{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TCUVVFXG45NRWH7P6L4S3JIOFW","short_pith_number":"pith:TCUVVFXG","canonical_record":{"source":{"id":"2606.01403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-31T19:02:00Z","cross_cats_sorted":[],"title_canon_sha256":"b11177adae5c79554e846398bfa3db493dab12113a9c4da36d9c01b45ac0708b","abstract_canon_sha256":"7129a2940967a9f638a7a3577e867687154a2d7a5a05c9e2982c5f5d77a801a6"},"schema_version":"1.0"},"canonical_sha256":"98a95a96e6e75b1b1feff2f92da50e2d903c3f70de1bb9a2b3e27ec6755497b1","source":{"kind":"arxiv","id":"2606.01403","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01403","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01403v1","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01403","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"TCUVVFXG45NR","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"TCUVVFXG45NRWH7P","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"TCUVVFXG","created_at":"2026-06-02T02:04:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TCUVVFXG45NRWH7P6L4S3JIOFW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-31T19:02:00Z","cross_cats_sorted":[],"title_canon_sha256":"b11177adae5c79554e846398bfa3db493dab12113a9c4da36d9c01b45ac0708b","abstract_canon_sha256":"7129a2940967a9f638a7a3577e867687154a2d7a5a05c9e2982c5f5d77a801a6"},"schema_version":"1.0"},"canonical_sha256":"98a95a96e6e75b1b1feff2f92da50e2d903c3f70de1bb9a2b3e27ec6755497b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:32.439234Z","signature_b64":"MtKzkwzDW5MYYI6l05focK4bSBK07dTPMhK2UMOaYv7DBwx9xX24DRuckgrhjMegih82Q36NIzj11UwEVmzlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98a95a96e6e75b1b1feff2f92da50e2d903c3f70de1bb9a2b3e27ec6755497b1","last_reissued_at":"2026-06-02T02:04:32.438844Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:32.438844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01403","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":"2026-06-02T02:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfkMNGeMRdWeenOqeGiN5Mj1FbMC3fxe29Nq12oNHqpD3AJ/G9KvXJXzQSbZqhSROVcMCADDmZe89BLm5p6uCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:35:31.611085Z"},"content_sha256":"32b9efe32b0366da58a924616b636071871298578bdc390d879b99ae43d9601f","schema_version":"1.0","event_id":"sha256:32b9efe32b0366da58a924616b636071871298578bdc390d879b99ae43d9601f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TCUVVFXG45NRWH7P6L4S3JIOFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial Search by Nonlinear Quantum Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David A. Meyer, Thomas G. Wong","submitted_at":"2026-05-31T19:02:00Z","abstract_excerpt":"Many-body quantum systems with effective nonlinearities have been shown to speed up quantum search on the complete graph, \\textit{i.e.}, the combinatorial version of Grover's algorithm, at the expense of the number of particles needed for the effective nonlinearity to hold. Physically, however, data may not be arranged in an all-to-all network, and the task of searching incomplete graphs is the spatial search problem. We explore spatial search using a continuous-time nonlinear quantum walk on a variety of graphs. First, we consider incomplete graphs that are ``sufficiently complete'' so as to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01403","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/2606.01403/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":"2026-06-02T02:04:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0WL9FJRSrBdv7l1xYoOvA4SKKsXX5svrNOzT5LnqMYNKSmSn7b236BfVofNqfR2TmDAwu0cblXmnwIvFh3kAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:35:31.611798Z"},"content_sha256":"00b2c093fc57d347272cf798732a0cc2ac632262fd850696911ba07c4d4a31d2","schema_version":"1.0","event_id":"sha256:00b2c093fc57d347272cf798732a0cc2ac632262fd850696911ba07c4d4a31d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/bundle.json","state_url":"https://pith.science/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/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":"2026-06-06T16:35:31Z","links":{"resolver":"https://pith.science/pith/TCUVVFXG45NRWH7P6L4S3JIOFW","bundle":"https://pith.science/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/bundle.json","state":"https://pith.science/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCUVVFXG45NRWH7P6L4S3JIOFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TCUVVFXG45NRWH7P6L4S3JIOFW","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":"7129a2940967a9f638a7a3577e867687154a2d7a5a05c9e2982c5f5d77a801a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-31T19:02:00Z","title_canon_sha256":"b11177adae5c79554e846398bfa3db493dab12113a9c4da36d9c01b45ac0708b"},"schema_version":"1.0","source":{"id":"2606.01403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01403","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01403v1","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01403","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_12","alias_value":"TCUVVFXG45NR","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_16","alias_value":"TCUVVFXG45NRWH7P","created_at":"2026-06-02T02:04:32Z"},{"alias_kind":"pith_short_8","alias_value":"TCUVVFXG","created_at":"2026-06-02T02:04:32Z"}],"graph_snapshots":[{"event_id":"sha256:00b2c093fc57d347272cf798732a0cc2ac632262fd850696911ba07c4d4a31d2","target":"graph","created_at":"2026-06-02T02:04:32Z","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/2606.01403/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many-body quantum systems with effective nonlinearities have been shown to speed up quantum search on the complete graph, \\textit{i.e.}, the combinatorial version of Grover's algorithm, at the expense of the number of particles needed for the effective nonlinearity to hold. Physically, however, data may not be arranged in an all-to-all network, and the task of searching incomplete graphs is the spatial search problem. We explore spatial search using a continuous-time nonlinear quantum walk on a variety of graphs. First, we consider incomplete graphs that are ``sufficiently complete'' so as to ","authors_text":"David A. Meyer, Thomas G. Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-31T19:02:00Z","title":"Spatial Search by Nonlinear Quantum Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01403","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":"sha256:32b9efe32b0366da58a924616b636071871298578bdc390d879b99ae43d9601f","target":"record","created_at":"2026-06-02T02:04:32Z","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":"7129a2940967a9f638a7a3577e867687154a2d7a5a05c9e2982c5f5d77a801a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-31T19:02:00Z","title_canon_sha256":"b11177adae5c79554e846398bfa3db493dab12113a9c4da36d9c01b45ac0708b"},"schema_version":"1.0","source":{"id":"2606.01403","kind":"arxiv","version":1}},"canonical_sha256":"98a95a96e6e75b1b1feff2f92da50e2d903c3f70de1bb9a2b3e27ec6755497b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98a95a96e6e75b1b1feff2f92da50e2d903c3f70de1bb9a2b3e27ec6755497b1","first_computed_at":"2026-06-02T02:04:32.438844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:32.438844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MtKzkwzDW5MYYI6l05focK4bSBK07dTPMhK2UMOaYv7DBwx9xX24DRuckgrhjMegih82Q36NIzj11UwEVmzlAw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:32.439234Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32b9efe32b0366da58a924616b636071871298578bdc390d879b99ae43d9601f","sha256:00b2c093fc57d347272cf798732a0cc2ac632262fd850696911ba07c4d4a31d2"],"state_sha256":"54922d39c15464edaede1eb9f7ac6db82c2a1d08702c8bf19a8f5611e446cbc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuackNG97s0PZlZbXVmdwSxZ0kMBN00vio7PxLhGPmCYEJ87rodstbsjY5X7O/L5m+BS0/vcETxOfGczA2skAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:35:31.615445Z","bundle_sha256":"abaa9a3a299c4c155e68e78a96afea1e34d4480110e9a23b972081b8f729c794"}}