{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S7TPSNZCNYPWPR3QJ7DJHEDOPU","short_pith_number":"pith:S7TPSNZC","canonical_record":{"source":{"id":"2605.30428","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T18:00:10Z","cross_cats_sorted":[],"title_canon_sha256":"932c5429faa3ee5d1949a2c2821e8b717f78558289afa30e3f9e2da17b5b75dd","abstract_canon_sha256":"d84fcbd7d4b5193157b6c77bd5a98e0b4fb070507dbf84272fed4c7bb2b905c5"},"schema_version":"1.0"},"canonical_sha256":"97e6f937226e1f67c7704fc693906e7d2b78726b5ad0f63a9c26fceb68969d53","source":{"kind":"arxiv","id":"2605.30428","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30428","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30428v1","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30428","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"S7TPSNZCNYPW","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_16","alias_value":"S7TPSNZCNYPWPR3Q","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_8","alias_value":"S7TPSNZC","created_at":"2026-06-01T00:02:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S7TPSNZCNYPWPR3QJ7DJHEDOPU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30428","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T18:00:10Z","cross_cats_sorted":[],"title_canon_sha256":"932c5429faa3ee5d1949a2c2821e8b717f78558289afa30e3f9e2da17b5b75dd","abstract_canon_sha256":"d84fcbd7d4b5193157b6c77bd5a98e0b4fb070507dbf84272fed4c7bb2b905c5"},"schema_version":"1.0"},"canonical_sha256":"97e6f937226e1f67c7704fc693906e7d2b78726b5ad0f63a9c26fceb68969d53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T00:02:10.520949Z","signature_b64":"1yS7TJ4HHJqVTGiXupzZDlgRfRAzp8oI6IQyqgmQyX7hUWc8cBxmRzovWT1PUalxLofasktGbIqmW7k9TJ7MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e6f937226e1f67c7704fc693906e7d2b78726b5ad0f63a9c26fceb68969d53","last_reissued_at":"2026-06-01T00:02:10.520533Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T00:02:10.520533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30428","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":"2026-06-01T00:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yqXSZXgUT+H2vHXgdoUQrdNLHAnvz1u7gxyC9OARlgjf43Im7xj5MyURheGd8pNiIcu/rpr8mRed8gYUEr+lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:23:18.682243Z"},"content_sha256":"ff4fc67000ff748082fc1a453a0366d0ff40056d97905fe191b083fcd0cfc886","schema_version":"1.0","event_id":"sha256:ff4fc67000ff748082fc1a453a0366d0ff40056d97905fe191b083fcd0cfc886"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S7TPSNZCNYPWPR3QJ7DJHEDOPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph automorphisms to obtain Clifford symmetries in open and closed qudit models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alessandro Ricottone, Charlie Nation, Federico Cerisola, Francesco Martini, Luca Dellantonio, Rick P. A. Simon, Shreya Banerjee","submitted_at":"2026-05-28T18:00:10Z","abstract_excerpt":"In the recent article [arXiv:2605.18966], we demonstrated that finding Clifford symmetries can be mapped to a Graph Automorphism (GA) problem. Here, we provide an algorithm to obtain such symmetries on general qudit systems, that works on the principle of encoding Clifford invariants of a Hamiltonian onto properties of a graph. Labelling Hamiltonian terms as vertices, a permutation of such vertices that respects the Clifford invariants (a GA) is both a valid Clifford, and a symmetry up to phase correction checks. We test this on multiple physical models and discuss the scaling with respect to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30428","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/2605.30428/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":"2026-06-01T00:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4ieXmTtnS5g1U+cz4kXMLkT07sp8b+HliNw8ozkZ+0KHF0KCaLOFjrV1YfQP6ByABTpx5XKsVf4Um/hohOvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:23:18.682642Z"},"content_sha256":"5d26f25edde667be36769be8834d156565e8547f450399985da995b3cd519970","schema_version":"1.0","event_id":"sha256:5d26f25edde667be36769be8834d156565e8547f450399985da995b3cd519970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/bundle.json","state_url":"https://pith.science/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/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":"2026-06-02T10:23:18Z","links":{"resolver":"https://pith.science/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU","bundle":"https://pith.science/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/bundle.json","state":"https://pith.science/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7TPSNZCNYPWPR3QJ7DJHEDOPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S7TPSNZCNYPWPR3QJ7DJHEDOPU","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":"d84fcbd7d4b5193157b6c77bd5a98e0b4fb070507dbf84272fed4c7bb2b905c5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T18:00:10Z","title_canon_sha256":"932c5429faa3ee5d1949a2c2821e8b717f78558289afa30e3f9e2da17b5b75dd"},"schema_version":"1.0","source":{"id":"2605.30428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30428","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30428v1","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30428","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"S7TPSNZCNYPW","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_16","alias_value":"S7TPSNZCNYPWPR3Q","created_at":"2026-06-01T00:02:10Z"},{"alias_kind":"pith_short_8","alias_value":"S7TPSNZC","created_at":"2026-06-01T00:02:10Z"}],"graph_snapshots":[{"event_id":"sha256:5d26f25edde667be36769be8834d156565e8547f450399985da995b3cd519970","target":"graph","created_at":"2026-06-01T00:02:10Z","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/2605.30428/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the recent article [arXiv:2605.18966], we demonstrated that finding Clifford symmetries can be mapped to a Graph Automorphism (GA) problem. Here, we provide an algorithm to obtain such symmetries on general qudit systems, that works on the principle of encoding Clifford invariants of a Hamiltonian onto properties of a graph. Labelling Hamiltonian terms as vertices, a permutation of such vertices that respects the Clifford invariants (a GA) is both a valid Clifford, and a symmetry up to phase correction checks. We test this on multiple physical models and discuss the scaling with respect to ","authors_text":"Alessandro Ricottone, Charlie Nation, Federico Cerisola, Francesco Martini, Luca Dellantonio, Rick P. A. Simon, Shreya Banerjee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T18:00:10Z","title":"Graph automorphisms to obtain Clifford symmetries in open and closed qudit models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30428","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:ff4fc67000ff748082fc1a453a0366d0ff40056d97905fe191b083fcd0cfc886","target":"record","created_at":"2026-06-01T00:02:10Z","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":"d84fcbd7d4b5193157b6c77bd5a98e0b4fb070507dbf84272fed4c7bb2b905c5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T18:00:10Z","title_canon_sha256":"932c5429faa3ee5d1949a2c2821e8b717f78558289afa30e3f9e2da17b5b75dd"},"schema_version":"1.0","source":{"id":"2605.30428","kind":"arxiv","version":1}},"canonical_sha256":"97e6f937226e1f67c7704fc693906e7d2b78726b5ad0f63a9c26fceb68969d53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e6f937226e1f67c7704fc693906e7d2b78726b5ad0f63a9c26fceb68969d53","first_computed_at":"2026-06-01T00:02:10.520533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T00:02:10.520533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1yS7TJ4HHJqVTGiXupzZDlgRfRAzp8oI6IQyqgmQyX7hUWc8cBxmRzovWT1PUalxLofasktGbIqmW7k9TJ7MDQ==","signature_status":"signed_v1","signed_at":"2026-06-01T00:02:10.520949Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff4fc67000ff748082fc1a453a0366d0ff40056d97905fe191b083fcd0cfc886","sha256:5d26f25edde667be36769be8834d156565e8547f450399985da995b3cd519970"],"state_sha256":"e47912672bb35743a24a7ae16931b5d525b771c1421dba353c52f66211469469"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bcmA5D6FzWsyNOmD11Ty27u6JSPNFDngmXxBl91EAswB1TdjMcv3SydJu7WDv25pZSw+7QAhKaSbFE4T4TJPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:23:18.684702Z","bundle_sha256":"8d54a213ee8a3cd0ae112a43f081a9e70a4398e3e32e4ce889ca69d73c1cb3d6"}}