{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:M5P2A3TXR5SJEE2FWM2SJ2PYTX","short_pith_number":"pith:M5P2A3TX","canonical_record":{"source":{"id":"2109.11702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-24T01:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"886ae0fa7be33c7622cb3eb3bc10dda3708bede95ab6b602d470749225a39ce8","abstract_canon_sha256":"33173232c47990b3b773ba2d88969de90d3fa39ecc697b918a7c903b612f7ee0"},"schema_version":"1.0"},"canonical_sha256":"675fa06e778f64921345b33524e9f89dc39bf9ba631d62cfdade2315399460d0","source":{"kind":"arxiv","id":"2109.11702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11702","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11702v1","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11702","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"M5P2A3TXR5SJ","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"M5P2A3TXR5SJEE2F","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"M5P2A3TX","created_at":"2026-07-05T03:17:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:M5P2A3TXR5SJEE2FWM2SJ2PYTX","target":"record","payload":{"canonical_record":{"source":{"id":"2109.11702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-24T01:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"886ae0fa7be33c7622cb3eb3bc10dda3708bede95ab6b602d470749225a39ce8","abstract_canon_sha256":"33173232c47990b3b773ba2d88969de90d3fa39ecc697b918a7c903b612f7ee0"},"schema_version":"1.0"},"canonical_sha256":"675fa06e778f64921345b33524e9f89dc39bf9ba631d62cfdade2315399460d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:17:06.625876Z","signature_b64":"/a4s1g2R8L0/uwjpG0TwN5y06Kzgp0731ht6WNjCgq7uUwrgpeC1yPPbAKXgTzbP8DXo7Ad1HgtJGuPFzEpfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675fa06e778f64921345b33524e9f89dc39bf9ba631d62cfdade2315399460d0","last_reissued_at":"2026-07-05T03:17:06.625392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:17:06.625392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.11702","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":"2026-07-05T03:17:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNOwtN6loY+Dwv0I5/Y4vEi9YdX/GweKxtYz9kRTK1U1Ugml0THDzstjjwTYxWBwHKqO+e78HMom5Yi/UKIpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:59:26.917188Z"},"content_sha256":"af831e1939d3dbb1c348a37cbab41e4dcbbb4f24c6e027f600dda834550053b9","schema_version":"1.0","event_id":"sha256:af831e1939d3dbb1c348a37cbab41e4dcbbb4f24c6e027f600dda834550053b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:M5P2A3TXR5SJEE2FWM2SJ2PYTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable representation theory: beyond the classical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew Snowden","submitted_at":"2021-09-24T01:34:29Z","abstract_excerpt":"The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed as the limit of this non-existent series, were it to exist. We show that the representation theory of this object is well-behaved, and similar to the stable representation theory of orthogonal groups. Our theory is not specific to symmetric trilinear forms, and applies to any kind of tensorial forms. Our results can be also be viewed from the perspective of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11702","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/2109.11702/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":"2026-07-05T03:17:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YPICgtPXfRzCjK+W5wdRkdzG1lF/BGn8vsqeoJwDRhEgE4hvEyM+7VKUDXvosfPRGqsU5Tp6/Gyks2vrHsuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:59:26.917678Z"},"content_sha256":"a3e6c790187abef1654382a3f733548518b0b9b49dcebfc4f94995c4b2095b59","schema_version":"1.0","event_id":"sha256:a3e6c790187abef1654382a3f733548518b0b9b49dcebfc4f94995c4b2095b59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/bundle.json","state_url":"https://pith.science/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/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":"2026-08-09T03:59:26Z","links":{"resolver":"https://pith.science/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX","bundle":"https://pith.science/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/bundle.json","state":"https://pith.science/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5P2A3TXR5SJEE2FWM2SJ2PYTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:M5P2A3TXR5SJEE2FWM2SJ2PYTX","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":"33173232c47990b3b773ba2d88969de90d3fa39ecc697b918a7c903b612f7ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-24T01:34:29Z","title_canon_sha256":"886ae0fa7be33c7622cb3eb3bc10dda3708bede95ab6b602d470749225a39ce8"},"schema_version":"1.0","source":{"id":"2109.11702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.11702","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"2109.11702v1","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.11702","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"M5P2A3TXR5SJ","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"M5P2A3TXR5SJEE2F","created_at":"2026-07-05T03:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"M5P2A3TX","created_at":"2026-07-05T03:17:06Z"}],"graph_snapshots":[{"event_id":"sha256:a3e6c790187abef1654382a3f733548518b0b9b49dcebfc4f94995c4b2095b59","target":"graph","created_at":"2026-07-05T03:17:06Z","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/2109.11702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed as the limit of this non-existent series, were it to exist. We show that the representation theory of this object is well-behaved, and similar to the stable representation theory of orthogonal groups. Our theory is not specific to symmetric trilinear forms, and applies to any kind of tensorial forms. Our results can be also be viewed from the perspective of ","authors_text":"Andrew Snowden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-24T01:34:29Z","title":"Stable representation theory: beyond the classical groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.11702","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:af831e1939d3dbb1c348a37cbab41e4dcbbb4f24c6e027f600dda834550053b9","target":"record","created_at":"2026-07-05T03:17:06Z","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":"33173232c47990b3b773ba2d88969de90d3fa39ecc697b918a7c903b612f7ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-09-24T01:34:29Z","title_canon_sha256":"886ae0fa7be33c7622cb3eb3bc10dda3708bede95ab6b602d470749225a39ce8"},"schema_version":"1.0","source":{"id":"2109.11702","kind":"arxiv","version":1}},"canonical_sha256":"675fa06e778f64921345b33524e9f89dc39bf9ba631d62cfdade2315399460d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"675fa06e778f64921345b33524e9f89dc39bf9ba631d62cfdade2315399460d0","first_computed_at":"2026-07-05T03:17:06.625392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:17:06.625392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/a4s1g2R8L0/uwjpG0TwN5y06Kzgp0731ht6WNjCgq7uUwrgpeC1yPPbAKXgTzbP8DXo7Ad1HgtJGuPFzEpfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:17:06.625876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.11702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af831e1939d3dbb1c348a37cbab41e4dcbbb4f24c6e027f600dda834550053b9","sha256:a3e6c790187abef1654382a3f733548518b0b9b49dcebfc4f94995c4b2095b59"],"state_sha256":"63a426c468cd55e0909682d3215488240fda9ec124e40533f982b589d042777f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLNd1xF5uHiYKFpb80HiFqfcdj/Bbb1XRKA5rk8WHlQWc7j7RUIpxqC9ezvkiy2uBqtrRsV9XA/Lm2nqvo1GAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:59:26.921715Z","bundle_sha256":"fc9bcf3b322d790ff08e4e9200a43a4bdbe0c427d8f309c405a66f0df111def5"}}