{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IGRUFF7G6W4CFW5OHGKRCUT7SN","short_pith_number":"pith:IGRUFF7G","canonical_record":{"source":{"id":"2607.01671","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-02T03:52:23Z","cross_cats_sorted":["cs.DS","cs.IT","cs.LO","math.IT"],"title_canon_sha256":"842ce12c1ca7b9766c0ffee709c5c676b6e328b1ff322f63a3734bb88ee795ba","abstract_canon_sha256":"e00ba91d94421c4956602ced148b71277844fbba1fb12412869d0f75f55f5067"},"schema_version":"1.0"},"canonical_sha256":"41a34297e6f5b822dbae399511527f9375f61a6cbaf0e1dc2c0f14c2e6fdb921","source":{"kind":"arxiv","id":"2607.01671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01671","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01671v1","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01671","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"IGRUFF7G6W4C","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_16","alias_value":"IGRUFF7G6W4CFW5O","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_8","alias_value":"IGRUFF7G","created_at":"2026-07-03T01:17:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IGRUFF7G6W4CFW5OHGKRCUT7SN","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01671","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-02T03:52:23Z","cross_cats_sorted":["cs.DS","cs.IT","cs.LO","math.IT"],"title_canon_sha256":"842ce12c1ca7b9766c0ffee709c5c676b6e328b1ff322f63a3734bb88ee795ba","abstract_canon_sha256":"e00ba91d94421c4956602ced148b71277844fbba1fb12412869d0f75f55f5067"},"schema_version":"1.0"},"canonical_sha256":"41a34297e6f5b822dbae399511527f9375f61a6cbaf0e1dc2c0f14c2e6fdb921","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:26.286693Z","signature_b64":"1ecq+5j55ewyMmekv/iN07rI0bAZr4izjmqcu0N87FSowFzpteRr0vpJYim6ngNdDy5at3o3CtI54mvwaz5SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41a34297e6f5b822dbae399511527f9375f61a6cbaf0e1dc2c0f14c2e6fdb921","last_reissued_at":"2026-07-03T01:17:26.286140Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:26.286140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01671","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":"2026-07-03T01:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMndASpmz7qcDFhaouoVHhmZfsvjf+TvxgsBNn7/SVqWoQPW787hjKM+My1oGWwwNVCIhg1TGVbQUPjXc+gtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T21:30:14.403797Z"},"content_sha256":"3df449fa5598285532359dbe6016d067d322fe2817add774ce2a751f5342a050","schema_version":"1.0","event_id":"sha256:3df449fa5598285532359dbe6016d067d322fe2817add774ce2a751f5342a050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IGRUFF7G6W4CFW5OHGKRCUT7SN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Referential $K$-SAT and the Finite Analogue of G\\\"odel's Incompleteness Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.IT","cs.LO","math.IT"],"primary_cat":"cs.CC","authors_text":"Jie Luo, Jun Liu, Ke Xu, Wen Fang, Xianxian Li, Yongxin Tong","submitted_at":"2026-07-02T03:52:23Z","abstract_excerpt":"Self-reference and solution independence are core properties underlying intractability. This paper establishes a finite combinatorial analogue of G\\\"odel's incompleteness theorems within Boolean $K$-SAT. While standard random $K$-SAT has assignment correlations that disrupt solution independence, we resolve this via a logarithmic-width ensemble ($K = O(\\log N)$). Here, satisfying assignments converge to a Poisson distribution, letting unsatisfiable and uniquely satisfiable formulas coexist. By executing a single-clause substitution conditioned on the unique solution, we construct structurally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01671","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/2607.01671/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":"2026-07-03T01:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OwoyG1rB2HXp4QDVdhiV+kNPv4ZE9SZ1zYd93l9leDHK6vClOiRd7dms+MpalCdHsDXHSdPo3aQsQ9wa7ZeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T21:30:14.404173Z"},"content_sha256":"be8a92c3e5420768659731d06979b9f3f9bc838b451377429b6f5de9544373c6","schema_version":"1.0","event_id":"sha256:be8a92c3e5420768659731d06979b9f3f9bc838b451377429b6f5de9544373c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/bundle.json","state_url":"https://pith.science/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/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":"2026-07-03T21:30:14Z","links":{"resolver":"https://pith.science/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN","bundle":"https://pith.science/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/bundle.json","state":"https://pith.science/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGRUFF7G6W4CFW5OHGKRCUT7SN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IGRUFF7G6W4CFW5OHGKRCUT7SN","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":"e00ba91d94421c4956602ced148b71277844fbba1fb12412869d0f75f55f5067","cross_cats_sorted":["cs.DS","cs.IT","cs.LO","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-02T03:52:23Z","title_canon_sha256":"842ce12c1ca7b9766c0ffee709c5c676b6e328b1ff322f63a3734bb88ee795ba"},"schema_version":"1.0","source":{"id":"2607.01671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01671","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01671v1","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01671","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"IGRUFF7G6W4C","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_16","alias_value":"IGRUFF7G6W4CFW5O","created_at":"2026-07-03T01:17:26Z"},{"alias_kind":"pith_short_8","alias_value":"IGRUFF7G","created_at":"2026-07-03T01:17:26Z"}],"graph_snapshots":[{"event_id":"sha256:be8a92c3e5420768659731d06979b9f3f9bc838b451377429b6f5de9544373c6","target":"graph","created_at":"2026-07-03T01:17:26Z","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/2607.01671/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Self-reference and solution independence are core properties underlying intractability. This paper establishes a finite combinatorial analogue of G\\\"odel's incompleteness theorems within Boolean $K$-SAT. While standard random $K$-SAT has assignment correlations that disrupt solution independence, we resolve this via a logarithmic-width ensemble ($K = O(\\log N)$). Here, satisfying assignments converge to a Poisson distribution, letting unsatisfiable and uniquely satisfiable formulas coexist. By executing a single-clause substitution conditioned on the unique solution, we construct structurally ","authors_text":"Jie Luo, Jun Liu, Ke Xu, Wen Fang, Xianxian Li, Yongxin Tong","cross_cats":["cs.DS","cs.IT","cs.LO","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-02T03:52:23Z","title":"Self-Referential $K$-SAT and the Finite Analogue of G\\\"odel's Incompleteness Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01671","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":"sha256:3df449fa5598285532359dbe6016d067d322fe2817add774ce2a751f5342a050","target":"record","created_at":"2026-07-03T01:17:26Z","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":"e00ba91d94421c4956602ced148b71277844fbba1fb12412869d0f75f55f5067","cross_cats_sorted":["cs.DS","cs.IT","cs.LO","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-07-02T03:52:23Z","title_canon_sha256":"842ce12c1ca7b9766c0ffee709c5c676b6e328b1ff322f63a3734bb88ee795ba"},"schema_version":"1.0","source":{"id":"2607.01671","kind":"arxiv","version":1}},"canonical_sha256":"41a34297e6f5b822dbae399511527f9375f61a6cbaf0e1dc2c0f14c2e6fdb921","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41a34297e6f5b822dbae399511527f9375f61a6cbaf0e1dc2c0f14c2e6fdb921","first_computed_at":"2026-07-03T01:17:26.286140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:26.286140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ecq+5j55ewyMmekv/iN07rI0bAZr4izjmqcu0N87FSowFzpteRr0vpJYim6ngNdDy5at3o3CtI54mvwaz5SBQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:26.286693Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3df449fa5598285532359dbe6016d067d322fe2817add774ce2a751f5342a050","sha256:be8a92c3e5420768659731d06979b9f3f9bc838b451377429b6f5de9544373c6"],"state_sha256":"e5eec6597176d70b055aa41e753bc9200133d44263cb9216391570860e132b68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpC2sP7RWDema7LuwyWErHUDmg7or7jLZk/e1YsmG5nzWAeGm3CXEy+b+dAZwGN+7OIfutSnB9Sr7EAQb2+QAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T21:30:14.408602Z","bundle_sha256":"608951e30b414cd8e7aeaa87b92fbc44b31ca3aae72b9feb67f90933211f064a"}}