{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:33AWK4ICDAVWFUJXTWSSIENGNF","short_pith_number":"pith:33AWK4IC","canonical_record":{"source":{"id":"2102.08205","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-02-16T15:01:46Z","cross_cats_sorted":[],"title_canon_sha256":"bb1c16c96aa63b9bc48045f94049026689fe63a9c60570286cb201d7cfaddadd","abstract_canon_sha256":"3c401c222a3e50e1e099e0fd356583ceef80eb1815188df14a8811ca2cccf08b"},"schema_version":"1.0"},"canonical_sha256":"dec1657102182b62d1379da52411a6694f6a6a855a80a307a78bea78c2189a61","source":{"kind":"arxiv","id":"2102.08205","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.08205","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"2102.08205v3","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.08205","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"33AWK4ICDAVW","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_16","alias_value":"33AWK4ICDAVWFUJX","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_8","alias_value":"33AWK4IC","created_at":"2026-07-05T04:18:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:33AWK4ICDAVWFUJXTWSSIENGNF","target":"record","payload":{"canonical_record":{"source":{"id":"2102.08205","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-02-16T15:01:46Z","cross_cats_sorted":[],"title_canon_sha256":"bb1c16c96aa63b9bc48045f94049026689fe63a9c60570286cb201d7cfaddadd","abstract_canon_sha256":"3c401c222a3e50e1e099e0fd356583ceef80eb1815188df14a8811ca2cccf08b"},"schema_version":"1.0"},"canonical_sha256":"dec1657102182b62d1379da52411a6694f6a6a855a80a307a78bea78c2189a61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:14.262801Z","signature_b64":"4EXpyCUoQu/sxzdPgDaL9+xxxhp98saRPadviRluePRGuDpu4QN1xWE8G+AHR8nMTk9K0n/vrP9uKwqS6VVyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dec1657102182b62d1379da52411a6694f6a6a855a80a307a78bea78c2189a61","last_reissued_at":"2026-07-05T04:18:14.262377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:14.262377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.08205","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":"2026-07-05T04:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0K0mQ+xog9CEFDjanDKWxWNJRIfuL15BCuAUfsYIjSnRJxZuzqsfN3EudkNBIQUZmsxvhNQEvxNCDcImtXjfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:14:18.450638Z"},"content_sha256":"4bc5f710f221e3dfff49086c86dc531d68811e1c87749f3bf5b38c5ab660bed7","schema_version":"1.0","event_id":"sha256:4bc5f710f221e3dfff49086c86dc531d68811e1c87749f3bf5b38c5ab660bed7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:33AWK4ICDAVWFUJXTWSSIENGNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$(\\ell,p)$-Jones-Wenzl Idempotents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"R. A. Spencer, Stuart Martin","submitted_at":"2021-02-16T15:01:46Z","abstract_excerpt":"The Jones-Wenzl idempotents of the Temperley-Lieb algebra are celebrated elements defined over characteristic zero and for generic loop parameter.\n  Given pointed field $(R, \\delta)$, we extend the existing results of Burrull, Libedinsky and Sentinelli to determine a recursive form for the idempotents describing the projective cover of the trivial ${\\rm TL}_n^R(\\delta)$-module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08205","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.08205/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":"2026-07-05T04:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2haOtg4U0JZDSD1FAbkLANAQrooLc/PfzE5RfZ0D0gJiz3O9xJmRSMMd5xriWKMMYPPkyzJ/bXkcjfwb0NEtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:14:18.451133Z"},"content_sha256":"de8f087ceb4b9363f0a0cffb52b3c5de266061e16e0a1e780d073a9842543af7","schema_version":"1.0","event_id":"sha256:de8f087ceb4b9363f0a0cffb52b3c5de266061e16e0a1e780d073a9842543af7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33AWK4ICDAVWFUJXTWSSIENGNF/bundle.json","state_url":"https://pith.science/pith/33AWK4ICDAVWFUJXTWSSIENGNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33AWK4ICDAVWFUJXTWSSIENGNF/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":"2026-08-08T21:14:18Z","links":{"resolver":"https://pith.science/pith/33AWK4ICDAVWFUJXTWSSIENGNF","bundle":"https://pith.science/pith/33AWK4ICDAVWFUJXTWSSIENGNF/bundle.json","state":"https://pith.science/pith/33AWK4ICDAVWFUJXTWSSIENGNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33AWK4ICDAVWFUJXTWSSIENGNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:33AWK4ICDAVWFUJXTWSSIENGNF","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":"3c401c222a3e50e1e099e0fd356583ceef80eb1815188df14a8811ca2cccf08b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-02-16T15:01:46Z","title_canon_sha256":"bb1c16c96aa63b9bc48045f94049026689fe63a9c60570286cb201d7cfaddadd"},"schema_version":"1.0","source":{"id":"2102.08205","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.08205","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"2102.08205v3","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.08205","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"33AWK4ICDAVW","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_16","alias_value":"33AWK4ICDAVWFUJX","created_at":"2026-07-05T04:18:14Z"},{"alias_kind":"pith_short_8","alias_value":"33AWK4IC","created_at":"2026-07-05T04:18:14Z"}],"graph_snapshots":[{"event_id":"sha256:de8f087ceb4b9363f0a0cffb52b3c5de266061e16e0a1e780d073a9842543af7","target":"graph","created_at":"2026-07-05T04:18:14Z","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/2102.08205/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Jones-Wenzl idempotents of the Temperley-Lieb algebra are celebrated elements defined over characteristic zero and for generic loop parameter.\n  Given pointed field $(R, \\delta)$, we extend the existing results of Burrull, Libedinsky and Sentinelli to determine a recursive form for the idempotents describing the projective cover of the trivial ${\\rm TL}_n^R(\\delta)$-module.","authors_text":"R. A. Spencer, Stuart Martin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-02-16T15:01:46Z","title":"$(\\ell,p)$-Jones-Wenzl Idempotents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08205","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":"sha256:4bc5f710f221e3dfff49086c86dc531d68811e1c87749f3bf5b38c5ab660bed7","target":"record","created_at":"2026-07-05T04:18:14Z","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":"3c401c222a3e50e1e099e0fd356583ceef80eb1815188df14a8811ca2cccf08b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-02-16T15:01:46Z","title_canon_sha256":"bb1c16c96aa63b9bc48045f94049026689fe63a9c60570286cb201d7cfaddadd"},"schema_version":"1.0","source":{"id":"2102.08205","kind":"arxiv","version":3}},"canonical_sha256":"dec1657102182b62d1379da52411a6694f6a6a855a80a307a78bea78c2189a61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dec1657102182b62d1379da52411a6694f6a6a855a80a307a78bea78c2189a61","first_computed_at":"2026-07-05T04:18:14.262377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:14.262377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4EXpyCUoQu/sxzdPgDaL9+xxxhp98saRPadviRluePRGuDpu4QN1xWE8G+AHR8nMTk9K0n/vrP9uKwqS6VVyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:14.262801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.08205","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bc5f710f221e3dfff49086c86dc531d68811e1c87749f3bf5b38c5ab660bed7","sha256:de8f087ceb4b9363f0a0cffb52b3c5de266061e16e0a1e780d073a9842543af7"],"state_sha256":"cfee3f42d515e180607ab06a21c80484f7f638c8ec3017040bd8ee38b523c3ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqrnvIyVHygpCkoTdX1SK0soUdmfhd74A22FZgu1qp6VBJtuRRkWEXF1haDIDVQgjfla4p5Bk10gjgGlwfbLAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T21:14:18.456731Z","bundle_sha256":"c77048c4e3eae1efc279e4e2b9c65a6e261516b3356f5212bedc262add2c8d5f"}}