{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LTRFX2YH3Y3M3MNHZIWOBQTWXZ","short_pith_number":"pith:LTRFX2YH","canonical_record":{"source":{"id":"1107.3667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-07-19T10:00:22Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"ff4f46a3bb2a7cc18374059a623966c2739476684ff42529d1228421e005b891","abstract_canon_sha256":"caf0281becb7d5ef7cb9b15e3feab5adae5a4c6335d19af4f706bed761880651"},"schema_version":"1.0"},"canonical_sha256":"5ce25beb07de36cdb1a7ca2ce0c276be7d61e3204008de17f0abc064c76b3cc5","source":{"kind":"arxiv","id":"1107.3667","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3667","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3667v1","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3667","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"LTRFX2YH3Y3M","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTRFX2YH3Y3M3MNH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTRFX2YH","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LTRFX2YH3Y3M3MNHZIWOBQTWXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-07-19T10:00:22Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"ff4f46a3bb2a7cc18374059a623966c2739476684ff42529d1228421e005b891","abstract_canon_sha256":"caf0281becb7d5ef7cb9b15e3feab5adae5a4c6335d19af4f706bed761880651"},"schema_version":"1.0"},"canonical_sha256":"5ce25beb07de36cdb1a7ca2ce0c276be7d61e3204008de17f0abc064c76b3cc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:24.245705Z","signature_b64":"yyRIL+nC+gUUoX3JHsWU+lfz+2W6yzy7nioNoWobcQhd6OM9hNWgyk2jNVJ90ccRz6527PLtqOumfyLQH4XRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ce25beb07de36cdb1a7ca2ce0c276be7d61e3204008de17f0abc064c76b3cc5","last_reissued_at":"2026-05-18T04:17:24.245032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:24.245032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3667","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":"2026-05-18T04:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+xjMTZVEoGKzJxfTZM8Hlj0jAGeC6g4pbM/HaynjWFk/BhBSoFz1sHsYV2j/9kLZiF/eGMgm8WDt36tVdL5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:27:23.070513Z"},"content_sha256":"c9e69495e5437c85e8c4dd2b30b90bc5aa6c6539990f4ce9ee2e5f0408e979b8","schema_version":"1.0","event_id":"sha256:c9e69495e5437c85e8c4dd2b30b90bc5aa6c6539990f4ce9ee2e5f0408e979b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LTRFX2YH3Y3M3MNHZIWOBQTWXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new algebraic and arithmetic framework for interval computations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Abdel Kenoufi, Elisabeth Remm, Michel Goze, Nicolas Goze","submitted_at":"2011-07-19T10:00:22Z","abstract_excerpt":"In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3667","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":"2026-05-18T04:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3lVVufA1y+x54gQMhHCGv+pRFCU4zDXUNcBba+VJRpVIDTJX7ubIv21vlcqGFPUUt2rtgA/zrg+zFFnim+1YAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:27:23.071113Z"},"content_sha256":"bcded1136d0320ac43f03657e18dee96a408c8989c33811add8b0c0f16b426d7","schema_version":"1.0","event_id":"sha256:bcded1136d0320ac43f03657e18dee96a408c8989c33811add8b0c0f16b426d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/bundle.json","state_url":"https://pith.science/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/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":"2026-05-25T09:27:23Z","links":{"resolver":"https://pith.science/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ","bundle":"https://pith.science/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/bundle.json","state":"https://pith.science/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTRFX2YH3Y3M3MNHZIWOBQTWXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LTRFX2YH3Y3M3MNHZIWOBQTWXZ","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":"caf0281becb7d5ef7cb9b15e3feab5adae5a4c6335d19af4f706bed761880651","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-07-19T10:00:22Z","title_canon_sha256":"ff4f46a3bb2a7cc18374059a623966c2739476684ff42529d1228421e005b891"},"schema_version":"1.0","source":{"id":"1107.3667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3667","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3667v1","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3667","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"LTRFX2YH3Y3M","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTRFX2YH3Y3M3MNH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTRFX2YH","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:bcded1136d0320ac43f03657e18dee96a408c8989c33811add8b0c0f16b426d7","target":"graph","created_at":"2026-05-18T04:17:24Z","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":"In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python.","authors_text":"Abdel Kenoufi, Elisabeth Remm, Michel Goze, Nicolas Goze","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-07-19T10:00:22Z","title":"A new algebraic and arithmetic framework for interval computations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3667","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:c9e69495e5437c85e8c4dd2b30b90bc5aa6c6539990f4ce9ee2e5f0408e979b8","target":"record","created_at":"2026-05-18T04:17:24Z","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":"caf0281becb7d5ef7cb9b15e3feab5adae5a4c6335d19af4f706bed761880651","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2011-07-19T10:00:22Z","title_canon_sha256":"ff4f46a3bb2a7cc18374059a623966c2739476684ff42529d1228421e005b891"},"schema_version":"1.0","source":{"id":"1107.3667","kind":"arxiv","version":1}},"canonical_sha256":"5ce25beb07de36cdb1a7ca2ce0c276be7d61e3204008de17f0abc064c76b3cc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce25beb07de36cdb1a7ca2ce0c276be7d61e3204008de17f0abc064c76b3cc5","first_computed_at":"2026-05-18T04:17:24.245032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:24.245032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyRIL+nC+gUUoX3JHsWU+lfz+2W6yzy7nioNoWobcQhd6OM9hNWgyk2jNVJ90ccRz6527PLtqOumfyLQH4XRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:24.245705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9e69495e5437c85e8c4dd2b30b90bc5aa6c6539990f4ce9ee2e5f0408e979b8","sha256:bcded1136d0320ac43f03657e18dee96a408c8989c33811add8b0c0f16b426d7"],"state_sha256":"1316900ef0efae06db47d6de2a989247847ade7c8a9db197f578c5747f7c8baa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBHXOqYuk1kyzHguVwGAXjW179DHpM8WQdIM6hAFOAU0+2ox1IxD9Q07MhNzNIpMgx0FAlwyPF3vGyKOl/l5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:27:23.074507Z","bundle_sha256":"8c068cb0cb89a6f8ecb4b1e2c90e13f5123b65bb0801d3ea6d5eb97971835464"}}