{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TSOLDXVYGZXXZYEF64CENC4FDJ","short_pith_number":"pith:TSOLDXVY","canonical_record":{"source":{"id":"1812.00349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-12-02T07:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"35c98ce27679cb1098045d9cca4ccf391b3f5c942fe400a6bc0269905992e468","abstract_canon_sha256":"b172265caac2df0c463578994cf2ed86f536966e1cb1de9e6a3f6cfd4520251e"},"schema_version":"1.0"},"canonical_sha256":"9c9cb1deb8366f7ce085f704468b851a6d7d492a615ab875f18bb584d4a07358","source":{"kind":"arxiv","id":"1812.00349","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00349","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00349v2","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00349","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"TSOLDXVYGZXX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TSOLDXVYGZXXZYEF","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TSOLDXVY","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TSOLDXVYGZXXZYEF64CENC4FDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-12-02T07:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"35c98ce27679cb1098045d9cca4ccf391b3f5c942fe400a6bc0269905992e468","abstract_canon_sha256":"b172265caac2df0c463578994cf2ed86f536966e1cb1de9e6a3f6cfd4520251e"},"schema_version":"1.0"},"canonical_sha256":"9c9cb1deb8366f7ce085f704468b851a6d7d492a615ab875f18bb584d4a07358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:47.120113Z","signature_b64":"+3DNpoYxUa9wcK4mAKvOCXDX7nCKDLu/lrlUe61/UDBm60xBQp9SFPtZ3ShKtg9djczRZrLqwspYFlLh7KzZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c9cb1deb8366f7ce085f704468b851a6d7d492a615ab875f18bb584d4a07358","last_reissued_at":"2026-05-17T23:58:47.119764Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:47.119764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00349","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yUL//853GTdUhsSOoPwbIE0zAZgbZI9qHGW8EZlUoicas1AsQs2z42XV4fHXbD5JJiPPDyL3fHxC69fBIH6tBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:08:45.745858Z"},"content_sha256":"ef1f480bba71caaf2feab6104ff523580bc0ea4a451bd0b50af1e9e1487573c1","schema_version":"1.0","event_id":"sha256:ef1f480bba71caaf2feab6104ff523580bc0ea4a451bd0b50af1e9e1487573c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TSOLDXVYGZXXZYEF64CENC4FDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Logic for Recursive Quantum Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Mingsheng Ying, Shenggang Ying, Zhaowei Xu","submitted_at":"2018-12-02T07:50:45Z","abstract_excerpt":"Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of non-recursive quantum programs. However, there are as yet no general methods for reasoning about recursive procedures in quantum computing. We fill the gap in this paper by presenting a logic for recursive quantum p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00349","kind":"arxiv","version":2},"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":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MFesTUdHjPzgWW//jk/LGKHq3lQ5C1JRzolpAkQmSoybUCC8pqGJWVZ3kUq2QHevwexaIxT2f8tIlQzVIuefBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:08:45.746570Z"},"content_sha256":"4d718b88de21eb204ab44b5dec9bd38b73ec19162707b5b63314d13c7f88e2ef","schema_version":"1.0","event_id":"sha256:4d718b88de21eb204ab44b5dec9bd38b73ec19162707b5b63314d13c7f88e2ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/bundle.json","state_url":"https://pith.science/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/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":"2026-05-22T05:08:45Z","links":{"resolver":"https://pith.science/pith/TSOLDXVYGZXXZYEF64CENC4FDJ","bundle":"https://pith.science/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/bundle.json","state":"https://pith.science/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSOLDXVYGZXXZYEF64CENC4FDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TSOLDXVYGZXXZYEF64CENC4FDJ","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":"b172265caac2df0c463578994cf2ed86f536966e1cb1de9e6a3f6cfd4520251e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-12-02T07:50:45Z","title_canon_sha256":"35c98ce27679cb1098045d9cca4ccf391b3f5c942fe400a6bc0269905992e468"},"schema_version":"1.0","source":{"id":"1812.00349","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00349","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00349v2","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00349","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"TSOLDXVYGZXX","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TSOLDXVYGZXXZYEF","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TSOLDXVY","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4d718b88de21eb204ab44b5dec9bd38b73ec19162707b5b63314d13c7f88e2ef","target":"graph","created_at":"2026-05-17T23:58:47Z","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":"Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of non-recursive quantum programs. However, there are as yet no general methods for reasoning about recursive procedures in quantum computing. We fill the gap in this paper by presenting a logic for recursive quantum p","authors_text":"Mingsheng Ying, Shenggang Ying, Zhaowei Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-12-02T07:50:45Z","title":"A Logic for Recursive Quantum Programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00349","kind":"arxiv","version":2},"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:ef1f480bba71caaf2feab6104ff523580bc0ea4a451bd0b50af1e9e1487573c1","target":"record","created_at":"2026-05-17T23:58:47Z","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":"b172265caac2df0c463578994cf2ed86f536966e1cb1de9e6a3f6cfd4520251e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-12-02T07:50:45Z","title_canon_sha256":"35c98ce27679cb1098045d9cca4ccf391b3f5c942fe400a6bc0269905992e468"},"schema_version":"1.0","source":{"id":"1812.00349","kind":"arxiv","version":2}},"canonical_sha256":"9c9cb1deb8366f7ce085f704468b851a6d7d492a615ab875f18bb584d4a07358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c9cb1deb8366f7ce085f704468b851a6d7d492a615ab875f18bb584d4a07358","first_computed_at":"2026-05-17T23:58:47.119764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:47.119764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+3DNpoYxUa9wcK4mAKvOCXDX7nCKDLu/lrlUe61/UDBm60xBQp9SFPtZ3ShKtg9djczRZrLqwspYFlLh7KzZBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:47.120113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00349","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef1f480bba71caaf2feab6104ff523580bc0ea4a451bd0b50af1e9e1487573c1","sha256:4d718b88de21eb204ab44b5dec9bd38b73ec19162707b5b63314d13c7f88e2ef"],"state_sha256":"353ec5040536d0bca7549183c5327858c2d696605fe749dde6dac12d4aab76ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAwbP6ZonCVrOFFyjbLkR+XIgvMIzPN2JX5ozxV2hgQ83xdK2zN2ovoFBvxkg5wt9vV5IsDewVFsQuEI35JBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T05:08:45.750205Z","bundle_sha256":"d61097cae2b02e986bee3397be2a07b3c7f3bfe60f328249c7cc993260ce063d"}}