{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HSPRX7BAZ27B6GD3LX5BA5J3ZA","short_pith_number":"pith:HSPRX7BA","canonical_record":{"source":{"id":"1412.0541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-01T16:59:30Z","cross_cats_sorted":[],"title_canon_sha256":"7045e7cb7fcb2d9f40939242d46927637c665dd3bec045f9c63a85d4c5d89af5","abstract_canon_sha256":"99dd457a812c49c9fe87e9a812faebba9a369ec778de491ec19fb81be7541e63"},"schema_version":"1.0"},"canonical_sha256":"3c9f1bfc20cebe1f187b5dfa10753bc82051eb1f7ab1c4003ced0e2bb7195fed","source":{"kind":"arxiv","id":"1412.0541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0541","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0541v1","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0541","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"pith_short_12","alias_value":"HSPRX7BAZ27B","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HSPRX7BAZ27B6GD3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HSPRX7BA","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HSPRX7BAZ27B6GD3LX5BA5J3ZA","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-01T16:59:30Z","cross_cats_sorted":[],"title_canon_sha256":"7045e7cb7fcb2d9f40939242d46927637c665dd3bec045f9c63a85d4c5d89af5","abstract_canon_sha256":"99dd457a812c49c9fe87e9a812faebba9a369ec778de491ec19fb81be7541e63"},"schema_version":"1.0"},"canonical_sha256":"3c9f1bfc20cebe1f187b5dfa10753bc82051eb1f7ab1c4003ced0e2bb7195fed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:23.146385Z","signature_b64":"NY0qsw2lEWivto+PiuLvpGnEv3GJaQBfarTmi2xJGN0R1oC9oHo4Fg8JFM2AZj7vXBbNIoHpb1QkoqURoSKZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c9f1bfc20cebe1f187b5dfa10753bc82051eb1f7ab1c4003ced0e2bb7195fed","last_reissued_at":"2026-05-18T02:32:23.145934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:23.145934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0541","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":"2026-05-18T02:32:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GeJh6rJcxj7l8N177oSyHooaafO2RQaVIPiIh41ghsB7VhK2PKhVSifuIStbgn70dSJtHf8esN2f5J3kYm8nCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:25:08.186962Z"},"content_sha256":"ca7113bf7fbc79a77ed3774070218925ab60850edf15e92e2c16d435cb840ba4","schema_version":"1.0","event_id":"sha256:ca7113bf7fbc79a77ed3774070218925ab60850edf15e92e2c16d435cb840ba4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HSPRX7BAZ27B6GD3LX5BA5J3ZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the diameter of the commuting graph of the full matrix ring over the real numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Antonio Oller-Marcen, Carmen Tasis, Jose Maria Grau","submitted_at":"2014-12-01T16:59:30Z","abstract_excerpt":"In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring $\\mathrm{M}_n(\\mathbb{R})$ is equal to $4$ either if $n=3$ or $n>4$. But the case $n=4$ remained open, since the diameter could be $4$ or $5$. In this work we close the problem showing that also in this case the diameter is equal to $4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0541","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":"2026-05-18T02:32:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5O0UzenKB1mDfJpVxSNnSRZwBpf+f7nEkCbINqi6orIAaEf6kBMwLEv9dNh6CmRjMRYpUoLmlldn1kITGCCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:25:08.187647Z"},"content_sha256":"2f83f4d16028d6fc6c3334b566e56aa7761551f63d66ef7c9b31a7933adb633a","schema_version":"1.0","event_id":"sha256:2f83f4d16028d6fc6c3334b566e56aa7761551f63d66ef7c9b31a7933adb633a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/bundle.json","state_url":"https://pith.science/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/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":"2026-05-25T20:25:08Z","links":{"resolver":"https://pith.science/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA","bundle":"https://pith.science/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/bundle.json","state":"https://pith.science/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSPRX7BAZ27B6GD3LX5BA5J3ZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HSPRX7BAZ27B6GD3LX5BA5J3ZA","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":"99dd457a812c49c9fe87e9a812faebba9a369ec778de491ec19fb81be7541e63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-01T16:59:30Z","title_canon_sha256":"7045e7cb7fcb2d9f40939242d46927637c665dd3bec045f9c63a85d4c5d89af5"},"schema_version":"1.0","source":{"id":"1412.0541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0541","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0541v1","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0541","created_at":"2026-05-18T02:32:23Z"},{"alias_kind":"pith_short_12","alias_value":"HSPRX7BAZ27B","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HSPRX7BAZ27B6GD3","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HSPRX7BA","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:2f83f4d16028d6fc6c3334b566e56aa7761551f63d66ef7c9b31a7933adb633a","target":"graph","created_at":"2026-05-18T02:32:23Z","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":"In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring $\\mathrm{M}_n(\\mathbb{R})$ is equal to $4$ either if $n=3$ or $n>4$. But the case $n=4$ remained open, since the diameter could be $4$ or $5$. In this work we close the problem showing that also in this case the diameter is equal to $4$.","authors_text":"Antonio Oller-Marcen, Carmen Tasis, Jose Maria Grau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-01T16:59:30Z","title":"On the diameter of the commuting graph of the full matrix ring over the real numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0541","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:ca7113bf7fbc79a77ed3774070218925ab60850edf15e92e2c16d435cb840ba4","target":"record","created_at":"2026-05-18T02:32:23Z","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":"99dd457a812c49c9fe87e9a812faebba9a369ec778de491ec19fb81be7541e63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-01T16:59:30Z","title_canon_sha256":"7045e7cb7fcb2d9f40939242d46927637c665dd3bec045f9c63a85d4c5d89af5"},"schema_version":"1.0","source":{"id":"1412.0541","kind":"arxiv","version":1}},"canonical_sha256":"3c9f1bfc20cebe1f187b5dfa10753bc82051eb1f7ab1c4003ced0e2bb7195fed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c9f1bfc20cebe1f187b5dfa10753bc82051eb1f7ab1c4003ced0e2bb7195fed","first_computed_at":"2026-05-18T02:32:23.145934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:23.145934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NY0qsw2lEWivto+PiuLvpGnEv3GJaQBfarTmi2xJGN0R1oC9oHo4Fg8JFM2AZj7vXBbNIoHpb1QkoqURoSKZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:23.146385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca7113bf7fbc79a77ed3774070218925ab60850edf15e92e2c16d435cb840ba4","sha256:2f83f4d16028d6fc6c3334b566e56aa7761551f63d66ef7c9b31a7933adb633a"],"state_sha256":"58a0e81c6e5a7d95317d7ff83060a2a20562d613a8a1a012dda8df69104f375b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhTlIYwFzWVOeqTtAsXmV8T8Bnv6METkqxikB7sznhl10Tbn282UYmOA9Kn0DiQHNxhH48yNSbUEdU5ZrNKaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:25:08.191425Z","bundle_sha256":"3813c97fc6786bc882768c2fd6f196102dd87e34577f46006620c59733dc6cae"}}