{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TLDM7JNCS5MYOYRYEQ4JIQ74WX","short_pith_number":"pith:TLDM7JNC","canonical_record":{"source":{"id":"2606.06656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-06-04T19:03:32Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5b50aaf6c09ddf7bacbc8808db67a43b1668c2958594662af6939e7e28ae5a3e","abstract_canon_sha256":"37fe23de828d8b16c7491755264fa50ebde8e106bc3e7fe64ae3977b320b6d66"},"schema_version":"1.0"},"canonical_sha256":"9ac6cfa5a2975987623824389443fcb5ddfa27881cdf048a06e7edfec6d4c8ce","source":{"kind":"arxiv","id":"2606.06656","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06656","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06656v1","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06656","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"TLDM7JNCS5MY","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"TLDM7JNCS5MYOYRY","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"TLDM7JNC","created_at":"2026-06-08T01:04:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TLDM7JNCS5MYOYRYEQ4JIQ74WX","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-06-04T19:03:32Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5b50aaf6c09ddf7bacbc8808db67a43b1668c2958594662af6939e7e28ae5a3e","abstract_canon_sha256":"37fe23de828d8b16c7491755264fa50ebde8e106bc3e7fe64ae3977b320b6d66"},"schema_version":"1.0"},"canonical_sha256":"9ac6cfa5a2975987623824389443fcb5ddfa27881cdf048a06e7edfec6d4c8ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:21.171217Z","signature_b64":"hLgxzjLS/KbewimbjB3rAfsDgMeiOPWf32w9ie1+WLDNCFJ4KvNmuwhEycd5JDhtxUfJAPgLRdptjKoQ0n/GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ac6cfa5a2975987623824389443fcb5ddfa27881cdf048a06e7edfec6d4c8ce","last_reissued_at":"2026-06-08T01:04:21.170373Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:21.170373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06656","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":"2026-06-08T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmtyumlBC9dBBAazIztn1YN9NI/ozAFZUgGuu7uHDkcC8+9mjYysILqidMl/U35dGRYooiVI+mmbwYTf43IyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:15:48.370770Z"},"content_sha256":"c677b447258419c55b2c3426f99dd9f72b6e1cbe7b910314233a15bca3d58ebe","schema_version":"1.0","event_id":"sha256:c677b447258419c55b2c3426f99dd9f72b6e1cbe7b910314233a15bca3d58ebe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TLDM7JNCS5MYOYRYEQ4JIQ74WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Study of Parallel Continuous Local Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.AI","authors_text":"Charles Gretton, Cody J Christopher","submitted_at":"2026-06-04T19:03:32Z","abstract_excerpt":"We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand. We present several novel findings via empirical experiments: (i) redundant constraints can inhibit rather than accelerate convergen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06656","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/2606.06656/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":"2026-06-08T01:04:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8OFiZ58Lc6yUnjDtGPSrOLRuHU8lPUXuX7NVDUkBHevLUU+0RCzZcJCIcjJceumhGMbL8aby4b8N8rLU9OEIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:15:48.371139Z"},"content_sha256":"f6f67d1f2de3e5fcb58de63be494a123300594c0448f6b85c47811f4d1d7e280","schema_version":"1.0","event_id":"sha256:f6f67d1f2de3e5fcb58de63be494a123300594c0448f6b85c47811f4d1d7e280"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/bundle.json","state_url":"https://pith.science/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/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":"2026-06-29T18:15:48Z","links":{"resolver":"https://pith.science/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX","bundle":"https://pith.science/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/bundle.json","state":"https://pith.science/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLDM7JNCS5MYOYRYEQ4JIQ74WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TLDM7JNCS5MYOYRYEQ4JIQ74WX","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":"37fe23de828d8b16c7491755264fa50ebde8e106bc3e7fe64ae3977b320b6d66","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-06-04T19:03:32Z","title_canon_sha256":"5b50aaf6c09ddf7bacbc8808db67a43b1668c2958594662af6939e7e28ae5a3e"},"schema_version":"1.0","source":{"id":"2606.06656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06656","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06656v1","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06656","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_12","alias_value":"TLDM7JNCS5MY","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_16","alias_value":"TLDM7JNCS5MYOYRY","created_at":"2026-06-08T01:04:21Z"},{"alias_kind":"pith_short_8","alias_value":"TLDM7JNC","created_at":"2026-06-08T01:04:21Z"}],"graph_snapshots":[{"event_id":"sha256:f6f67d1f2de3e5fcb58de63be494a123300594c0448f6b85c47811f4d1d7e280","target":"graph","created_at":"2026-06-08T01:04:21Z","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/2606.06656/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand. We present several novel findings via empirical experiments: (i) redundant constraints can inhibit rather than accelerate convergen","authors_text":"Charles Gretton, Cody J Christopher","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-06-04T19:03:32Z","title":"A Study of Parallel Continuous Local Search"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06656","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:c677b447258419c55b2c3426f99dd9f72b6e1cbe7b910314233a15bca3d58ebe","target":"record","created_at":"2026-06-08T01:04:21Z","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":"37fe23de828d8b16c7491755264fa50ebde8e106bc3e7fe64ae3977b320b6d66","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-06-04T19:03:32Z","title_canon_sha256":"5b50aaf6c09ddf7bacbc8808db67a43b1668c2958594662af6939e7e28ae5a3e"},"schema_version":"1.0","source":{"id":"2606.06656","kind":"arxiv","version":1}},"canonical_sha256":"9ac6cfa5a2975987623824389443fcb5ddfa27881cdf048a06e7edfec6d4c8ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ac6cfa5a2975987623824389443fcb5ddfa27881cdf048a06e7edfec6d4c8ce","first_computed_at":"2026-06-08T01:04:21.170373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:21.170373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hLgxzjLS/KbewimbjB3rAfsDgMeiOPWf32w9ie1+WLDNCFJ4KvNmuwhEycd5JDhtxUfJAPgLRdptjKoQ0n/GAQ==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:21.171217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c677b447258419c55b2c3426f99dd9f72b6e1cbe7b910314233a15bca3d58ebe","sha256:f6f67d1f2de3e5fcb58de63be494a123300594c0448f6b85c47811f4d1d7e280"],"state_sha256":"a0ca540cdd5db81f291d5a5c77a26ec7f76a7b3f0ebe03d812a8d1bbecee614a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"13wwzz9+KKeL2jeXH9JtINbu4zObvrGs+7RIlXAEchaXTuF90Gi7gtorzIN1KqZLTRlDlsI11a48MBo0O8tSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T18:15:48.373392Z","bundle_sha256":"187a8384e6d72a06e6829dff474637305e6d808971ea4b04c1ae93d31bef627f"}}