{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UJ5OFDHQDGYEBJPZREXWIB6X5E","short_pith_number":"pith:UJ5OFDHQ","canonical_record":{"source":{"id":"1908.01096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-03T00:38:56Z","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"title_canon_sha256":"6e1b287599efba25da495c3cf768e2b33df5854361bb37ce27c2d765c9c74b76","abstract_canon_sha256":"2f24cce0ecdef1e034f0e45875447b6b308139d3b3e0fb142077b57449aedc0e"},"schema_version":"1.0"},"canonical_sha256":"a27ae28cf019b040a5f9892f6407d7e932d2c39b098327a5bb91234002a14a40","source":{"kind":"arxiv","id":"1908.01096","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01096","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01096v3","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01096","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"UJ5OFDHQDGYE","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_16","alias_value":"UJ5OFDHQDGYEBJPZ","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_8","alias_value":"UJ5OFDHQ","created_at":"2026-07-05T00:04:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UJ5OFDHQDGYEBJPZREXWIB6X5E","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01096","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-03T00:38:56Z","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"title_canon_sha256":"6e1b287599efba25da495c3cf768e2b33df5854361bb37ce27c2d765c9c74b76","abstract_canon_sha256":"2f24cce0ecdef1e034f0e45875447b6b308139d3b3e0fb142077b57449aedc0e"},"schema_version":"1.0"},"canonical_sha256":"a27ae28cf019b040a5f9892f6407d7e932d2c39b098327a5bb91234002a14a40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:04:43.778214Z","signature_b64":"Tf94UApper1ujTjhzCx+o4S7ffRuludr1uSkjj5+yHxsEjfhE9e2lYjf1L0tcRW4ZqBJLDX8SQL+7C5SrYckDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a27ae28cf019b040a5f9892f6407d7e932d2c39b098327a5bb91234002a14a40","last_reissued_at":"2026-07-05T00:04:43.777791Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:04:43.777791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01096","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":"2026-07-05T00:04:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGp+H0/p+PzJeF7ReHFdmiZHJSZqNT0laiSUcZ+f8x3fi/SthANHBRPYKGRwEYHb/Tx14jXmhjuEznhTx6VNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:24:05.960997Z"},"content_sha256":"8ad65bebbecb22182217ce1fb3ae17e3ab9ddc51588d8143572d0aff96d41fa4","schema_version":"1.0","event_id":"sha256:8ad65bebbecb22182217ce1fb3ae17e3ab9ddc51588d8143572d0aff96d41fa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UJ5OFDHQDGYEBJPZREXWIB6X5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the discrete Wigner function for SU(N)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Diogenes Galetti, Marcelo A. Marchiolli","submitted_at":"2019-08-03T00:38:56Z","abstract_excerpt":"We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group $\\mathrm{SU(N)}$. This general mathematical construction provides a sound pathway to the formulation of a genuinely discrete Wigner function for arbitrary quantum systems described by finite-dimensional state vector spaces. To illustrate our results, we obtain a general discrete Wigner function for the group $\\mathrm{SU(3)}$ and apply this to the study of a partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01096","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01096/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":"2026-07-05T00:04:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzfl1HhAzmJr3Shicxwc2KwxmCPLpVcwzWGmZTEtI445qCOGg0Ah8LeCnBFoDeNmES2KXJYvaiOALmcosBssBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:24:05.961797Z"},"content_sha256":"4b2c3b6b2445b8c85c34ed08c37fc854bcb13d144b52938db1ffd483728b8f95","schema_version":"1.0","event_id":"sha256:4b2c3b6b2445b8c85c34ed08c37fc854bcb13d144b52938db1ffd483728b8f95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/bundle.json","state_url":"https://pith.science/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/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":"2026-08-16T14:24:06Z","links":{"resolver":"https://pith.science/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E","bundle":"https://pith.science/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/bundle.json","state":"https://pith.science/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJ5OFDHQDGYEBJPZREXWIB6X5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UJ5OFDHQDGYEBJPZREXWIB6X5E","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":"2f24cce0ecdef1e034f0e45875447b6b308139d3b3e0fb142077b57449aedc0e","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-03T00:38:56Z","title_canon_sha256":"6e1b287599efba25da495c3cf768e2b33df5854361bb37ce27c2d765c9c74b76"},"schema_version":"1.0","source":{"id":"1908.01096","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01096","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01096v3","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01096","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"UJ5OFDHQDGYE","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_16","alias_value":"UJ5OFDHQDGYEBJPZ","created_at":"2026-07-05T00:04:43Z"},{"alias_kind":"pith_short_8","alias_value":"UJ5OFDHQ","created_at":"2026-07-05T00:04:43Z"}],"graph_snapshots":[{"event_id":"sha256:4b2c3b6b2445b8c85c34ed08c37fc854bcb13d144b52938db1ffd483728b8f95","target":"graph","created_at":"2026-07-05T00:04:43Z","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/1908.01096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group $\\mathrm{SU(N)}$. This general mathematical construction provides a sound pathway to the formulation of a genuinely discrete Wigner function for arbitrary quantum systems described by finite-dimensional state vector spaces. To illustrate our results, we obtain a general discrete Wigner function for the group $\\mathrm{SU(3)}$ and apply this to the study of a partic","authors_text":"Diogenes Galetti, Marcelo A. Marchiolli","cross_cats":["hep-lat","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-03T00:38:56Z","title":"On the discrete Wigner function for SU(N)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01096","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":"sha256:8ad65bebbecb22182217ce1fb3ae17e3ab9ddc51588d8143572d0aff96d41fa4","target":"record","created_at":"2026-07-05T00:04:43Z","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":"2f24cce0ecdef1e034f0e45875447b6b308139d3b3e0fb142077b57449aedc0e","cross_cats_sorted":["hep-lat","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-08-03T00:38:56Z","title_canon_sha256":"6e1b287599efba25da495c3cf768e2b33df5854361bb37ce27c2d765c9c74b76"},"schema_version":"1.0","source":{"id":"1908.01096","kind":"arxiv","version":3}},"canonical_sha256":"a27ae28cf019b040a5f9892f6407d7e932d2c39b098327a5bb91234002a14a40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a27ae28cf019b040a5f9892f6407d7e932d2c39b098327a5bb91234002a14a40","first_computed_at":"2026-07-05T00:04:43.777791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:04:43.777791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tf94UApper1ujTjhzCx+o4S7ffRuludr1uSkjj5+yHxsEjfhE9e2lYjf1L0tcRW4ZqBJLDX8SQL+7C5SrYckDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:04:43.778214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01096","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ad65bebbecb22182217ce1fb3ae17e3ab9ddc51588d8143572d0aff96d41fa4","sha256:4b2c3b6b2445b8c85c34ed08c37fc854bcb13d144b52938db1ffd483728b8f95"],"state_sha256":"8af59219ca3a5d0cb9d33c2b7c3dde7eba701ba38a422f803e2e1d5055e5967d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V31UoWXSpyQ5nANB6zcrzbSbgcJKCz6C4XQy9Duzqu5HzmUkXVXr6lLpUz8N0URvLOB9maSzVzIKtCyLaEAmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:24:06.039293Z","bundle_sha256":"656722d0d5e2db5c519e1a6b5bd79f213c7e3fe2eca65eb14f72f4a10545b92d"}}