{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IVWGEYZXBGDKBZSXPTX3W3WWIW","short_pith_number":"pith:IVWGEYZX","canonical_record":{"source":{"id":"1401.8213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-31T16:18:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e5ffbdc1cda5b5c7b855019ad72319b2b9cd9db3a641b668882acce379b45f85","abstract_canon_sha256":"a15d07c006a487b1c9ccdc19de1c77c635dab23ba176b4548837c0f0985dabac"},"schema_version":"1.0"},"canonical_sha256":"456c6263370986a0e6577cefbb6ed645a5c628b0c6b85a3c548ae03ebd666140","source":{"kind":"arxiv","id":"1401.8213","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.8213","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.8213v2","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8213","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"IVWGEYZXBGDK","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IVWGEYZXBGDKBZSX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IVWGEYZX","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IVWGEYZXBGDKBZSXPTX3W3WWIW","target":"record","payload":{"canonical_record":{"source":{"id":"1401.8213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-31T16:18:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e5ffbdc1cda5b5c7b855019ad72319b2b9cd9db3a641b668882acce379b45f85","abstract_canon_sha256":"a15d07c006a487b1c9ccdc19de1c77c635dab23ba176b4548837c0f0985dabac"},"schema_version":"1.0"},"canonical_sha256":"456c6263370986a0e6577cefbb6ed645a5c628b0c6b85a3c548ae03ebd666140","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:01.884505Z","signature_b64":"usKiN6JmhEj9giK0fa0ZwNr5WyyK9pEvDVsMsqfYo+slBJSU+Q/PNqF83C2P31ivzR8vE9vjTFQ5yte8TkowAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"456c6263370986a0e6577cefbb6ed645a5c628b0c6b85a3c548ae03ebd666140","last_reissued_at":"2026-05-18T02:44:01.884023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:01.884023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.8213","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":"2026-05-18T02:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSqHzAVnC2ppx8sQeApQeGIOzQ54zfPlShaQifK+d29HGPKK4kAOB7hAwcJrwXoRX2taZMsBNY0upp+AAF8UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:00:06.791445Z"},"content_sha256":"7ffc59f5bbdf0854da10da9cd919c2e5be4494c65da937f0d1bfc3f4065763c8","schema_version":"1.0","event_id":"sha256:7ffc59f5bbdf0854da10da9cd919c2e5be4494c65da937f0d1bfc3f4065763c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IVWGEYZXBGDKBZSXPTX3W3WWIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On graphs and valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Andrei S. Rapinchuk, Ido Efrat, Yoav Segev","submitted_at":"2014-01-31T16:18:57Z","abstract_excerpt":"In the last two decades new techniques emerged to construct valuations on an infinite division ring $D,$ given a normal subgroup $N\\subseteq D$ of finite index. These techniques were based on the commuting graph of $D^{\\times}/N$ in the case where $D$ is non-commutative, and on the Milnor K-graph on $D^{\\times}/N,$ in the case where $D$ is commutative. In this paper we unify these two approaches and consider V-graphs on $D^{\\times}/N$ and how they lead to valuations. We furthermore generalize previous results to situations of finitely many valuations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8213","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":"2026-05-18T02:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5aGFtV6oLtXL5qnqz6ukDFm3tfcloV5kBGFL6DSsOX5Ard0i9huKshIfIQ7LMzXkti+5jo5SxneZdM8r0uH4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:00:06.791789Z"},"content_sha256":"6e34f36c29101cdce45cfd33b80b4faae33ad5bafd01b147f88a70d95156f566","schema_version":"1.0","event_id":"sha256:6e34f36c29101cdce45cfd33b80b4faae33ad5bafd01b147f88a70d95156f566"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/bundle.json","state_url":"https://pith.science/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/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":"2026-05-28T08:00:06Z","links":{"resolver":"https://pith.science/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW","bundle":"https://pith.science/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/bundle.json","state":"https://pith.science/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVWGEYZXBGDKBZSXPTX3W3WWIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IVWGEYZXBGDKBZSXPTX3W3WWIW","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":"a15d07c006a487b1c9ccdc19de1c77c635dab23ba176b4548837c0f0985dabac","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-31T16:18:57Z","title_canon_sha256":"e5ffbdc1cda5b5c7b855019ad72319b2b9cd9db3a641b668882acce379b45f85"},"schema_version":"1.0","source":{"id":"1401.8213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.8213","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1401.8213v2","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8213","created_at":"2026-05-18T02:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"IVWGEYZXBGDK","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IVWGEYZXBGDKBZSX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IVWGEYZX","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6e34f36c29101cdce45cfd33b80b4faae33ad5bafd01b147f88a70d95156f566","target":"graph","created_at":"2026-05-18T02:44:01Z","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 the last two decades new techniques emerged to construct valuations on an infinite division ring $D,$ given a normal subgroup $N\\subseteq D$ of finite index. These techniques were based on the commuting graph of $D^{\\times}/N$ in the case where $D$ is non-commutative, and on the Milnor K-graph on $D^{\\times}/N,$ in the case where $D$ is commutative. In this paper we unify these two approaches and consider V-graphs on $D^{\\times}/N$ and how they lead to valuations. We furthermore generalize previous results to situations of finitely many valuations.","authors_text":"Andrei S. Rapinchuk, Ido Efrat, Yoav Segev","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-31T16:18:57Z","title":"On graphs and valuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8213","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":"sha256:7ffc59f5bbdf0854da10da9cd919c2e5be4494c65da937f0d1bfc3f4065763c8","target":"record","created_at":"2026-05-18T02:44:01Z","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":"a15d07c006a487b1c9ccdc19de1c77c635dab23ba176b4548837c0f0985dabac","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-31T16:18:57Z","title_canon_sha256":"e5ffbdc1cda5b5c7b855019ad72319b2b9cd9db3a641b668882acce379b45f85"},"schema_version":"1.0","source":{"id":"1401.8213","kind":"arxiv","version":2}},"canonical_sha256":"456c6263370986a0e6577cefbb6ed645a5c628b0c6b85a3c548ae03ebd666140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"456c6263370986a0e6577cefbb6ed645a5c628b0c6b85a3c548ae03ebd666140","first_computed_at":"2026-05-18T02:44:01.884023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:01.884023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"usKiN6JmhEj9giK0fa0ZwNr5WyyK9pEvDVsMsqfYo+slBJSU+Q/PNqF83C2P31ivzR8vE9vjTFQ5yte8TkowAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:01.884505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.8213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ffc59f5bbdf0854da10da9cd919c2e5be4494c65da937f0d1bfc3f4065763c8","sha256:6e34f36c29101cdce45cfd33b80b4faae33ad5bafd01b147f88a70d95156f566"],"state_sha256":"6139cde5d84ba6803581bfbd8be33457c4eeab3a3a5f4d3048b97fbbe49274c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhR6JZt0JvgYvMYfXnxpmvQJc7naEITp4Qr5fSgzmwHbxTenqoiIWXV9nARrEWXZ0TRJq+xaw8yvk7Fq+UnzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:00:06.793822Z","bundle_sha256":"522fb753845678dc579927720ddea6f5cbd6795cc7a8585fd0eb286e7a765c3d"}}