{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O6N6HR26GA45UMKRR4C3WD4APM","short_pith_number":"pith:O6N6HR26","canonical_record":{"source":{"id":"1406.4712","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-18T13:42:52Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"422ad32cc7d636670c9e4863564074a469e02009ce214f1c9bd63a4343cae9e0","abstract_canon_sha256":"083fc9b538f9b677b1d91866c8a7d91e9f7a3cf31af575862ba4a69d97d4ad8f"},"schema_version":"1.0"},"canonical_sha256":"779be3c75e3039da31518f05bb0f807b2a67b27c42f74e6f689f8a4c538cbb58","source":{"kind":"arxiv","id":"1406.4712","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4712","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4712v3","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4712","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"O6N6HR26GA45","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6N6HR26GA45UMKR","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6N6HR26","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O6N6HR26GA45UMKRR4C3WD4APM","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4712","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-18T13:42:52Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"422ad32cc7d636670c9e4863564074a469e02009ce214f1c9bd63a4343cae9e0","abstract_canon_sha256":"083fc9b538f9b677b1d91866c8a7d91e9f7a3cf31af575862ba4a69d97d4ad8f"},"schema_version":"1.0"},"canonical_sha256":"779be3c75e3039da31518f05bb0f807b2a67b27c42f74e6f689f8a4c538cbb58","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:32.673014Z","signature_b64":"J8ORwTYKAVN68ENH09Tc64pGXZB9NdBmaXGtzndpcJnRphV5blllW+D3jMv6IykYm15ePzOAptHg2pbznVHJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"779be3c75e3039da31518f05bb0f807b2a67b27c42f74e6f689f8a4c538cbb58","last_reissued_at":"2026-05-18T02:47:32.672485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:32.672485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4712","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGlwcmo92NlWHMycqtLMAPC0ayx2Qa6cK1eFBNqIkDHYpX2sBkF98Qr/W+T7E2DFtHqsiSS0y/C+tBebwJrkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:11:24.256667Z"},"content_sha256":"3877afd0affd09e4b697f8e39e5eaa66658d33479e1fb386956bcd32df572476","schema_version":"1.0","event_id":"sha256:3877afd0affd09e4b697f8e39e5eaa66658d33479e1fb386956bcd32df572476"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O6N6HR26GA45UMKRR4C3WD4APM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for Boolean satisfiability based on generalized orthonormal expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.DS","authors_text":"Virendra Sule","submitted_at":"2014-06-18T13:42:52Z","abstract_excerpt":"This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\\{0,1\\}$ and find all satisfying assignments. The algorithm is based on the application of a well known generalized Boole-Shannon orthonormal (ON) expansion of Boolean functions. A necessary and sufficient consistency condition for a special class of functions was developed in \\cite{sule} using such an expansion. Paper \\cite{sule} develops a condition for consistency of the equation $f(X)=0$ for the special classes of Boolea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4712","kind":"arxiv","version":3},"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":"2026-05-18T02:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpK8QUdNBNMn1Vo/IoVymraqp0UF1oVrMVoVEl7d4AV+MHZ6wx+qSpFNF648ZyUzY64j55ZD2yT5jiMhjHYuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:11:24.257199Z"},"content_sha256":"1e3abe01562c36f9600b46314924ce3cfb13077c02ad56e5f610d084f3ef63e2","schema_version":"1.0","event_id":"sha256:1e3abe01562c36f9600b46314924ce3cfb13077c02ad56e5f610d084f3ef63e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6N6HR26GA45UMKRR4C3WD4APM/bundle.json","state_url":"https://pith.science/pith/O6N6HR26GA45UMKRR4C3WD4APM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6N6HR26GA45UMKRR4C3WD4APM/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":"2026-06-06T11:11:24Z","links":{"resolver":"https://pith.science/pith/O6N6HR26GA45UMKRR4C3WD4APM","bundle":"https://pith.science/pith/O6N6HR26GA45UMKRR4C3WD4APM/bundle.json","state":"https://pith.science/pith/O6N6HR26GA45UMKRR4C3WD4APM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6N6HR26GA45UMKRR4C3WD4APM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O6N6HR26GA45UMKRR4C3WD4APM","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":"083fc9b538f9b677b1d91866c8a7d91e9f7a3cf31af575862ba4a69d97d4ad8f","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-18T13:42:52Z","title_canon_sha256":"422ad32cc7d636670c9e4863564074a469e02009ce214f1c9bd63a4343cae9e0"},"schema_version":"1.0","source":{"id":"1406.4712","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4712","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4712v3","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4712","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"O6N6HR26GA45","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6N6HR26GA45UMKR","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6N6HR26","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:1e3abe01562c36f9600b46314924ce3cfb13077c02ad56e5f610d084f3ef63e2","target":"graph","created_at":"2026-05-18T02:47:32Z","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":"This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\\{0,1\\}$ and find all satisfying assignments. The algorithm is based on the application of a well known generalized Boole-Shannon orthonormal (ON) expansion of Boolean functions. A necessary and sufficient consistency condition for a special class of functions was developed in \\cite{sule} using such an expansion. Paper \\cite{sule} develops a condition for consistency of the equation $f(X)=0$ for the special classes of Boolea","authors_text":"Virendra Sule","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-18T13:42:52Z","title":"An algorithm for Boolean satisfiability based on generalized orthonormal expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4712","kind":"arxiv","version":3},"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":"sha256:3877afd0affd09e4b697f8e39e5eaa66658d33479e1fb386956bcd32df572476","target":"record","created_at":"2026-05-18T02:47:32Z","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":"083fc9b538f9b677b1d91866c8a7d91e9f7a3cf31af575862ba4a69d97d4ad8f","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-18T13:42:52Z","title_canon_sha256":"422ad32cc7d636670c9e4863564074a469e02009ce214f1c9bd63a4343cae9e0"},"schema_version":"1.0","source":{"id":"1406.4712","kind":"arxiv","version":3}},"canonical_sha256":"779be3c75e3039da31518f05bb0f807b2a67b27c42f74e6f689f8a4c538cbb58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"779be3c75e3039da31518f05bb0f807b2a67b27c42f74e6f689f8a4c538cbb58","first_computed_at":"2026-05-18T02:47:32.672485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:32.672485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8ORwTYKAVN68ENH09Tc64pGXZB9NdBmaXGtzndpcJnRphV5blllW+D3jMv6IykYm15ePzOAptHg2pbznVHJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:32.673014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4712","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3877afd0affd09e4b697f8e39e5eaa66658d33479e1fb386956bcd32df572476","sha256:1e3abe01562c36f9600b46314924ce3cfb13077c02ad56e5f610d084f3ef63e2"],"state_sha256":"ad34d749d8332743e6560541d8207eb793e23b3cde16db02b636508aebc88724"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+SorYKNkInngVdxyfJeGQUtR8Z+wAi2hRaknF6POoXSCL4ym2pxapI3rq5RFqhxw0omY0O1mCmIwBNMqHDCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T11:11:24.260768Z","bundle_sha256":"02c614e591dc315f936a12f985277ad7f67570590a2c62104c7d29c148b37ff3"}}