{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DA4FDHWAA5VMWKKPLL2AHAIYOJ","short_pith_number":"pith:DA4FDHWA","canonical_record":{"source":{"id":"1712.09940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","cross_cats_sorted":[],"title_canon_sha256":"2777f1deaa3a1caac9233961507d89506120037efe0ea0920cf7bb938e0a5042","abstract_canon_sha256":"b5a8b95cdaa320f5a3a6b88102a3e3ee9851573c7ecca82e78af8c9fb69df55a"},"schema_version":"1.0"},"canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","source":{"kind":"arxiv","id":"1712.09940","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09940","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09940v3","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09940","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"DA4FDHWAA5VM","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DA4FDHWAA5VMWKKP","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DA4FDHWA","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DA4FDHWAA5VMWKKPLL2AHAIYOJ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.09940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","cross_cats_sorted":[],"title_canon_sha256":"2777f1deaa3a1caac9233961507d89506120037efe0ea0920cf7bb938e0a5042","abstract_canon_sha256":"b5a8b95cdaa320f5a3a6b88102a3e3ee9851573c7ecca82e78af8c9fb69df55a"},"schema_version":"1.0"},"canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:15.718401Z","signature_b64":"8msmX+GOGPR07vti8aRNbQDZp7u5ML0q1aKRTeaDRh0vkV3oNveF93ld73FEcF6MoFbMYfLlUBziXIup8xDKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","last_reissued_at":"2026-05-18T00:22:15.717836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:15.717836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.09940","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":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tterlcMpq/DsDeKAuIrFySRfCPqQLgpap5yI9jJv/wfyytkEGGn02r6rwJ3drq+TmW5HHnWBTac6uWiquFjSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:40:37.316591Z"},"content_sha256":"7ecf730b7e9279830b2989b5376a043eab47e9e9d9e1e8141566550ac639d20e","schema_version":"1.0","event_id":"sha256:7ecf730b7e9279830b2989b5376a043eab47e9e9d9e1e8141566550ac639d20e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DA4FDHWAA5VMWKKPLL2AHAIYOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On rank range of interval matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Elena Rubei","submitted_at":"2017-12-28T17:16:37Z","abstract_excerpt":"An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q $ be nonzero natural numbers and let $\\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \\times q$ interval matrix; given a $p \\times q$ matrix $A$ with entries in the set of real numbers, we say that $ A \\in \\mu $ if $a_{i,j} \\in [m_{i,j}, M_{i,j}] $ for any $i,j$. We establish a criterion to say if an interval matrix contains a matrix of rank $1$. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix $\\mu$ with no more than $3$ colum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09940","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":"2026-05-18T00:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biD2tj8r9eAwneuy8fbue1aLKaXT4VrAsrQq8V2aglBt67XwTj9ZVItW+XL1O8YlzdeazzZmLAMTScVDZpBBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T19:40:37.317398Z"},"content_sha256":"758f28cfad5ae2cb1e7ed76cf98234426567ddeaa79382ee71276999c4422e1d","schema_version":"1.0","event_id":"sha256:758f28cfad5ae2cb1e7ed76cf98234426567ddeaa79382ee71276999c4422e1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/bundle.json","state_url":"https://pith.science/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/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":"2026-06-11T19:40:37Z","links":{"resolver":"https://pith.science/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ","bundle":"https://pith.science/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/bundle.json","state":"https://pith.science/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DA4FDHWAA5VMWKKPLL2AHAIYOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DA4FDHWAA5VMWKKPLL2AHAIYOJ","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":"b5a8b95cdaa320f5a3a6b88102a3e3ee9851573c7ecca82e78af8c9fb69df55a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","title_canon_sha256":"2777f1deaa3a1caac9233961507d89506120037efe0ea0920cf7bb938e0a5042"},"schema_version":"1.0","source":{"id":"1712.09940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09940","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09940v3","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09940","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"DA4FDHWAA5VM","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DA4FDHWAA5VMWKKP","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DA4FDHWA","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:758f28cfad5ae2cb1e7ed76cf98234426567ddeaa79382ee71276999c4422e1d","target":"graph","created_at":"2026-05-18T00:22:15Z","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":"An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q $ be nonzero natural numbers and let $\\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \\times q$ interval matrix; given a $p \\times q$ matrix $A$ with entries in the set of real numbers, we say that $ A \\in \\mu $ if $a_{i,j} \\in [m_{i,j}, M_{i,j}] $ for any $i,j$. We establish a criterion to say if an interval matrix contains a matrix of rank $1$. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix $\\mu$ with no more than $3$ colum","authors_text":"Elena Rubei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","title":"On rank range of interval matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09940","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":"sha256:7ecf730b7e9279830b2989b5376a043eab47e9e9d9e1e8141566550ac639d20e","target":"record","created_at":"2026-05-18T00:22:15Z","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":"b5a8b95cdaa320f5a3a6b88102a3e3ee9851573c7ecca82e78af8c9fb69df55a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-28T17:16:37Z","title_canon_sha256":"2777f1deaa3a1caac9233961507d89506120037efe0ea0920cf7bb938e0a5042"},"schema_version":"1.0","source":{"id":"1712.09940","kind":"arxiv","version":3}},"canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1838519ec0076acb294f5af403811872682fcf28ad50ce8f26bdf084ebc9192e","first_computed_at":"2026-05-18T00:22:15.717836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:15.717836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8msmX+GOGPR07vti8aRNbQDZp7u5ML0q1aKRTeaDRh0vkV3oNveF93ld73FEcF6MoFbMYfLlUBziXIup8xDKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:15.718401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ecf730b7e9279830b2989b5376a043eab47e9e9d9e1e8141566550ac639d20e","sha256:758f28cfad5ae2cb1e7ed76cf98234426567ddeaa79382ee71276999c4422e1d"],"state_sha256":"377d00c9f4044a01fcbd73347f019582511e900cc7a5f9969e17f022b282ea64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"785FjYtDkaXf+UqUNaKQMxmB8LflIYHB01WEONCSlTAv2n40jk7IYmPHHZTSiiuK/g0sYJrwWYzXWC22eWasBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T19:40:37.321213Z","bundle_sha256":"593aac7bf1deddc6ba2c085e9eda655e99b4dce0a1dd9547670b100b6576d9f2"}}