{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CUWS5ZFNHRZZFXAYKGPTN7DIWX","short_pith_number":"pith:CUWS5ZFN","canonical_record":{"source":{"id":"2106.10729","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-06-20T17:24:46Z","cross_cats_sorted":[],"title_canon_sha256":"e0bee392b10aa8af1fae49b21da0283aaa1ab494d1bf6ff50fb0e4889b97d739","abstract_canon_sha256":"aaf141435aac3fef4529d43a596aa09512cd69a0a7f174900a26e3eef79bd86b"},"schema_version":"1.0"},"canonical_sha256":"152d2ee4ad3c7392dc18519f36fc68b5cd6bad9f0dc0beb3e87d807314d7baef","source":{"kind":"arxiv","id":"2106.10729","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.10729","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"2106.10729v1","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.10729","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"CUWS5ZFNHRZZ","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_16","alias_value":"CUWS5ZFNHRZZFXAY","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_8","alias_value":"CUWS5ZFN","created_at":"2026-07-05T02:50:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CUWS5ZFNHRZZFXAYKGPTN7DIWX","target":"record","payload":{"canonical_record":{"source":{"id":"2106.10729","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-06-20T17:24:46Z","cross_cats_sorted":[],"title_canon_sha256":"e0bee392b10aa8af1fae49b21da0283aaa1ab494d1bf6ff50fb0e4889b97d739","abstract_canon_sha256":"aaf141435aac3fef4529d43a596aa09512cd69a0a7f174900a26e3eef79bd86b"},"schema_version":"1.0"},"canonical_sha256":"152d2ee4ad3c7392dc18519f36fc68b5cd6bad9f0dc0beb3e87d807314d7baef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:50:52.688118Z","signature_b64":"wDAACb3rB25ljAAR8OaxSFI35VmzXN87TopdRvnC9gZQnD2XIE08m+Ze7dnI8wgcZKFpBXwHw6Qh+exciaKHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"152d2ee4ad3c7392dc18519f36fc68b5cd6bad9f0dc0beb3e87d807314d7baef","last_reissued_at":"2026-07-05T02:50:52.687676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:50:52.687676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.10729","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":"2026-07-05T02:50:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKLb5IngT2dbMDjWhKLZqTIB+Hu9R0emUpnSifUqUxZAYRJb56vlDkgTjQVlLL+lCa7AcyQ1TDXB+XXJL/3FAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:02:02.691785Z"},"content_sha256":"a7699eb8412d9f40dc610e2c9b3d1c92b217d8f2f3b7e91d0bff76ae646473bf","schema_version":"1.0","event_id":"sha256:a7699eb8412d9f40dc610e2c9b3d1c92b217d8f2f3b7e91d0bff76ae646473bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CUWS5ZFNHRZZFXAYKGPTN7DIWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived Langlands VIII: Local GLn","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor P. Snaith","submitted_at":"2021-06-20T17:24:46Z","abstract_excerpt":"In this, the eighth article in my Derived Langlands series, I describe the construction of a 2-variable L-function for two representations of general linear groups of a $p$-adic local field. Due to extenuating health circumstances, many of the proofs and ideas herein are suggestive rather than the finished definitive versions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.10729","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.10729/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":"2026-07-05T02:50:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJKqSxkIwuLPsA6NRTo773gWoNLGCPZeRnn3JfV2blFHS99pYNXAxt60olBebsp7B91jsvd0YXmB6Pp3aY99Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:02:02.692277Z"},"content_sha256":"39384a1808d671d3b7fa24f05262594463b53c5e7ee9e805fb074cb463d65702","schema_version":"1.0","event_id":"sha256:39384a1808d671d3b7fa24f05262594463b53c5e7ee9e805fb074cb463d65702"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/bundle.json","state_url":"https://pith.science/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/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":"2026-08-04T17:02:02Z","links":{"resolver":"https://pith.science/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX","bundle":"https://pith.science/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/bundle.json","state":"https://pith.science/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUWS5ZFNHRZZFXAYKGPTN7DIWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CUWS5ZFNHRZZFXAYKGPTN7DIWX","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":"aaf141435aac3fef4529d43a596aa09512cd69a0a7f174900a26e3eef79bd86b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-06-20T17:24:46Z","title_canon_sha256":"e0bee392b10aa8af1fae49b21da0283aaa1ab494d1bf6ff50fb0e4889b97d739"},"schema_version":"1.0","source":{"id":"2106.10729","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.10729","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"2106.10729v1","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.10729","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"CUWS5ZFNHRZZ","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_16","alias_value":"CUWS5ZFNHRZZFXAY","created_at":"2026-07-05T02:50:52Z"},{"alias_kind":"pith_short_8","alias_value":"CUWS5ZFN","created_at":"2026-07-05T02:50:52Z"}],"graph_snapshots":[{"event_id":"sha256:39384a1808d671d3b7fa24f05262594463b53c5e7ee9e805fb074cb463d65702","target":"graph","created_at":"2026-07-05T02:50:52Z","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/2106.10729/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this, the eighth article in my Derived Langlands series, I describe the construction of a 2-variable L-function for two representations of general linear groups of a $p$-adic local field. Due to extenuating health circumstances, many of the proofs and ideas herein are suggestive rather than the finished definitive versions.","authors_text":"Victor P. Snaith","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-06-20T17:24:46Z","title":"Derived Langlands VIII: Local GLn"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.10729","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:a7699eb8412d9f40dc610e2c9b3d1c92b217d8f2f3b7e91d0bff76ae646473bf","target":"record","created_at":"2026-07-05T02:50:52Z","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":"aaf141435aac3fef4529d43a596aa09512cd69a0a7f174900a26e3eef79bd86b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-06-20T17:24:46Z","title_canon_sha256":"e0bee392b10aa8af1fae49b21da0283aaa1ab494d1bf6ff50fb0e4889b97d739"},"schema_version":"1.0","source":{"id":"2106.10729","kind":"arxiv","version":1}},"canonical_sha256":"152d2ee4ad3c7392dc18519f36fc68b5cd6bad9f0dc0beb3e87d807314d7baef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"152d2ee4ad3c7392dc18519f36fc68b5cd6bad9f0dc0beb3e87d807314d7baef","first_computed_at":"2026-07-05T02:50:52.687676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:50:52.687676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wDAACb3rB25ljAAR8OaxSFI35VmzXN87TopdRvnC9gZQnD2XIE08m+Ze7dnI8wgcZKFpBXwHw6Qh+exciaKHCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:50:52.688118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.10729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7699eb8412d9f40dc610e2c9b3d1c92b217d8f2f3b7e91d0bff76ae646473bf","sha256:39384a1808d671d3b7fa24f05262594463b53c5e7ee9e805fb074cb463d65702"],"state_sha256":"5308a0ef91d7cb512b0034b4971ac443be6ca2ddb8a03add3e54d11034b89183"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CoZIqHa5WMd7DGzkygFyrEY0KAl4U1bGD3ovtSsIWG/2Tn9lgaFn/Rd12DpB3rjrZ7cmuFp7Hb3F8iFycPxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:02:02.697356Z","bundle_sha256":"088f1bcbc99371ccf2c1de97222faa6e8664dfab53c36cc71ee191280a0e2fca"}}