{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2OGBBQXLBP7JH7WCHM5LO5G7B4","short_pith_number":"pith:2OGBBQXL","canonical_record":{"source":{"id":"1603.03075","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"1f254bc363377fa6aa0b19279b6ba0749f66acf065378673d625c344be619dd5","abstract_canon_sha256":"7d80f5d12db20a314d6496994031f27d4f3437c9f2ba5dd2cf43a1f245c743f1"},"schema_version":"1.0"},"canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","source":{"kind":"arxiv","id":"1603.03075","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03075","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03075v3","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03075","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"2OGBBQXLBP7J","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OGBBQXLBP7JH7WC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OGBBQXL","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2OGBBQXLBP7JH7WCHM5LO5G7B4","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03075","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"1f254bc363377fa6aa0b19279b6ba0749f66acf065378673d625c344be619dd5","abstract_canon_sha256":"7d80f5d12db20a314d6496994031f27d4f3437c9f2ba5dd2cf43a1f245c743f1"},"schema_version":"1.0"},"canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:03.055377Z","signature_b64":"9bhDZbh0SnrT6MEjmRLd/INZFOX8ew2rQg6Pk3GZqS5yJ5abGBQXYHE/Z390pXv3xW299y3XVB/pbAAVxKF1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","last_reissued_at":"2026-05-18T00:39:03.054835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:03.054835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03075","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQ9zQh6vaX4F+IP1I7LpahPWhRp4EwxCkdJqFxlb+K3PkJDU1SwDKTBM4+mdKURkPQYuI8XohJWRJ4nACQhrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:05:11.182965Z"},"content_sha256":"61182eef486f5ffede714ad1a8d75159b8e62a6c7e53e9b98c084a59cdace62b","schema_version":"1.0","event_id":"sha256:61182eef486f5ffede714ad1a8d75159b8e62a6c7e53e9b98c084a59cdace62b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2OGBBQXLBP7JH7WCHM5LO5G7B4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fock representations of $Q$-deformed commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Eugene Lytvynov, Janusz Wysocza\\'nski, Marek Bo\\.zejko","submitted_at":"2016-03-08T09:39:05Z","abstract_excerpt":"We consider Fock representations of the $Q$-deformed commutation relations $$\\partial_s\\partial^\\dag_t=Q(s,t)\\partial_t^\\dag\\partial_s+\\delta(s,t), \\quad s,t\\in T.$$ Here\n  $T:=\\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the function $Q:T^2\\to \\mathbb C$ satisfies $|Q(s,t)|\\le1$ and $Q(s,t)=\\overline{Q(t,s)}$, and $$\\int_{T^2}h(s)g(t)\\delta(s,t)\\,\\sigma(ds)\\sigma(dt):=\\int_T h(t)g(t)\\,\\sigma(dt),$$\n  $\\sigma$ being a fixed reference measure on $T$. In the case where $|Q(s,t)|\\equiv 1$, the $Q$-deformed commutation relations describe a generalized statistics studied "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03075","kind":"arxiv","version":3},"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":"2026-05-18T00:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgtDU7KgYuunFxPDmtzonWIas0CAcdL9/YOXOWv16BfhAyX2m5H414rVmvdil6TLcEoTJfPbMQ+AOA/RuRzbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T00:05:11.183324Z"},"content_sha256":"42cc1966789127d6b7d474f11e39acbf78813d6cdf630e6dcd142cb6ae70bf76","schema_version":"1.0","event_id":"sha256:42cc1966789127d6b7d474f11e39acbf78813d6cdf630e6dcd142cb6ae70bf76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/bundle.json","state_url":"https://pith.science/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/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":"2026-06-25T00:05:11Z","links":{"resolver":"https://pith.science/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4","bundle":"https://pith.science/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/bundle.json","state":"https://pith.science/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2OGBBQXLBP7JH7WCHM5LO5G7B4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2OGBBQXLBP7JH7WCHM5LO5G7B4","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":"7d80f5d12db20a314d6496994031f27d4f3437c9f2ba5dd2cf43a1f245c743f1","cross_cats_sorted":["math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","title_canon_sha256":"1f254bc363377fa6aa0b19279b6ba0749f66acf065378673d625c344be619dd5"},"schema_version":"1.0","source":{"id":"1603.03075","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03075","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03075v3","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03075","created_at":"2026-05-18T00:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"2OGBBQXLBP7J","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OGBBQXLBP7JH7WC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OGBBQXL","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:42cc1966789127d6b7d474f11e39acbf78813d6cdf630e6dcd142cb6ae70bf76","target":"graph","created_at":"2026-05-18T00:39:03Z","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":"We consider Fock representations of the $Q$-deformed commutation relations $$\\partial_s\\partial^\\dag_t=Q(s,t)\\partial_t^\\dag\\partial_s+\\delta(s,t), \\quad s,t\\in T.$$ Here\n  $T:=\\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the function $Q:T^2\\to \\mathbb C$ satisfies $|Q(s,t)|\\le1$ and $Q(s,t)=\\overline{Q(t,s)}$, and $$\\int_{T^2}h(s)g(t)\\delta(s,t)\\,\\sigma(ds)\\sigma(dt):=\\int_T h(t)g(t)\\,\\sigma(dt),$$\n  $\\sigma$ being a fixed reference measure on $T$. In the case where $|Q(s,t)|\\equiv 1$, the $Q$-deformed commutation relations describe a generalized statistics studied ","authors_text":"Eugene Lytvynov, Janusz Wysocza\\'nski, Marek Bo\\.zejko","cross_cats":["math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","title":"Fock representations of $Q$-deformed commutation relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03075","kind":"arxiv","version":3},"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":"sha256:61182eef486f5ffede714ad1a8d75159b8e62a6c7e53e9b98c084a59cdace62b","target":"record","created_at":"2026-05-18T00:39:03Z","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":"7d80f5d12db20a314d6496994031f27d4f3437c9f2ba5dd2cf43a1f245c743f1","cross_cats_sorted":["math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","title_canon_sha256":"1f254bc363377fa6aa0b19279b6ba0749f66acf065378673d625c344be619dd5"},"schema_version":"1.0","source":{"id":"1603.03075","kind":"arxiv","version":3}},"canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","first_computed_at":"2026-05-18T00:39:03.054835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:03.054835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9bhDZbh0SnrT6MEjmRLd/INZFOX8ew2rQg6Pk3GZqS5yJ5abGBQXYHE/Z390pXv3xW299y3XVB/pbAAVxKF1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:03.055377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03075","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61182eef486f5ffede714ad1a8d75159b8e62a6c7e53e9b98c084a59cdace62b","sha256:42cc1966789127d6b7d474f11e39acbf78813d6cdf630e6dcd142cb6ae70bf76"],"state_sha256":"0e013d38a38a84092f5d8b892e56bf78256883c4b6ea473dc3af067430ba993b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgHHfm1cxR1n2yrG0rw0RfVNJ7AahJ8JPeLBRngy2b0LtbEidyWkDk6/733b9rYJh2XaoRT0qopOIGmmF6TTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T00:05:11.185252Z","bundle_sha256":"7c6c440746ef512b78f61cd6c50afa7b63da033f2a4c1b5e17eed3a1b4fa219c"}}