{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4BCWPEPGBNE5T6MRJQILXVUTUZ","short_pith_number":"pith:4BCWPEPG","canonical_record":{"source":{"id":"1804.10591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-27T16:59:54Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"a83fde10680c2f0076805c3767ceb34a758aab3a0caf4130a3ee1599a6d20287","abstract_canon_sha256":"91fa2e335241cf870ea19f546bcda578a6a12db40c5a8f1940e5c2703b85880d"},"schema_version":"1.0"},"canonical_sha256":"e0456791e60b49d9f9914c10bbd693a679af2ee3d2707642d69e85ddfbea0524","source":{"kind":"arxiv","id":"1804.10591","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10591","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10591v1","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10591","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"4BCWPEPGBNE5","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BCWPEPGBNE5T6MR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BCWPEPG","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4BCWPEPGBNE5T6MRJQILXVUTUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-27T16:59:54Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"a83fde10680c2f0076805c3767ceb34a758aab3a0caf4130a3ee1599a6d20287","abstract_canon_sha256":"91fa2e335241cf870ea19f546bcda578a6a12db40c5a8f1940e5c2703b85880d"},"schema_version":"1.0"},"canonical_sha256":"e0456791e60b49d9f9914c10bbd693a679af2ee3d2707642d69e85ddfbea0524","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:43.504856Z","signature_b64":"e+z1CLtWeTL5p7lQqpIDDyFWTCpszQhU46FbJ/Ac0GtuCA2tZGlErugN5CFCSXmKYTJb4SVNVDWTrBaBDOORCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0456791e60b49d9f9914c10bbd693a679af2ee3d2707642d69e85ddfbea0524","last_reissued_at":"2026-05-18T00:01:43.504341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:43.504341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10591","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":"2026-05-18T00:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6aLFk/ZtIDdyGEueZVwM6tgkrsr/3/37h7ldAXEbeZYPHfx1BNcQkRJCV3w1+uv4J6DENnZcc9K4uoGr1V7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:33:34.196551Z"},"content_sha256":"08123cbfce57a89a29fe91528100a32841653f03b41d36d74e4f8555439935c4","schema_version":"1.0","event_id":"sha256:08123cbfce57a89a29fe91528100a32841653f03b41d36d74e4f8555439935c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4BCWPEPGBNE5T6MRJQILXVUTUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Algorithms for Connectivity and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Alvaro Piedrafita, Michael Jarret, Shelby Kimmel, Stacey Jeffery","submitted_at":"2018-04-27T16:59:54Z","abstract_excerpt":"An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. The complexity of the resulting algorithms depends on the largest positive witness size of any 1-input, and the largest negative witness size of any 0-input. Belovs and Reichardt first showed that the positive witness size is exactly characterized by the effective resistance of the input graph, but only rough upper bounds were known previously on the negative witness size. We show that the neg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10591","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":"2026-05-18T00:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"96Eunw8BgjADyPvpeso33/sfEqNqwTJrpDUiJbaD/eJ+iGfbeSMmNCIqNJzMp6egZ0Lf/Fwn4lzRW6u4NshoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:33:34.197020Z"},"content_sha256":"324705312b9797aaa041015f5dd76314b195a65796236d51eb4732b6953f8a9f","schema_version":"1.0","event_id":"sha256:324705312b9797aaa041015f5dd76314b195a65796236d51eb4732b6953f8a9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/bundle.json","state_url":"https://pith.science/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/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":"2026-05-27T17:33:34Z","links":{"resolver":"https://pith.science/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ","bundle":"https://pith.science/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/bundle.json","state":"https://pith.science/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BCWPEPGBNE5T6MRJQILXVUTUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4BCWPEPGBNE5T6MRJQILXVUTUZ","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":"91fa2e335241cf870ea19f546bcda578a6a12db40c5a8f1940e5c2703b85880d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-27T16:59:54Z","title_canon_sha256":"a83fde10680c2f0076805c3767ceb34a758aab3a0caf4130a3ee1599a6d20287"},"schema_version":"1.0","source":{"id":"1804.10591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10591","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10591v1","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10591","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"4BCWPEPGBNE5","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4BCWPEPGBNE5T6MR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4BCWPEPG","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:324705312b9797aaa041015f5dd76314b195a65796236d51eb4732b6953f8a9f","target":"graph","created_at":"2026-05-18T00:01:43Z","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":"An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. The complexity of the resulting algorithms depends on the largest positive witness size of any 1-input, and the largest negative witness size of any 0-input. Belovs and Reichardt first showed that the positive witness size is exactly characterized by the effective resistance of the input graph, but only rough upper bounds were known previously on the negative witness size. We show that the neg","authors_text":"Alvaro Piedrafita, Michael Jarret, Shelby Kimmel, Stacey Jeffery","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-27T16:59:54Z","title":"Quantum Algorithms for Connectivity and Related Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10591","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":"sha256:08123cbfce57a89a29fe91528100a32841653f03b41d36d74e4f8555439935c4","target":"record","created_at":"2026-05-18T00:01:43Z","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":"91fa2e335241cf870ea19f546bcda578a6a12db40c5a8f1940e5c2703b85880d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-27T16:59:54Z","title_canon_sha256":"a83fde10680c2f0076805c3767ceb34a758aab3a0caf4130a3ee1599a6d20287"},"schema_version":"1.0","source":{"id":"1804.10591","kind":"arxiv","version":1}},"canonical_sha256":"e0456791e60b49d9f9914c10bbd693a679af2ee3d2707642d69e85ddfbea0524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0456791e60b49d9f9914c10bbd693a679af2ee3d2707642d69e85ddfbea0524","first_computed_at":"2026-05-18T00:01:43.504341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:43.504341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e+z1CLtWeTL5p7lQqpIDDyFWTCpszQhU46FbJ/Ac0GtuCA2tZGlErugN5CFCSXmKYTJb4SVNVDWTrBaBDOORCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:43.504856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08123cbfce57a89a29fe91528100a32841653f03b41d36d74e4f8555439935c4","sha256:324705312b9797aaa041015f5dd76314b195a65796236d51eb4732b6953f8a9f"],"state_sha256":"44e6862b3e803054bc3315dff08e8252c827e854bc2be3dd54c45938fdc9a5d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvg0YCVKbHiKJ18BR88YkSRu35wigbXlPnsCDDmetG7pj9n91rX3bjZqUZ0p8OdMUa7qvz3DA3kVofAmFcRlBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:33:34.200549Z","bundle_sha256":"cee1a72023024e43e0f9d793535db3d2d10a5b1795583e01d0c998a9f2307e10"}}