p$-Jones-Wenzl projector ${}^p\\operatorname{JW}_n$, an element of the Temperley-Lieb algebra $TL_n(2)$ with coefficients in ${\\mathbb F}_p$. We prove that these projectors give the indecomposable objects in the $\\tilde{A}_1$-Hecke category over ${\\mathbb F}_p$, or equivalently, they give the projector in $\\mathrm{End}_{\\mathrm{SL}_2(\\overline{{\\mathbb F}_p})}(({\\mathbb F}_p^2)^{\\otimes n})$ to the top tilting module. The way in which we find these projectors is by categorifying the fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00305","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":""},"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":"2026-05-17T23:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6AfvFhKe+U9eWil1sXEbBxsuLQXyrQ+LYxLmxJxS6Zxb7xVBhX6EZJ5BiyW0gTa0yOgvU2KNV8CQaBx0+QACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:39:59.264653Z"},"content_sha256":"e95d4b3874eae651dc42713c7bb2a4bf6a1af8090a09fa5c10c7b0c1ddcf3172","schema_version":"1.0","event_id":"sha256:e95d4b3874eae651dc42713c7bb2a4bf6a1af8090a09fa5c10c7b0c1ddcf3172"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/bundle.json","state_url":"https://pith.science/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/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":"2026-05-26T01:39:59Z","links":{"resolver":"https://pith.science/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT","bundle":"https://pith.science/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/bundle.json","state":"https://pith.science/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CW3DJJS3XVHHLVAJEF7JPGZRXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CW3DJJS3XVHHLVAJEF7JPGZRXT","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":"e0245d8f5b027151654caca3cf7661068db3a74b03fc1b8863c6bd68ba86b82d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-01T12:36:28Z","title_canon_sha256":"ca93a8ffdb8083f4d5186ca9a9022c3a14988abe0de71a9c5c68e555553e3aea"},"schema_version":"1.0","source":{"id":"1902.00305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00305","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00305v2","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00305","created_at":"2026-05-17T23:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"CW3DJJS3XVHH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CW3DJJS3XVHHLVAJ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CW3DJJS3","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:e95d4b3874eae651dc42713c7bb2a4bf6a1af8090a09fa5c10c7b0c1ddcf3172","target":"graph","created_at":"2026-05-17T23:44:47Z","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 a prime number $p$ and any natural number $n$ we introduce, by giving an explicit recursive formula, the $p$-Jones-Wenzl projector ${}^p\\operatorname{JW}_n$, an element of the Temperley-Lieb algebra $TL_n(2)$ with coefficients in ${\\mathbb F}_p$. We prove that these projectors give the indecomposable objects in the $\\tilde{A}_1$-Hecke category over ${\\mathbb F}_p$, or equivalently, they give the projector in $\\mathrm{End}_{\\mathrm{SL}_2(\\overline{{\\mathbb F}_p})}(({\\mathbb F}_p^2)^{\\otimes n})$ to the top tilting module. The way in which we find these projectors is by categorifying the fra","authors_text":"Gaston Burrull, Nicolas Libedinsky, Paolo Sentinelli","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-01T12:36:28Z","title":"$p$-Jones-Wenzl idempotents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00305","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":"sha256:12d8d884e42f0b1eed0d43c8c89a693d6d0341d571c454178f37d3f53ca24b7d","target":"record","created_at":"2026-05-17T23:44:47Z","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":"e0245d8f5b027151654caca3cf7661068db3a74b03fc1b8863c6bd68ba86b82d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-01T12:36:28Z","title_canon_sha256":"ca93a8ffdb8083f4d5186ca9a9022c3a14988abe0de71a9c5c68e555553e3aea"},"schema_version":"1.0","source":{"id":"1902.00305","kind":"arxiv","version":2}},"canonical_sha256":"15b634a65bbd4e75d409217e979b31bcc6045bfa6db35593cbd36ea37e9b05fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b634a65bbd4e75d409217e979b31bcc6045bfa6db35593cbd36ea37e9b05fa","first_computed_at":"2026-05-17T23:44:47.617532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:47.617532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"swQBJUgO3oRBNcb7VzfEGMiLnKcEAjZcvX0qhakes7N68UmBSTqoEl5tCgnsN2dFJMF8UlrZH8+RFWW8IJIrBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:47.618057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d8d884e42f0b1eed0d43c8c89a693d6d0341d571c454178f37d3f53ca24b7d","sha256:e95d4b3874eae651dc42713c7bb2a4bf6a1af8090a09fa5c10c7b0c1ddcf3172"],"state_sha256":"36ed8b0ca2b5772f4ad2d4f822a0b1144c331242a855881e4f2977aab8f41e3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqQb9ev6hGYygxxL6em2TGC1dJdgNduVRsysT5R31vozGrof7Q7rHVmUSFtlNBRq0wooOmLaplLjiLCdnlknBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:39:59.267970Z","bundle_sha256":"adcc45b09cb472cb8c72e7c436734ae361cdaf6ca1a45517fb0ce6abe2d783d2"}}