{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WUSODU67FNIZ2OWSVX244HZJFW","short_pith_number":"pith:WUSODU67","canonical_record":{"source":{"id":"1111.5032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-21T21:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"40880ede39ce6f25114c164b42ebf0d98e735423fbdb99fccfa1d85bcc9cd704","abstract_canon_sha256":"333f77bfd7ace2f295a3c97b96fcfa2d6a3294484afe7531b12d0feadab00482"},"schema_version":"1.0"},"canonical_sha256":"b524e1d3df2b519d3ad2adf5ce1f292d9713e9d937891a9001d8deed81db4bd1","source":{"kind":"arxiv","id":"1111.5032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5032","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5032v1","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5032","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"WUSODU67FNIZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WUSODU67FNIZ2OWS","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WUSODU67","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WUSODU67FNIZ2OWSVX244HZJFW","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-21T21:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"40880ede39ce6f25114c164b42ebf0d98e735423fbdb99fccfa1d85bcc9cd704","abstract_canon_sha256":"333f77bfd7ace2f295a3c97b96fcfa2d6a3294484afe7531b12d0feadab00482"},"schema_version":"1.0"},"canonical_sha256":"b524e1d3df2b519d3ad2adf5ce1f292d9713e9d937891a9001d8deed81db4bd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:20.877631Z","signature_b64":"2LqlOD0VTGHTtMhDXH8eKvv6kuUyZzn63GPzkppO0n1+jt9ciFSf1bneGqErtlb1P1CiWD4+zD/Ul3KWNUfADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b524e1d3df2b519d3ad2adf5ce1f292d9713e9d937891a9001d8deed81db4bd1","last_reissued_at":"2026-05-18T04:03:20.877204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:20.877204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5032","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":"2026-05-18T04:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nP55CQaJ2m2jkjeU7uxo5r2b6N2znxN0Kx//gZDfC6DBi8SW3q0gPlHsPxP42GvIoiWHMpOoIVPTT3d6R9MbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:27:34.090287Z"},"content_sha256":"cfbe89bdbe0670e309ff94fd833c0d193213cf1b5abbda18ec2cc604acf1a2bf","schema_version":"1.0","event_id":"sha256:cfbe89bdbe0670e309ff94fd833c0d193213cf1b5abbda18ec2cc604acf1a2bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WUSODU67FNIZ2OWSVX244HZJFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Single-qubit unitary gates by graph scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Benjamin A. Blumer, David L. Feder, Michael S. Underwood","submitted_at":"2011-11-21T21:21:28Z","abstract_excerpt":"We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5032","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":"2026-05-18T04:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tz7cTjAnLb96QW3EUBxAhF6eRgKmS/htGIUa0u28tjuqBnUxUMvFuPWvdXUpfhsDHvXGCkqd3tPw2lxZU7bkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:27:34.090650Z"},"content_sha256":"6dc400b03d5e8ad00e603f47ef2450cde6d04609c4ce54b260f11f66d2805ccc","schema_version":"1.0","event_id":"sha256:6dc400b03d5e8ad00e603f47ef2450cde6d04609c4ce54b260f11f66d2805ccc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUSODU67FNIZ2OWSVX244HZJFW/bundle.json","state_url":"https://pith.science/pith/WUSODU67FNIZ2OWSVX244HZJFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUSODU67FNIZ2OWSVX244HZJFW/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":"2026-06-03T04:27:34Z","links":{"resolver":"https://pith.science/pith/WUSODU67FNIZ2OWSVX244HZJFW","bundle":"https://pith.science/pith/WUSODU67FNIZ2OWSVX244HZJFW/bundle.json","state":"https://pith.science/pith/WUSODU67FNIZ2OWSVX244HZJFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUSODU67FNIZ2OWSVX244HZJFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WUSODU67FNIZ2OWSVX244HZJFW","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":"333f77bfd7ace2f295a3c97b96fcfa2d6a3294484afe7531b12d0feadab00482","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-21T21:21:28Z","title_canon_sha256":"40880ede39ce6f25114c164b42ebf0d98e735423fbdb99fccfa1d85bcc9cd704"},"schema_version":"1.0","source":{"id":"1111.5032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5032","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5032v1","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5032","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"WUSODU67FNIZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WUSODU67FNIZ2OWS","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WUSODU67","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:6dc400b03d5e8ad00e603f47ef2450cde6d04609c4ce54b260f11f66d2805ccc","target":"graph","created_at":"2026-05-18T04:03:20Z","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 the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for ","authors_text":"Benjamin A. Blumer, David L. Feder, Michael S. Underwood","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-21T21:21:28Z","title":"Single-qubit unitary gates by graph scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5032","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:cfbe89bdbe0670e309ff94fd833c0d193213cf1b5abbda18ec2cc604acf1a2bf","target":"record","created_at":"2026-05-18T04:03:20Z","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":"333f77bfd7ace2f295a3c97b96fcfa2d6a3294484afe7531b12d0feadab00482","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-21T21:21:28Z","title_canon_sha256":"40880ede39ce6f25114c164b42ebf0d98e735423fbdb99fccfa1d85bcc9cd704"},"schema_version":"1.0","source":{"id":"1111.5032","kind":"arxiv","version":1}},"canonical_sha256":"b524e1d3df2b519d3ad2adf5ce1f292d9713e9d937891a9001d8deed81db4bd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b524e1d3df2b519d3ad2adf5ce1f292d9713e9d937891a9001d8deed81db4bd1","first_computed_at":"2026-05-18T04:03:20.877204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:20.877204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LqlOD0VTGHTtMhDXH8eKvv6kuUyZzn63GPzkppO0n1+jt9ciFSf1bneGqErtlb1P1CiWD4+zD/Ul3KWNUfADg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:20.877631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfbe89bdbe0670e309ff94fd833c0d193213cf1b5abbda18ec2cc604acf1a2bf","sha256:6dc400b03d5e8ad00e603f47ef2450cde6d04609c4ce54b260f11f66d2805ccc"],"state_sha256":"c06a241b6ff9bced4c9129fdc140b9553e9bc51a097a4c79ed20cb31565407c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PA16yuCMRdoUKwvWrKMfqin8w6vvqnXJ775fpKdsWrQ12f3ZC9DcN+ec5ky5Ft7O+apV+R0PMtFjdm0VPFMyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:27:34.092606Z","bundle_sha256":"b4cfbc0ea5adade036a92432d2025918f0bf69172c10ca12e111766c6714b422"}}