{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2LYLMZZWZA7QSHOM2L3BT7V7M7","short_pith_number":"pith:2LYLMZZW","canonical_record":{"source":{"id":"1108.4616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-23T14:35:29Z","cross_cats_sorted":["math.GT","math.RT"],"title_canon_sha256":"ecacdc7b4b827a4e96daace2f18999e1b78946834cad07172bc419876cf651d1","abstract_canon_sha256":"14afd1a6d02f4d5e01c1ebcfdc87992080e59e24a8197398f9fe03595fdcf151"},"schema_version":"1.0"},"canonical_sha256":"d2f0b66736c83f091dccd2f619febf67df65c664ab2cb291fd6083e01f4ab0c1","source":{"kind":"arxiv","id":"1108.4616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4616","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4616v1","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4616","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"2LYLMZZWZA7Q","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2LYLMZZWZA7QSHOM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2LYLMZZW","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2LYLMZZWZA7QSHOM2L3BT7V7M7","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-23T14:35:29Z","cross_cats_sorted":["math.GT","math.RT"],"title_canon_sha256":"ecacdc7b4b827a4e96daace2f18999e1b78946834cad07172bc419876cf651d1","abstract_canon_sha256":"14afd1a6d02f4d5e01c1ebcfdc87992080e59e24a8197398f9fe03595fdcf151"},"schema_version":"1.0"},"canonical_sha256":"d2f0b66736c83f091dccd2f619febf67df65c664ab2cb291fd6083e01f4ab0c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:54.079157Z","signature_b64":"0bENlK9A0vfptaF92hCzWzaC0h0gBogNaW657eyJDgvqys20zlcqQgRnNxA3J7oa+2DjxacrqGNQ9aDoQn+rCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2f0b66736c83f091dccd2f619febf67df65c664ab2cb291fd6083e01f4ab0c1","last_reissued_at":"2026-05-18T04:14:54.078526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:54.078526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4616","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WxSSDkVEx7eX5eLTDpR+nobDGrrc+akJzTMECzV4wYHuaS01jeQc7Y9AvCGP6gBDpa94HdManbOa4PLHmhIkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:36:23.587269Z"},"content_sha256":"e3f9fc4385cc4056555646f58bc2372e4afbbf27dd54eadc07abc35297584cf3","schema_version":"1.0","event_id":"sha256:e3f9fc4385cc4056555646f58bc2372e4afbbf27dd54eadc07abc35297584cf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2LYLMZZWZA7QSHOM2L3BT7V7M7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generating basis webs for $\\SL_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.QA","authors_text":"Bruce Fontaine","submitted_at":"2011-08-23T14:35:29Z","abstract_excerpt":"Given a simple algebraic group $G$, a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\\SL_n$ which form a basis for the invariant space via the geometric Satake correspondence. In fact, there is an upper unitriangular change of basis to the Satake basis. This set of webs agrees with previous work in the cases $n=2,3$ and generalizes the work of Westbury in the case $n\\geq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4616","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":"2026-05-18T04:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKjqF4CtFM9s/Mjx81fVXozU35h7HrO9zguVWtCaziezzVL+bdQX5xsX6o6YLYSx/mR4MDNFv59rVC5QlubeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:36:23.587814Z"},"content_sha256":"45c9de3bf8c0153dd89078ea6f2e60b0bacdb178f6fb62fbc49412811382655d","schema_version":"1.0","event_id":"sha256:45c9de3bf8c0153dd89078ea6f2e60b0bacdb178f6fb62fbc49412811382655d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/bundle.json","state_url":"https://pith.science/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/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":"2026-05-27T09:36:23Z","links":{"resolver":"https://pith.science/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7","bundle":"https://pith.science/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/bundle.json","state":"https://pith.science/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LYLMZZWZA7QSHOM2L3BT7V7M7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2LYLMZZWZA7QSHOM2L3BT7V7M7","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":"14afd1a6d02f4d5e01c1ebcfdc87992080e59e24a8197398f9fe03595fdcf151","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-23T14:35:29Z","title_canon_sha256":"ecacdc7b4b827a4e96daace2f18999e1b78946834cad07172bc419876cf651d1"},"schema_version":"1.0","source":{"id":"1108.4616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4616","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4616v1","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4616","created_at":"2026-05-18T04:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"2LYLMZZWZA7Q","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2LYLMZZWZA7QSHOM","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2LYLMZZW","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:45c9de3bf8c0153dd89078ea6f2e60b0bacdb178f6fb62fbc49412811382655d","target":"graph","created_at":"2026-05-18T04:14:54Z","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":"Given a simple algebraic group $G$, a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\\SL_n$ which form a basis for the invariant space via the geometric Satake correspondence. In fact, there is an upper unitriangular change of basis to the Satake basis. This set of webs agrees with previous work in the cases $n=2,3$ and generalizes the work of Westbury in the case $n\\geq 4$.","authors_text":"Bruce Fontaine","cross_cats":["math.GT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-23T14:35:29Z","title":"Generating basis webs for $\\SL_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4616","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:e3f9fc4385cc4056555646f58bc2372e4afbbf27dd54eadc07abc35297584cf3","target":"record","created_at":"2026-05-18T04:14:54Z","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":"14afd1a6d02f4d5e01c1ebcfdc87992080e59e24a8197398f9fe03595fdcf151","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-23T14:35:29Z","title_canon_sha256":"ecacdc7b4b827a4e96daace2f18999e1b78946834cad07172bc419876cf651d1"},"schema_version":"1.0","source":{"id":"1108.4616","kind":"arxiv","version":1}},"canonical_sha256":"d2f0b66736c83f091dccd2f619febf67df65c664ab2cb291fd6083e01f4ab0c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2f0b66736c83f091dccd2f619febf67df65c664ab2cb291fd6083e01f4ab0c1","first_computed_at":"2026-05-18T04:14:54.078526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:54.078526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0bENlK9A0vfptaF92hCzWzaC0h0gBogNaW657eyJDgvqys20zlcqQgRnNxA3J7oa+2DjxacrqGNQ9aDoQn+rCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:54.079157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3f9fc4385cc4056555646f58bc2372e4afbbf27dd54eadc07abc35297584cf3","sha256:45c9de3bf8c0153dd89078ea6f2e60b0bacdb178f6fb62fbc49412811382655d"],"state_sha256":"efc7bd9db17be20fcb5030d4eab893ec1b5dec379f212fe897e6f6490102a56a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ah2LzCy1Klqr0FjhVnCUtScwxyRhl7GuhGOISoPp9PbYIJM7Mvp3niafJjcsM4UVjun3zElHt0SFkE/oERElBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:36:23.591353Z","bundle_sha256":"3deb17e6879b9d6c33089f2fee8915d286120af2652cdb58b33e71175208fd2f"}}