{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:LMK7GC7D2INML75SKTJKWZTWKN","short_pith_number":"pith:LMK7GC7D","canonical_record":{"source":{"id":"math/9611219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4ae68e4f633a8d69715774b2cda7bf7a723161e67506ac81a121ec872d2f2df8","abstract_canon_sha256":"862ed128d7c4bbf5c325aba68ee725fd02876cf3547c331f2db1829235e770d9"},"schema_version":"1.0"},"canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","source":{"kind":"arxiv","id":"math/9611219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9611219","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/9611219v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9611219","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"LMK7GC7D2INM","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"LMK7GC7D2INML75S","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"LMK7GC7D","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:LMK7GC7D2INML75SKTJKWZTWKN","target":"record","payload":{"canonical_record":{"source":{"id":"math/9611219","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4ae68e4f633a8d69715774b2cda7bf7a723161e67506ac81a121ec872d2f2df8","abstract_canon_sha256":"862ed128d7c4bbf5c325aba68ee725fd02876cf3547c331f2db1829235e770d9"},"schema_version":"1.0"},"canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.879695Z","signature_b64":"hKruerHvotcqlOgZP1EIN2v/PGABmuV/9i9kPZUfoUG6oMtoNkgtvX0yA6yTF8CJfW+jZaxwxjY7PScKVmBHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","last_reissued_at":"2026-05-18T01:05:46.879250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.879250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9611219","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mdqWXI8MmR3h3QD8tNbShnMguB6GmZQeZRWfew1nMDFYHeSPIlhPioyx5W8F7ZVwT2mMwOlEmC3493iSlr6jAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:22:31.346782Z"},"content_sha256":"609ced681ef59096219019ca072c4d57cae7d8c7e57a4a72fe7a8dec55040d33","schema_version":"1.0","event_id":"sha256:609ced681ef59096219019ca072c4d57cae7d8c7e57a4a72fe7a8dec55040d33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:LMK7GC7D2INML75SKTJKWZTWKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Archimedean superrigidity of solvable S-arithmetic groups","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dave Witte","submitted_at":"1996-11-19T00:00:00Z","abstract_excerpt":"Let $\\Ga$ be a connected, solvable linear algebraic group over a number field~$K$, let $S$ be a finite set of places of~$K$ that contains all the infinite places, and let $\\theints$ be the ring of $S$-integers of~$K$. We define a certain closed subgroup~$\\GOS$ of $\\Ga_S = \\prod_{v \\in S} \\Ga_{K_v}$ that contains $\\Ga_{\\theints}$, and prove that $\\Ga_{\\theints}$ is a superrigid lattice in~$\\GOS$, by which we mean that finite-dimensional representations $\\alpha\\colon \\Ga_{\\theints} \\to \\GL_n(\\real)$ more-or-less extend to representations of~$\\GOS$.\n  The subgroup~$\\GOS$ may be a proper subgroup "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611219","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvEbiZq0U/MBVXvV2he6FqO8lrfrg7TQEq/WPMVEoFhwOLlhXaDAEPqvLbLwrdCwIKeErlwn45AAAmCXHdcnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:22:31.347128Z"},"content_sha256":"ebbef013f87bf9b27c0c6588f37d9f97445297207274e74a6b49734521a4eddc","schema_version":"1.0","event_id":"sha256:ebbef013f87bf9b27c0c6588f37d9f97445297207274e74a6b49734521a4eddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/bundle.json","state_url":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMK7GC7D2INML75SKTJKWZTWKN/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":"2026-06-21T14:22:31Z","links":{"resolver":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN","bundle":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/bundle.json","state":"https://pith.science/pith/LMK7GC7D2INML75SKTJKWZTWKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMK7GC7D2INML75SKTJKWZTWKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:LMK7GC7D2INML75SKTJKWZTWKN","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":"862ed128d7c4bbf5c325aba68ee725fd02876cf3547c331f2db1829235e770d9","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","title_canon_sha256":"4ae68e4f633a8d69715774b2cda7bf7a723161e67506ac81a121ec872d2f2df8"},"schema_version":"1.0","source":{"id":"math/9611219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9611219","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/9611219v1","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9611219","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"LMK7GC7D2INM","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"LMK7GC7D2INML75S","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"LMK7GC7D","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:ebbef013f87bf9b27c0c6588f37d9f97445297207274e74a6b49734521a4eddc","target":"graph","created_at":"2026-05-18T01:05:46Z","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":"Let $\\Ga$ be a connected, solvable linear algebraic group over a number field~$K$, let $S$ be a finite set of places of~$K$ that contains all the infinite places, and let $\\theints$ be the ring of $S$-integers of~$K$. We define a certain closed subgroup~$\\GOS$ of $\\Ga_S = \\prod_{v \\in S} \\Ga_{K_v}$ that contains $\\Ga_{\\theints}$, and prove that $\\Ga_{\\theints}$ is a superrigid lattice in~$\\GOS$, by which we mean that finite-dimensional representations $\\alpha\\colon \\Ga_{\\theints} \\to \\GL_n(\\real)$ more-or-less extend to representations of~$\\GOS$.\n  The subgroup~$\\GOS$ may be a proper subgroup ","authors_text":"Dave Witte","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","title":"Archimedean superrigidity of solvable S-arithmetic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611219","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":"sha256:609ced681ef59096219019ca072c4d57cae7d8c7e57a4a72fe7a8dec55040d33","target":"record","created_at":"2026-05-18T01:05:46Z","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":"862ed128d7c4bbf5c325aba68ee725fd02876cf3547c331f2db1829235e770d9","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.RT","submitted_at":"1996-11-19T00:00:00Z","title_canon_sha256":"4ae68e4f633a8d69715774b2cda7bf7a723161e67506ac81a121ec872d2f2df8"},"schema_version":"1.0","source":{"id":"math/9611219","kind":"arxiv","version":1}},"canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b15f30be3d21ac5ffb254d2ab66765348799dbecaa451f61ba7009f57df5dd8","first_computed_at":"2026-05-18T01:05:46.879250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.879250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hKruerHvotcqlOgZP1EIN2v/PGABmuV/9i9kPZUfoUG6oMtoNkgtvX0yA6yTF8CJfW+jZaxwxjY7PScKVmBHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.879695Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9611219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:609ced681ef59096219019ca072c4d57cae7d8c7e57a4a72fe7a8dec55040d33","sha256:ebbef013f87bf9b27c0c6588f37d9f97445297207274e74a6b49734521a4eddc"],"state_sha256":"5cc31499c5085b2c8dbcc77542a62820632cc8d111424068724cfe7cec346d6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OQ8uGQYbdb+gJWngXMCqWg7A6WSO+LBtf1D98FgHZlMHWqobAekHceGHEuzrkfru1VlOYNLKEtyI89vlgJfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:22:31.349019Z","bundle_sha256":"d5351042f4a74ae72747e5ab2adcd9b24982e173368bd88b5f3222f09c5f8972"}}