{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:W7CPBIDJVRQTXSZFEN6C5E2V6T","short_pith_number":"pith:W7CPBIDJ","canonical_record":{"source":{"id":"2606.06287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-04T15:25:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"c4c57285e506d6a8ccff8869c330a91fa866aad21dbe9d898627068c5ffcdaf6","abstract_canon_sha256":"c6844654d70939b848973f7514d7a334cbcca81677e2f7e8b67556ea1eae9749"},"schema_version":"1.0"},"canonical_sha256":"b7c4f0a069ac613bcb25237c2e9355f4e9aa8734c5075aaa1378cbf9f81840c1","source":{"kind":"arxiv","id":"2606.06287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06287","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06287v1","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06287","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_12","alias_value":"W7CPBIDJVRQT","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_16","alias_value":"W7CPBIDJVRQTXSZF","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_8","alias_value":"W7CPBIDJ","created_at":"2026-06-05T01:15:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:W7CPBIDJVRQTXSZFEN6C5E2V6T","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-04T15:25:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"c4c57285e506d6a8ccff8869c330a91fa866aad21dbe9d898627068c5ffcdaf6","abstract_canon_sha256":"c6844654d70939b848973f7514d7a334cbcca81677e2f7e8b67556ea1eae9749"},"schema_version":"1.0"},"canonical_sha256":"b7c4f0a069ac613bcb25237c2e9355f4e9aa8734c5075aaa1378cbf9f81840c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:40.598054Z","signature_b64":"GFuVoBx5XYzKaidVU86tqv61v/RCGDHrJEwvYRc7ygJcwA/z9zinjF2OnY1OtduddyshOLRIrQGBjE0sAHfSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c4f0a069ac613bcb25237c2e9355f4e9aa8734c5075aaa1378cbf9f81840c1","last_reissued_at":"2026-06-05T01:15:40.597699Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:40.597699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06287","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":"2026-06-05T01:15:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37/Z8b+nsLKgDK7sEHH7/UUU8o1RhtKWv11RwD+WGEKdP4ficqYek5opVVIAv7xDZptT6Q5D23CgY1eeWdj7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:59:14.918264Z"},"content_sha256":"738de277fc02d967d074cf09e8d88cad160acaa9976a2394ed06b330fcc98605","schema_version":"1.0","event_id":"sha256:738de277fc02d967d074cf09e8d88cad160acaa9976a2394ed06b330fcc98605"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:W7CPBIDJVRQTXSZFEN6C5E2V6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Algorithms for Triangle Cut Sparsification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Pan Peng, Shan Jiang","submitted_at":"2026-06-04T15:25:34Z","abstract_excerpt":"Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis.\n  To enable efficient use of such structures at scale, we study the problem of \\emph{triangle cut sparsification}, which aims to reduce the graph size while approximately preserving triangle counts across every cut.\n  We investigate \\emph{quantum algorithms} for this problem, using triangle listing as our main technical ingredient.\n  In particular, we present a quantum algorithm for triangle listing that, for a graph with $n$ vertices, $m$ edges, and $t$ triangles, r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06287","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/2606.06287/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":"2026-06-05T01:15:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOEoruX1suGGzVgpGBCb3W41XQlMqDNtfajNoqgPcjNjKU3qvQbdq7UBulhrhIE/C7EedXfQMWwUxNeHUqUACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:59:14.918659Z"},"content_sha256":"f9153dfab61c9fe92450358ba14043b0c2c10b396301df8ac6826f6148a9b1e4","schema_version":"1.0","event_id":"sha256:f9153dfab61c9fe92450358ba14043b0c2c10b396301df8ac6826f6148a9b1e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/bundle.json","state_url":"https://pith.science/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/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":"2026-06-05T14:59:14Z","links":{"resolver":"https://pith.science/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T","bundle":"https://pith.science/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/bundle.json","state":"https://pith.science/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7CPBIDJVRQTXSZFEN6C5E2V6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W7CPBIDJVRQTXSZFEN6C5E2V6T","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":"c6844654d70939b848973f7514d7a334cbcca81677e2f7e8b67556ea1eae9749","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-04T15:25:34Z","title_canon_sha256":"c4c57285e506d6a8ccff8869c330a91fa866aad21dbe9d898627068c5ffcdaf6"},"schema_version":"1.0","source":{"id":"2606.06287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06287","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06287v1","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06287","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_12","alias_value":"W7CPBIDJVRQT","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_16","alias_value":"W7CPBIDJVRQTXSZF","created_at":"2026-06-05T01:15:40Z"},{"alias_kind":"pith_short_8","alias_value":"W7CPBIDJ","created_at":"2026-06-05T01:15:40Z"}],"graph_snapshots":[{"event_id":"sha256:f9153dfab61c9fe92450358ba14043b0c2c10b396301df8ac6826f6148a9b1e4","target":"graph","created_at":"2026-06-05T01:15:40Z","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/2606.06287/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis.\n  To enable efficient use of such structures at scale, we study the problem of \\emph{triangle cut sparsification}, which aims to reduce the graph size while approximately preserving triangle counts across every cut.\n  We investigate \\emph{quantum algorithms} for this problem, using triangle listing as our main technical ingredient.\n  In particular, we present a quantum algorithm for triangle listing that, for a graph with $n$ vertices, $m$ edges, and $t$ triangles, r","authors_text":"Pan Peng, Shan Jiang","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-04T15:25:34Z","title":"Quantum Algorithms for Triangle Cut Sparsification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06287","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":"sha256:738de277fc02d967d074cf09e8d88cad160acaa9976a2394ed06b330fcc98605","target":"record","created_at":"2026-06-05T01:15:40Z","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":"c6844654d70939b848973f7514d7a334cbcca81677e2f7e8b67556ea1eae9749","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-04T15:25:34Z","title_canon_sha256":"c4c57285e506d6a8ccff8869c330a91fa866aad21dbe9d898627068c5ffcdaf6"},"schema_version":"1.0","source":{"id":"2606.06287","kind":"arxiv","version":1}},"canonical_sha256":"b7c4f0a069ac613bcb25237c2e9355f4e9aa8734c5075aaa1378cbf9f81840c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c4f0a069ac613bcb25237c2e9355f4e9aa8734c5075aaa1378cbf9f81840c1","first_computed_at":"2026-06-05T01:15:40.597699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:40.597699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GFuVoBx5XYzKaidVU86tqv61v/RCGDHrJEwvYRc7ygJcwA/z9zinjF2OnY1OtduddyshOLRIrQGBjE0sAHfSAw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:40.598054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:738de277fc02d967d074cf09e8d88cad160acaa9976a2394ed06b330fcc98605","sha256:f9153dfab61c9fe92450358ba14043b0c2c10b396301df8ac6826f6148a9b1e4"],"state_sha256":"64257f524d498ca4309462426b94742abce94b87c0635046a0d67751aaca6e2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHotwOEumG+6lk2lou89Wt5jzZx1NWVpgoyoQkvOz+tZbTqxGkW+APGa0T/TRsF1ZnqNnkCmef8JgTkUMZ/tBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:59:14.921118Z","bundle_sha256":"d2c1ecaf32f37e5fd55d478b2cf5e3388514d77e01884d92c5392fb95bd878cd"}}