{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:GK7N55ID2BKS6L33TFNKPDF5T7","short_pith_number":"pith:GK7N55ID","canonical_record":{"source":{"id":"quant-ph/0212096","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-12-16T22:37:51Z","cross_cats_sorted":[],"title_canon_sha256":"c47e49fa0f95b2631d5576b3e426ec70dfed5353595cb8f9769569b367fac1d8","abstract_canon_sha256":"e8cc6676cdee6ec0b6a32e447035cbb64625b630e320ca6670c1fd69f7ca4814"},"schema_version":"1.0"},"canonical_sha256":"32bedef503d0552f2f7b995aa78cbd9ff5c288f84d452e254cda4f77290da61f","source":{"kind":"arxiv","id":"quant-ph/0212096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0212096","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0212096v1","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0212096","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"GK7N55ID2BKS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"GK7N55ID2BKS6L33","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"GK7N55ID","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:GK7N55ID2BKS6L33TFNKPDF5T7","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0212096","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-12-16T22:37:51Z","cross_cats_sorted":[],"title_canon_sha256":"c47e49fa0f95b2631d5576b3e426ec70dfed5353595cb8f9769569b367fac1d8","abstract_canon_sha256":"e8cc6676cdee6ec0b6a32e447035cbb64625b630e320ca6670c1fd69f7ca4814"},"schema_version":"1.0"},"canonical_sha256":"32bedef503d0552f2f7b995aa78cbd9ff5c288f84d452e254cda4f77290da61f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:04.207363Z","signature_b64":"QraqJ6E5+mwe+8peaHDV9yU9S2CSfIgFgnwwkZke7j46H0ow35vpnILandZzwgjp9Yjvqwzlhth/zco+5PisBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32bedef503d0552f2f7b995aa78cbd9ff5c288f84d452e254cda4f77290da61f","last_reissued_at":"2026-05-18T01:05:04.206688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:04.206688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0212096","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":"2026-05-18T01:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7W+YmrYbtoBPE/YeIz7SBw1Ln6azyjmMaxFyyZro2CGFPdrd4+Ct8qhThHez7QVqpZFX4Cywg8RDzsor2YYTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:24:45.798234Z"},"content_sha256":"c374c4f4dc8ffe44387ccc12e15bdaffaeeee92f6ebd9a71368dd76d26950568","schema_version":"1.0","event_id":"sha256:c374c4f4dc8ffe44387ccc12e15bdaffaeeee92f6ebd9a71368dd76d26950568"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:GK7N55ID2BKS6L33TFNKPDF5T7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A common algebraic description for probabilistic and quantum computations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jose M. Fernandez, Markus Holzer, Martin Beaudry","submitted_at":"2002-12-16T22:37:51Z","abstract_excerpt":"We study the computational complexity of the problem SFT (Sum-free Formula partial Trace): given a tensor formula F over a subsemiring of the complex field (C,+,.) plus a positive integer k, under the restrictions that all inputs are column vectors of L2-norm 1 and norm-preserving square matrices, and that the output matrix is a column vector, decide whether the k-partial trace of $F\\dagg{F}$ is superior to 1/2. The k-partial trace of a matrix is the sum of its lowermost k diagonal elements. We also consider the promise version of this problem, where the 1/2 threshold is an isolated cutpoint. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0212096","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":""},"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":"2026-05-18T01:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6zEsgZo/p7EMBpr1LlcfEH+TcMA6U6mIYpDbhACZrwFe+A+00qY7b6SCpfaJJH7lb/0Q+34C5+B7v6tZnn2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:24:45.798662Z"},"content_sha256":"6b1f689c6703dada5e647c703ed6153a4cf26f23c890439259edb4477b6bfbf4","schema_version":"1.0","event_id":"sha256:6b1f689c6703dada5e647c703ed6153a4cf26f23c890439259edb4477b6bfbf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GK7N55ID2BKS6L33TFNKPDF5T7/bundle.json","state_url":"https://pith.science/pith/GK7N55ID2BKS6L33TFNKPDF5T7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GK7N55ID2BKS6L33TFNKPDF5T7/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":"2026-06-01T15:24:45Z","links":{"resolver":"https://pith.science/pith/GK7N55ID2BKS6L33TFNKPDF5T7","bundle":"https://pith.science/pith/GK7N55ID2BKS6L33TFNKPDF5T7/bundle.json","state":"https://pith.science/pith/GK7N55ID2BKS6L33TFNKPDF5T7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GK7N55ID2BKS6L33TFNKPDF5T7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:GK7N55ID2BKS6L33TFNKPDF5T7","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":"e8cc6676cdee6ec0b6a32e447035cbb64625b630e320ca6670c1fd69f7ca4814","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-12-16T22:37:51Z","title_canon_sha256":"c47e49fa0f95b2631d5576b3e426ec70dfed5353595cb8f9769569b367fac1d8"},"schema_version":"1.0","source":{"id":"quant-ph/0212096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0212096","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0212096v1","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0212096","created_at":"2026-05-18T01:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"GK7N55ID2BKS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"GK7N55ID2BKS6L33","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"GK7N55ID","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:6b1f689c6703dada5e647c703ed6153a4cf26f23c890439259edb4477b6bfbf4","target":"graph","created_at":"2026-05-18T01:05:04Z","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 study the computational complexity of the problem SFT (Sum-free Formula partial Trace): given a tensor formula F over a subsemiring of the complex field (C,+,.) plus a positive integer k, under the restrictions that all inputs are column vectors of L2-norm 1 and norm-preserving square matrices, and that the output matrix is a column vector, decide whether the k-partial trace of $F\\dagg{F}$ is superior to 1/2. The k-partial trace of a matrix is the sum of its lowermost k diagonal elements. We also consider the promise version of this problem, where the 1/2 threshold is an isolated cutpoint. ","authors_text":"Jose M. Fernandez, Markus Holzer, Martin Beaudry","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-12-16T22:37:51Z","title":"A common algebraic description for probabilistic and quantum computations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0212096","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:c374c4f4dc8ffe44387ccc12e15bdaffaeeee92f6ebd9a71368dd76d26950568","target":"record","created_at":"2026-05-18T01:05:04Z","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":"e8cc6676cdee6ec0b6a32e447035cbb64625b630e320ca6670c1fd69f7ca4814","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-12-16T22:37:51Z","title_canon_sha256":"c47e49fa0f95b2631d5576b3e426ec70dfed5353595cb8f9769569b367fac1d8"},"schema_version":"1.0","source":{"id":"quant-ph/0212096","kind":"arxiv","version":1}},"canonical_sha256":"32bedef503d0552f2f7b995aa78cbd9ff5c288f84d452e254cda4f77290da61f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32bedef503d0552f2f7b995aa78cbd9ff5c288f84d452e254cda4f77290da61f","first_computed_at":"2026-05-18T01:05:04.206688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:04.206688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QraqJ6E5+mwe+8peaHDV9yU9S2CSfIgFgnwwkZke7j46H0ow35vpnILandZzwgjp9Yjvqwzlhth/zco+5PisBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:04.207363Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0212096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c374c4f4dc8ffe44387ccc12e15bdaffaeeee92f6ebd9a71368dd76d26950568","sha256:6b1f689c6703dada5e647c703ed6153a4cf26f23c890439259edb4477b6bfbf4"],"state_sha256":"b27d9339a4720b9de93d34d5a6d5de3cfda38b0e6e2032db4324d042d4ae5316"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlao5DWffqEDxBB8rQCRfZjcMxGII9uJb0XsXziej9aVjGuLoBjtdUlqsnR3RCJnJqK7VeftV21QuSfUFMaWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:24:45.800656Z","bundle_sha256":"440fa25db39a6dd7f507f75f7e344d95ede8f1050408cb35b8c29785988435be"}}