{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6QY7TYADREFEXWCI3SS6QDV67N","short_pith_number":"pith:6QY7TYAD","canonical_record":{"source":{"id":"1503.01392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-04T17:15:00Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"6ee2093c8762e91f17da1e3e4487efe08410f65016c07fda5ed4aab1d9bb68c2","abstract_canon_sha256":"aa3b255038de821cbc5198e0f01750da5bfe759b4414d762593a79cc44f5b0ba"},"schema_version":"1.0"},"canonical_sha256":"f431f9e003890a4bd848dca5e80ebefb76aee3a8a85d49e4b20148548777a67d","source":{"kind":"arxiv","id":"1503.01392","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01392","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01392v2","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01392","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"pith_short_12","alias_value":"6QY7TYADREFE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6QY7TYADREFEXWCI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6QY7TYAD","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6QY7TYADREFEXWCI3SS6QDV67N","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-04T17:15:00Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"6ee2093c8762e91f17da1e3e4487efe08410f65016c07fda5ed4aab1d9bb68c2","abstract_canon_sha256":"aa3b255038de821cbc5198e0f01750da5bfe759b4414d762593a79cc44f5b0ba"},"schema_version":"1.0"},"canonical_sha256":"f431f9e003890a4bd848dca5e80ebefb76aee3a8a85d49e4b20148548777a67d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:51.407788Z","signature_b64":"bvtIAd2mMHZOJQSCnrA2luxIZshoRff9wgldxq2pa8AF5IA0nllJ9mqO51aD82FKEznk7kCIklOgaVJqFzG9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f431f9e003890a4bd848dca5e80ebefb76aee3a8a85d49e4b20148548777a67d","last_reissued_at":"2026-05-18T00:47:51.407002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:51.407002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01392","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":"2026-05-18T00:47:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vo/OKuNNDrGL0AydGN8N4qeq65JfAVG8chIspFGPLINdM5i7vVrzjcaNZEqq5XSKYBBL2PSp7D4Zm4fM6M3rAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:29:37.283343Z"},"content_sha256":"7aa712b3557beddc66604d9a78c0414df64c3bf82abec21693af27ff477fa589","schema_version":"1.0","event_id":"sha256:7aa712b3557beddc66604d9a78c0414df64c3bf82abec21693af27ff477fa589"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6QY7TYADREFEXWCI3SS6QDV67N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Valuations of Semirings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jaiung Jun","submitted_at":"2015-03-04T17:15:00Z","abstract_excerpt":"We develop notions of valuations on a semiring, with a view toward extending the classical theory of abstract nonsingular curves and discrete valuation rings to this general algebraic setting; the novelty of our approach lies in the implementation of hyperrings to yield a new definition (\\emph{hyperfield valuation}). In particular, we classify valuations on the semifield $\\mathbb{Q}_{max}$ (the max-plus semifield of rational numbers) and also valuations on the `function field' $\\mathbb{Q}_{max}(T)$ (the semifield of rational functions over $\\mathbb{Q}_{max}$) which are trivial on $\\mathbb{Q}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01392","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":"2026-05-18T00:47:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQCc4NwK8/Fx9AuvjidklPuFJ2sI25x4+ISZAj1MTkOxCpRmomQ1Hjr2/NAqMJWxftB4ZSCX89X72Qh9rcq7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:29:37.283704Z"},"content_sha256":"4da2618bd9c924e93240633d38d8878c88e350d843e4a492050522e1081bdca4","schema_version":"1.0","event_id":"sha256:4da2618bd9c924e93240633d38d8878c88e350d843e4a492050522e1081bdca4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QY7TYADREFEXWCI3SS6QDV67N/bundle.json","state_url":"https://pith.science/pith/6QY7TYADREFEXWCI3SS6QDV67N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QY7TYADREFEXWCI3SS6QDV67N/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":"2026-06-24T21:29:37Z","links":{"resolver":"https://pith.science/pith/6QY7TYADREFEXWCI3SS6QDV67N","bundle":"https://pith.science/pith/6QY7TYADREFEXWCI3SS6QDV67N/bundle.json","state":"https://pith.science/pith/6QY7TYADREFEXWCI3SS6QDV67N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QY7TYADREFEXWCI3SS6QDV67N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6QY7TYADREFEXWCI3SS6QDV67N","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":"aa3b255038de821cbc5198e0f01750da5bfe759b4414d762593a79cc44f5b0ba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-04T17:15:00Z","title_canon_sha256":"6ee2093c8762e91f17da1e3e4487efe08410f65016c07fda5ed4aab1d9bb68c2"},"schema_version":"1.0","source":{"id":"1503.01392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01392","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01392v2","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01392","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"pith_short_12","alias_value":"6QY7TYADREFE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6QY7TYADREFEXWCI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6QY7TYAD","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4da2618bd9c924e93240633d38d8878c88e350d843e4a492050522e1081bdca4","target":"graph","created_at":"2026-05-18T00:47:51Z","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":"We develop notions of valuations on a semiring, with a view toward extending the classical theory of abstract nonsingular curves and discrete valuation rings to this general algebraic setting; the novelty of our approach lies in the implementation of hyperrings to yield a new definition (\\emph{hyperfield valuation}). In particular, we classify valuations on the semifield $\\mathbb{Q}_{max}$ (the max-plus semifield of rational numbers) and also valuations on the `function field' $\\mathbb{Q}_{max}(T)$ (the semifield of rational functions over $\\mathbb{Q}_{max}$) which are trivial on $\\mathbb{Q}_{","authors_text":"Jaiung Jun","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-04T17:15:00Z","title":"Valuations of Semirings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01392","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":"sha256:7aa712b3557beddc66604d9a78c0414df64c3bf82abec21693af27ff477fa589","target":"record","created_at":"2026-05-18T00:47:51Z","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":"aa3b255038de821cbc5198e0f01750da5bfe759b4414d762593a79cc44f5b0ba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-04T17:15:00Z","title_canon_sha256":"6ee2093c8762e91f17da1e3e4487efe08410f65016c07fda5ed4aab1d9bb68c2"},"schema_version":"1.0","source":{"id":"1503.01392","kind":"arxiv","version":2}},"canonical_sha256":"f431f9e003890a4bd848dca5e80ebefb76aee3a8a85d49e4b20148548777a67d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f431f9e003890a4bd848dca5e80ebefb76aee3a8a85d49e4b20148548777a67d","first_computed_at":"2026-05-18T00:47:51.407002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:51.407002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bvtIAd2mMHZOJQSCnrA2luxIZshoRff9wgldxq2pa8AF5IA0nllJ9mqO51aD82FKEznk7kCIklOgaVJqFzG9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:51.407788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aa712b3557beddc66604d9a78c0414df64c3bf82abec21693af27ff477fa589","sha256:4da2618bd9c924e93240633d38d8878c88e350d843e4a492050522e1081bdca4"],"state_sha256":"c3d51e7228cfe36394f274ac31b81fdda42b370c18aefa78c29c76a3ffbd8f77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHrjTKMhKHv9U8KWSwsQmW/clS1HFG3TbZYy8wZ6WTNAnHddt0suSgScqyWl6SnPsX1SR4cTT2e6kfqAmvmSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:29:37.285683Z","bundle_sha256":"a13df6ef15a570fcbec01b7f85a4535f3658f654c8f8b02cf47df2ab73ba3d09"}}