{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7L75CHNJS7QFTJK25YBM2G63LE","short_pith_number":"pith:7L75CHNJ","canonical_record":{"source":{"id":"1503.04346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-14T20:40:26Z","cross_cats_sorted":[],"title_canon_sha256":"7fd77144df9a64c415fb58133d41fb6b2100f2c5f804e0396fa0712d9df9f4d3","abstract_canon_sha256":"e70517ef56071ec8aad80f0a189267d4bad196e01509d6aac5c4ab09db1ad571"},"schema_version":"1.0"},"canonical_sha256":"faffd11da997e059a55aee02cd1bdb59071a0a852a4b009ab968856ffbf7a171","source":{"kind":"arxiv","id":"1503.04346","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04346","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04346v2","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04346","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"7L75CHNJS7QF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L75CHNJS7QFTJK2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L75CHNJ","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7L75CHNJS7QFTJK25YBM2G63LE","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-14T20:40:26Z","cross_cats_sorted":[],"title_canon_sha256":"7fd77144df9a64c415fb58133d41fb6b2100f2c5f804e0396fa0712d9df9f4d3","abstract_canon_sha256":"e70517ef56071ec8aad80f0a189267d4bad196e01509d6aac5c4ab09db1ad571"},"schema_version":"1.0"},"canonical_sha256":"faffd11da997e059a55aee02cd1bdb59071a0a852a4b009ab968856ffbf7a171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:55.559697Z","signature_b64":"gnC2wcGP2jHFBK3J9ChkdgIEWTiwUHwS30mTV4V4AaLmFWwy64qpNCK3BTLSDt/+qvS4AuipQ4MI9TXmVxBXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faffd11da997e059a55aee02cd1bdb59071a0a852a4b009ab968856ffbf7a171","last_reissued_at":"2026-05-18T00:17:55.559180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:55.559180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04346","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":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jEr0B0aiQoy9hTOyM2petaY515ZgpbMJvJXYyU1hWuQLR1WaZYoNLautDVZGhdcGIDQBdhrp0oqG3cSTIOk6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:50:34.554976Z"},"content_sha256":"f2ba6219413a3ab18fb2adcb49f5da9824c20c22f504338f6bdd9414ec851906","schema_version":"1.0","event_id":"sha256:f2ba6219413a3ab18fb2adcb49f5da9824c20c22f504338f6bdd9414ec851906"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7L75CHNJS7QFTJK25YBM2G63LE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Archimedean classes of matrices over ordered fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jaka Cimpric","submitted_at":"2015-03-14T20:40:26Z","abstract_excerpt":"Let $(F,\\le)$ be an ordered field and let $A,B$ be square matrices over $F$ of the same size. We say that $A$ and $B$ belong to the same archimedean class if there exists an integer $r$ such that the matrices $r A^T A-B^T B$ and $r B^T B-A^T A$ are positive semidefinite with respect to $\\le$. We show that this is true if and only if $A=CB$ for some invertible matrix $C$ such that all entries of $C$ and $C^{-1}$ are bounded by some integer. We also show that every archimedean class contains a row echelon form and that its shape and archimedean classes (in $F$) of its pivots are uniquely determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04346","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":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8r+YnjEf5un/MSy+cpC67TzOlJMZUzbewDcfEjS8o4yy+3Jd7yxnnpjPNClkmeazt4fdLwwURGWA6NrSqevYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:50:34.555360Z"},"content_sha256":"63f4d86c80446fec6d5e0b19e9e6c95f110ce3f7abcbcba557677da9fbe6b13a","schema_version":"1.0","event_id":"sha256:63f4d86c80446fec6d5e0b19e9e6c95f110ce3f7abcbcba557677da9fbe6b13a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7L75CHNJS7QFTJK25YBM2G63LE/bundle.json","state_url":"https://pith.science/pith/7L75CHNJS7QFTJK25YBM2G63LE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7L75CHNJS7QFTJK25YBM2G63LE/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":"2026-06-22T08:50:34Z","links":{"resolver":"https://pith.science/pith/7L75CHNJS7QFTJK25YBM2G63LE","bundle":"https://pith.science/pith/7L75CHNJS7QFTJK25YBM2G63LE/bundle.json","state":"https://pith.science/pith/7L75CHNJS7QFTJK25YBM2G63LE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7L75CHNJS7QFTJK25YBM2G63LE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7L75CHNJS7QFTJK25YBM2G63LE","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":"e70517ef56071ec8aad80f0a189267d4bad196e01509d6aac5c4ab09db1ad571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-14T20:40:26Z","title_canon_sha256":"7fd77144df9a64c415fb58133d41fb6b2100f2c5f804e0396fa0712d9df9f4d3"},"schema_version":"1.0","source":{"id":"1503.04346","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04346","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04346v2","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04346","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"7L75CHNJS7QF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7L75CHNJS7QFTJK2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7L75CHNJ","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:63f4d86c80446fec6d5e0b19e9e6c95f110ce3f7abcbcba557677da9fbe6b13a","target":"graph","created_at":"2026-05-18T00:17:55Z","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":"Let $(F,\\le)$ be an ordered field and let $A,B$ be square matrices over $F$ of the same size. We say that $A$ and $B$ belong to the same archimedean class if there exists an integer $r$ such that the matrices $r A^T A-B^T B$ and $r B^T B-A^T A$ are positive semidefinite with respect to $\\le$. We show that this is true if and only if $A=CB$ for some invertible matrix $C$ such that all entries of $C$ and $C^{-1}$ are bounded by some integer. We also show that every archimedean class contains a row echelon form and that its shape and archimedean classes (in $F$) of its pivots are uniquely determi","authors_text":"Jaka Cimpric","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-14T20:40:26Z","title":"Archimedean classes of matrices over ordered fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04346","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:f2ba6219413a3ab18fb2adcb49f5da9824c20c22f504338f6bdd9414ec851906","target":"record","created_at":"2026-05-18T00:17:55Z","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":"e70517ef56071ec8aad80f0a189267d4bad196e01509d6aac5c4ab09db1ad571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-14T20:40:26Z","title_canon_sha256":"7fd77144df9a64c415fb58133d41fb6b2100f2c5f804e0396fa0712d9df9f4d3"},"schema_version":"1.0","source":{"id":"1503.04346","kind":"arxiv","version":2}},"canonical_sha256":"faffd11da997e059a55aee02cd1bdb59071a0a852a4b009ab968856ffbf7a171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faffd11da997e059a55aee02cd1bdb59071a0a852a4b009ab968856ffbf7a171","first_computed_at":"2026-05-18T00:17:55.559180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:55.559180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnC2wcGP2jHFBK3J9ChkdgIEWTiwUHwS30mTV4V4AaLmFWwy64qpNCK3BTLSDt/+qvS4AuipQ4MI9TXmVxBXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:55.559697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04346","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2ba6219413a3ab18fb2adcb49f5da9824c20c22f504338f6bdd9414ec851906","sha256:63f4d86c80446fec6d5e0b19e9e6c95f110ce3f7abcbcba557677da9fbe6b13a"],"state_sha256":"92776a41880523c28bc487fe452f394f6a0070f404435e789e78f3587c46788b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmLh5gqRcHU7Pcuc+IZrITmma8TYk32EkKJpbFf/P1rHZKwjl+nJjHYzh5XCB0Fgu2lu92t7PLJ1K4aQyY7WAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T08:50:34.557417Z","bundle_sha256":"c035e49741116ef4e02f86ce4d8fe4695cad6ff46f3f23fc4bb2aadc72fd1471"}}