{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3OSW3UFYIU4Y2OYTSOMSKNRDL3","short_pith_number":"pith:3OSW3UFY","canonical_record":{"source":{"id":"1412.2341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-07T10:53:38Z","cross_cats_sorted":[],"title_canon_sha256":"1a3fb35928c1733ee7e2fdf5a080d4e53f60a3e4fff6101a1f392264e2d72c17","abstract_canon_sha256":"d4ae4c565748f86e6896c1c1b4a02000a3d9511689932fcaa08390988a4c01e7"},"schema_version":"1.0"},"canonical_sha256":"dba56dd0b845398d3b1393992536235ec7b3e92ecdd65e220df0e6dedc5476f7","source":{"kind":"arxiv","id":"1412.2341","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2341","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2341v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2341","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"3OSW3UFYIU4Y","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3OSW3UFYIU4Y2OYT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3OSW3UFY","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3OSW3UFYIU4Y2OYTSOMSKNRDL3","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-07T10:53:38Z","cross_cats_sorted":[],"title_canon_sha256":"1a3fb35928c1733ee7e2fdf5a080d4e53f60a3e4fff6101a1f392264e2d72c17","abstract_canon_sha256":"d4ae4c565748f86e6896c1c1b4a02000a3d9511689932fcaa08390988a4c01e7"},"schema_version":"1.0"},"canonical_sha256":"dba56dd0b845398d3b1393992536235ec7b3e92ecdd65e220df0e6dedc5476f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:58.255997Z","signature_b64":"+FKVg98QnSyIGoB0jcPHpPVmskf2aEYjBWlwKls6xsNH9VRPbEswOBp3ZX9149SMuwD0x+HQohRY0yN0m6F+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dba56dd0b845398d3b1393992536235ec7b3e92ecdd65e220df0e6dedc5476f7","last_reissued_at":"2026-05-18T02:31:58.255338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:58.255338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2341","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":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAVqudm2WlqYQBCBk1ZCopsb1MFp054ONy1KUluJ3Zc7ow/85EVQY6VlfqJTeTWrH0M3rZgmSbAkpB7iz9/2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:42:04.729825Z"},"content_sha256":"32dc013e36e0977a670ef21a06ea31688f837ff06ce1580e05861627a3063fe6","schema_version":"1.0","event_id":"sha256:32dc013e36e0977a670ef21a06ea31688f837ff06ce1580e05861627a3063fe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3OSW3UFYIU4Y2OYTSOMSKNRDL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized cofactors and decomposition of Boolean satisfiability problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Madhav Desai, Virendra Sule","submitted_at":"2014-12-07T10:53:38Z","abstract_excerpt":"We propose an approach for decomposing Boolean satisfiability problems while extending recent results of \\cite{sul2} on solving Boolean systems of equations. Developments in \\cite{sul2} were aimed at the expansion of functions $f$ in orthonormal (ON) sets of base functions as a generalization of the Boole-Shannon expansion and the derivation of the consistency condition for the equation $f=0$ in terms of the expansion co-efficients. In this paper, we further extend the Boole-Shannon expansion over an arbitrary set of base functions and derive the consistency condition for $f=1$. The generaliza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2341","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":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jzpj45pcPsCOt02jIIhFDeXtV9bBmC4nzrCivKQpDLso2fZa7qZeEKpMyf73xKtzzDl0rbFlKZ4vBC324amkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:42:04.730171Z"},"content_sha256":"26d41e0453f744ae62c3326e290171eb1024f998b0291ff963dc731c958d605f","schema_version":"1.0","event_id":"sha256:26d41e0453f744ae62c3326e290171eb1024f998b0291ff963dc731c958d605f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/bundle.json","state_url":"https://pith.science/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/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":"2026-06-03T05:42:04Z","links":{"resolver":"https://pith.science/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3","bundle":"https://pith.science/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/bundle.json","state":"https://pith.science/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OSW3UFYIU4Y2OYTSOMSKNRDL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3OSW3UFYIU4Y2OYTSOMSKNRDL3","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":"d4ae4c565748f86e6896c1c1b4a02000a3d9511689932fcaa08390988a4c01e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-07T10:53:38Z","title_canon_sha256":"1a3fb35928c1733ee7e2fdf5a080d4e53f60a3e4fff6101a1f392264e2d72c17"},"schema_version":"1.0","source":{"id":"1412.2341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2341","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2341v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2341","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"3OSW3UFYIU4Y","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3OSW3UFYIU4Y2OYT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3OSW3UFY","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:26d41e0453f744ae62c3326e290171eb1024f998b0291ff963dc731c958d605f","target":"graph","created_at":"2026-05-18T02:31:58Z","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":"We propose an approach for decomposing Boolean satisfiability problems while extending recent results of \\cite{sul2} on solving Boolean systems of equations. Developments in \\cite{sul2} were aimed at the expansion of functions $f$ in orthonormal (ON) sets of base functions as a generalization of the Boole-Shannon expansion and the derivation of the consistency condition for the equation $f=0$ in terms of the expansion co-efficients. In this paper, we further extend the Boole-Shannon expansion over an arbitrary set of base functions and derive the consistency condition for $f=1$. The generaliza","authors_text":"Madhav Desai, Virendra Sule","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-07T10:53:38Z","title":"Generalized cofactors and decomposition of Boolean satisfiability problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2341","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":"sha256:32dc013e36e0977a670ef21a06ea31688f837ff06ce1580e05861627a3063fe6","target":"record","created_at":"2026-05-18T02:31:58Z","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":"d4ae4c565748f86e6896c1c1b4a02000a3d9511689932fcaa08390988a4c01e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-07T10:53:38Z","title_canon_sha256":"1a3fb35928c1733ee7e2fdf5a080d4e53f60a3e4fff6101a1f392264e2d72c17"},"schema_version":"1.0","source":{"id":"1412.2341","kind":"arxiv","version":1}},"canonical_sha256":"dba56dd0b845398d3b1393992536235ec7b3e92ecdd65e220df0e6dedc5476f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dba56dd0b845398d3b1393992536235ec7b3e92ecdd65e220df0e6dedc5476f7","first_computed_at":"2026-05-18T02:31:58.255338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:58.255338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+FKVg98QnSyIGoB0jcPHpPVmskf2aEYjBWlwKls6xsNH9VRPbEswOBp3ZX9149SMuwD0x+HQohRY0yN0m6F+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:58.255997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32dc013e36e0977a670ef21a06ea31688f837ff06ce1580e05861627a3063fe6","sha256:26d41e0453f744ae62c3326e290171eb1024f998b0291ff963dc731c958d605f"],"state_sha256":"14a3b2fd0ff22ab407da3be6ab220eb6c524d77f434b3fa39a9e90f5b53337d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1sHgK3R3SYdpig3urhwkNpQjqZXIKpE0YWxMuXZ3c+EijDdxYtcO3HDeZy4XTxDJi+8BbuDTrpHRahZppY9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:42:04.732064Z","bundle_sha256":"80b80aab02a8e8dd38a6a2f58a048d860fc944d07403afb287847ee19532f466"}}