{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:P4OV7ZL6FL43FCTY5HD4YWWKQ6","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":"fe4d7ad3eda75ee68d9f63597f42af527b1acef5eb7a4cd429282455ae78478b","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-01-26T19:48:41Z","title_canon_sha256":"58a9cd4482bd7ae2ebee18f62ca115102e88af96b3ef3550117c9f4725b4e7b6"},"schema_version":"1.0","source":{"id":"quant-ph/0701194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0701194","created_at":"2026-07-04T14:59:05Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0701194v1","created_at":"2026-07-04T14:59:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0701194","created_at":"2026-07-04T14:59:05Z"},{"alias_kind":"pith_short_12","alias_value":"P4OV7ZL6FL43","created_at":"2026-07-04T14:59:05Z"},{"alias_kind":"pith_short_16","alias_value":"P4OV7ZL6FL43FCTY","created_at":"2026-07-04T14:59:05Z"},{"alias_kind":"pith_short_8","alias_value":"P4OV7ZL6","created_at":"2026-07-04T14:59:05Z"}],"graph_snapshots":[{"event_id":"sha256:2bee02c657b300ecb9df058efd589379011e55acafa790c86acca0018f9537b3","target":"graph","created_at":"2026-07-04T14:59:05Z","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/quant-ph/0701194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natural lower bound of n-1 on circuit depth is nearly tight for a variety of problems, and we prove linear upper bounds for additional problems. In particular, using only gates adding a wire (mod 2) into an adjacent wire, we can realize any linear operation in GL_n(2) as a circuit of depth 5n. We show tha","authors_text":"David Petrie Moulton, Lawren M. Smithline, Samuel A. Kutin","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-01-26T19:48:41Z","title":"Computation at a distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0701194","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":"sha256:54bf12a5d0cc49054b1753a8dd7ef3bd017fd8615936d99b7d65da40a9af2b10","target":"record","created_at":"2026-07-04T14:59:05Z","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":"fe4d7ad3eda75ee68d9f63597f42af527b1acef5eb7a4cd429282455ae78478b","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-01-26T19:48:41Z","title_canon_sha256":"58a9cd4482bd7ae2ebee18f62ca115102e88af96b3ef3550117c9f4725b4e7b6"},"schema_version":"1.0","source":{"id":"quant-ph/0701194","kind":"arxiv","version":1}},"canonical_sha256":"7f1d5fe57e2af9b28a78e9c7cc5aca87b8ec160418a6304b06e70dbdca6e40f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f1d5fe57e2af9b28a78e9c7cc5aca87b8ec160418a6304b06e70dbdca6e40f6","first_computed_at":"2026-07-04T14:59:05.836256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:59:05.836256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewBM0A6Me6g9ceWjJcHW8TugnhM6y4575lAeWsFGjrjahl1WqXACXwdObtSn97j47SxRS7IizQRqr4jt18BTAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:59:05.836634Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0701194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54bf12a5d0cc49054b1753a8dd7ef3bd017fd8615936d99b7d65da40a9af2b10","sha256:2bee02c657b300ecb9df058efd589379011e55acafa790c86acca0018f9537b3"],"state_sha256":"48fad5d55f96eb3600b3dcb64191834bb23831ebdff12399909182f69da69f4d"}