{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JDSIODSPPZDFATRT2TCWHRBB7P","short_pith_number":"pith:JDSIODSP","canonical_record":{"source":{"id":"1210.7842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-29T21:10:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"418ab33ffd17e4e61176985762d0bc13d033cc073b045c5a29036e27e6fed1fa","abstract_canon_sha256":"debeaeac6178e3396f4cdac4520fcb678f6d6dabcc15b703dc27505a21892b89"},"schema_version":"1.0"},"canonical_sha256":"48e4870e4f7e46504e33d4c563c421fbf9f2ea952fa68d479d89e632ab3724dc","source":{"kind":"arxiv","id":"1210.7842","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7842","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7842v2","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7842","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"JDSIODSPPZDF","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JDSIODSPPZDFATRT","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JDSIODSP","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JDSIODSPPZDFATRT2TCWHRBB7P","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-29T21:10:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"418ab33ffd17e4e61176985762d0bc13d033cc073b045c5a29036e27e6fed1fa","abstract_canon_sha256":"debeaeac6178e3396f4cdac4520fcb678f6d6dabcc15b703dc27505a21892b89"},"schema_version":"1.0"},"canonical_sha256":"48e4870e4f7e46504e33d4c563c421fbf9f2ea952fa68d479d89e632ab3724dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:23.738860Z","signature_b64":"IU2VY81smnIi0/DklWRIyjDsMhqlqeGuloGhZ8fOGN9r1MXK/mqBTYcnxFlOjpcd9MJy3KNJMorQZ/34lymvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e4870e4f7e46504e33d4c563c421fbf9f2ea952fa68d479d89e632ab3724dc","last_reissued_at":"2026-05-18T02:52:23.738128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:23.738128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7842","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avEayrHPgWtZQ4XhJ8M39inl3gc1DC8FJhOtBiwfnvZ3slWCLZ24tBZNVIV9TMjGGTL03o0qenvi2W0GHoItDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:24:05.862435Z"},"content_sha256":"ca7dcb95ab480acddbd71d6d76e1704650eb139df14058b8d055c3bc7d7f4bf6","schema_version":"1.0","event_id":"sha256:ca7dcb95ab480acddbd71d6d76e1704650eb139df14058b8d055c3bc7d7f4bf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JDSIODSPPZDFATRT2TCWHRBB7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boolean Differential Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Jorge Catumba, Rafael Diaz","submitted_at":"2012-10-29T21:10:07Z","abstract_excerpt":"We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7842","kind":"arxiv","version":2},"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":"2026-05-18T02:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RjxvMQOCg2SgTSBxS6HzPEdS7gKwK9eHistJ+ZK5QuK2RDcZbqJY8unIN61FnNp7J3eMlqPtostcvLAUOX7hBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:24:05.863083Z"},"content_sha256":"196c9d8ce3914cb6e262e3b7b93013b243b9390f40fc3b8dd866fa6566641384","schema_version":"1.0","event_id":"sha256:196c9d8ce3914cb6e262e3b7b93013b243b9390f40fc3b8dd866fa6566641384"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDSIODSPPZDFATRT2TCWHRBB7P/bundle.json","state_url":"https://pith.science/pith/JDSIODSPPZDFATRT2TCWHRBB7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDSIODSPPZDFATRT2TCWHRBB7P/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":"2026-06-07T12:24:05Z","links":{"resolver":"https://pith.science/pith/JDSIODSPPZDFATRT2TCWHRBB7P","bundle":"https://pith.science/pith/JDSIODSPPZDFATRT2TCWHRBB7P/bundle.json","state":"https://pith.science/pith/JDSIODSPPZDFATRT2TCWHRBB7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDSIODSPPZDFATRT2TCWHRBB7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JDSIODSPPZDFATRT2TCWHRBB7P","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":"debeaeac6178e3396f4cdac4520fcb678f6d6dabcc15b703dc27505a21892b89","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-29T21:10:07Z","title_canon_sha256":"418ab33ffd17e4e61176985762d0bc13d033cc073b045c5a29036e27e6fed1fa"},"schema_version":"1.0","source":{"id":"1210.7842","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7842","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7842v2","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7842","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"JDSIODSPPZDF","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JDSIODSPPZDFATRT","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JDSIODSP","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:196c9d8ce3914cb6e262e3b7b93013b243b9390f40fc3b8dd866fa6566641384","target":"graph","created_at":"2026-05-18T02:52:23Z","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 consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.","authors_text":"Jorge Catumba, Rafael Diaz","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-29T21:10:07Z","title":"Boolean Differential Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7842","kind":"arxiv","version":2},"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:ca7dcb95ab480acddbd71d6d76e1704650eb139df14058b8d055c3bc7d7f4bf6","target":"record","created_at":"2026-05-18T02:52:23Z","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":"debeaeac6178e3396f4cdac4520fcb678f6d6dabcc15b703dc27505a21892b89","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-29T21:10:07Z","title_canon_sha256":"418ab33ffd17e4e61176985762d0bc13d033cc073b045c5a29036e27e6fed1fa"},"schema_version":"1.0","source":{"id":"1210.7842","kind":"arxiv","version":2}},"canonical_sha256":"48e4870e4f7e46504e33d4c563c421fbf9f2ea952fa68d479d89e632ab3724dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e4870e4f7e46504e33d4c563c421fbf9f2ea952fa68d479d89e632ab3724dc","first_computed_at":"2026-05-18T02:52:23.738128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:23.738128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IU2VY81smnIi0/DklWRIyjDsMhqlqeGuloGhZ8fOGN9r1MXK/mqBTYcnxFlOjpcd9MJy3KNJMorQZ/34lymvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:23.738860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7842","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca7dcb95ab480acddbd71d6d76e1704650eb139df14058b8d055c3bc7d7f4bf6","sha256:196c9d8ce3914cb6e262e3b7b93013b243b9390f40fc3b8dd866fa6566641384"],"state_sha256":"11a2979e4102acb7e93039ead0b1473115772878af111b0d9b88a1fbd63cd3c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOfzYBOvefMYPTG+d8HSt4lFklQbaJE1wVJ5MSXKbQ/3Ay7Hkdz+Jw+BQtpyvoHxSwGAGsrNIXidWrnK/jiMAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:24:05.867099Z","bundle_sha256":"7a545b6227d660dbaeca2b357e3ba22cd852f731db4c0e0f937c1d1352b2df28"}}