{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PT5JPHDMPAPLILCXHI7XOZPVOS","short_pith_number":"pith:PT5JPHDM","canonical_record":{"source":{"id":"1207.0975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-04T13:30:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"51d7baf16de6c966b62f575ebdff649a008ed6db8bb019f2ac1b20dd695e8d1c","abstract_canon_sha256":"c21b76b6f83dde660bc242997b3e4fd043aa73c78a7f2c1bc59ac9e5ba2b9627"},"schema_version":"1.0"},"canonical_sha256":"7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb","source":{"kind":"arxiv","id":"1207.0975","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0975","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0975v2","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0975","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"PT5JPHDMPAPL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PT5JPHDMPAPLILCX","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PT5JPHDM","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PT5JPHDMPAPLILCXHI7XOZPVOS","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-04T13:30:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"51d7baf16de6c966b62f575ebdff649a008ed6db8bb019f2ac1b20dd695e8d1c","abstract_canon_sha256":"c21b76b6f83dde660bc242997b3e4fd043aa73c78a7f2c1bc59ac9e5ba2b9627"},"schema_version":"1.0"},"canonical_sha256":"7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:17.376909Z","signature_b64":"4FcgSY66dVpgcKC8KrLqw5PzFpZMKUeqheyo1fFDa4QJlz40J06cautTU1EiLgyne6ESXPUvPLiVx3CQ88yeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb","last_reissued_at":"2026-05-18T02:39:17.376479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:17.376479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0975","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8V7cOtYIDhZWhReuZ0gWyt6eVBlFeY7iztEUDTM1wer1Lj026rT8IlfUczLXtjFhbnhSe35SfvGxvsb80nrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:43:45.407425Z"},"content_sha256":"f1301245431679bd1cf1dcdbeb30aca4e777c621be86513ef0778bba08067747","schema_version":"1.0","event_id":"sha256:f1301245431679bd1cf1dcdbeb30aca4e777c621be86513ef0778bba08067747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PT5JPHDMPAPLILCXHI7XOZPVOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Can you compute the operator norm?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.FA","authors_text":"Andreas Thom, Tim Netzer, Tobias Fritz","submitted_at":"2012-07-04T13:30:58Z","abstract_excerpt":"In this note we address various algorithmic problems that arise in the computation of the operator norm in unitary representations of a group on Hilbert space. We show that the operator norm in the universal unitary representation is computable if the group is residually finite-dimensional or amenable with decidable word problem. Moreover, we relate the computability of the operator norm on the product of non-abelian free groups to Kirchberg's QWEP Conjecture, a fundamental open problem in the theory of operator algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0975","kind":"arxiv","version":2},"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":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+rqbDCChjWvv633fqXb6St6sGgcYzOcrtljJeOm8UbM+KBikmXmEfYRwnVjTQTim01DctR/TO7fWAVFztBF5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:43:45.407792Z"},"content_sha256":"10104d66b72c6d8a1918ca16cd9721dc4f31127574c78fac0f3ce841fef8d227","schema_version":"1.0","event_id":"sha256:10104d66b72c6d8a1918ca16cd9721dc4f31127574c78fac0f3ce841fef8d227"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/bundle.json","state_url":"https://pith.science/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/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":"2026-06-25T09:43:45Z","links":{"resolver":"https://pith.science/pith/PT5JPHDMPAPLILCXHI7XOZPVOS","bundle":"https://pith.science/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/bundle.json","state":"https://pith.science/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PT5JPHDMPAPLILCXHI7XOZPVOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PT5JPHDMPAPLILCXHI7XOZPVOS","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":"c21b76b6f83dde660bc242997b3e4fd043aa73c78a7f2c1bc59ac9e5ba2b9627","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-04T13:30:58Z","title_canon_sha256":"51d7baf16de6c966b62f575ebdff649a008ed6db8bb019f2ac1b20dd695e8d1c"},"schema_version":"1.0","source":{"id":"1207.0975","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0975","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0975v2","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0975","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"PT5JPHDMPAPL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PT5JPHDMPAPLILCX","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PT5JPHDM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:10104d66b72c6d8a1918ca16cd9721dc4f31127574c78fac0f3ce841fef8d227","target":"graph","created_at":"2026-05-18T02:39:17Z","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":"In this note we address various algorithmic problems that arise in the computation of the operator norm in unitary representations of a group on Hilbert space. We show that the operator norm in the universal unitary representation is computable if the group is residually finite-dimensional or amenable with decidable word problem. Moreover, we relate the computability of the operator norm on the product of non-abelian free groups to Kirchberg's QWEP Conjecture, a fundamental open problem in the theory of operator algebras.","authors_text":"Andreas Thom, Tim Netzer, Tobias Fritz","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-04T13:30:58Z","title":"Can you compute the operator norm?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0975","kind":"arxiv","version":2},"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:f1301245431679bd1cf1dcdbeb30aca4e777c621be86513ef0778bba08067747","target":"record","created_at":"2026-05-18T02:39:17Z","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":"c21b76b6f83dde660bc242997b3e4fd043aa73c78a7f2c1bc59ac9e5ba2b9627","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-04T13:30:58Z","title_canon_sha256":"51d7baf16de6c966b62f575ebdff649a008ed6db8bb019f2ac1b20dd695e8d1c"},"schema_version":"1.0","source":{"id":"1207.0975","kind":"arxiv","version":2}},"canonical_sha256":"7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cfa979c6c781eb42c573a3f7765f574975f4036e3a61396c8fe21d06c5b5cfb","first_computed_at":"2026-05-18T02:39:17.376479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:17.376479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FcgSY66dVpgcKC8KrLqw5PzFpZMKUeqheyo1fFDa4QJlz40J06cautTU1EiLgyne6ESXPUvPLiVx3CQ88yeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:17.376909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0975","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1301245431679bd1cf1dcdbeb30aca4e777c621be86513ef0778bba08067747","sha256:10104d66b72c6d8a1918ca16cd9721dc4f31127574c78fac0f3ce841fef8d227"],"state_sha256":"b6cdfd9755e945b56bb1cf2d27495883bb3edba762b68d50918006b43ebf7cfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z0rPsnzmzV/o++vXMGJ5I1bNdYk+vvMhotvlSUB1by9SZdaVFj6270geDaVC6fL3iMkedHHqlrB2D0TnO99SCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:43:45.409665Z","bundle_sha256":"e14b96103915b2be20aed595235cf4dff0b185caaa3627218f9e8b31db1fd37e"}}