{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QTUXQNXZ473UZ2NI2BHQ4QVZHW","short_pith_number":"pith:QTUXQNXZ","canonical_record":{"source":{"id":"1307.7336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-28T06:22:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"edc02fc676184843936f9c5846d70a02a289155907a29ee5ef4e974be057878c","abstract_canon_sha256":"02a1adec824646245e140bd139244219a2a99ddc8bf7f2d0a51574d9996e5fc1"},"schema_version":"1.0"},"canonical_sha256":"84e97836f9e7f74ce9a8d04f0e42b93d8779e3484e4354c0c583a5aeecc2a684","source":{"kind":"arxiv","id":"1307.7336","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7336","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7336v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7336","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"QTUXQNXZ473U","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QTUXQNXZ473UZ2NI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QTUXQNXZ","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QTUXQNXZ473UZ2NI2BHQ4QVZHW","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-28T06:22:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"edc02fc676184843936f9c5846d70a02a289155907a29ee5ef4e974be057878c","abstract_canon_sha256":"02a1adec824646245e140bd139244219a2a99ddc8bf7f2d0a51574d9996e5fc1"},"schema_version":"1.0"},"canonical_sha256":"84e97836f9e7f74ce9a8d04f0e42b93d8779e3484e4354c0c583a5aeecc2a684","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:23.526531Z","signature_b64":"KVsR6tLbCeTPseqR2ByL4U//W/xnhl8fDpC1lnA2HGY/yizgudFAaNZneih+Y8ZwRb2Kp6F4MQoVVIHfv9PKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e97836f9e7f74ce9a8d04f0e42b93d8779e3484e4354c0c583a5aeecc2a684","last_reissued_at":"2026-05-18T03:17:23.525894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:23.525894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7336","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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9q1z2OzEj5BAI16i+URDxMhX1jZvTTdcN0JqR71DgKC3OKI+713W6OzEgxLl1rznp1Ju4+Lkla9kqFWQTEEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:39:03.518699Z"},"content_sha256":"20af4bf3b731afc3323d3681567456561555482142e043f309034347afc227df","schema_version":"1.0","event_id":"sha256:20af4bf3b731afc3323d3681567456561555482142e043f309034347afc227df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QTUXQNXZ473UZ2NI2BHQ4QVZHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform extensions of layered semifields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Tal Perri","submitted_at":"2013-07-28T06:22:04Z","abstract_excerpt":"In this paper we introduce a canonical method of constructing simple uniform semifield extensions of uniform layered semifields introduced by Izhakian Knebusch and Rowen in the paper 'Layered tropical mathematics'. Our construction includes a decomposition of a uniform extension of a uniformly layered (uniform) semifield to the bipotent semifield extension of its $\\nu$-values semifield and a cancellative semifields extension of its layers (sorting) semifield. We give a characterization of these two types of semifields extensions in the first two sections of the paper. The third section glues t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7336","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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1qzhg0g0LSvmI997d9WsvUXyesgt1qotI7Q5ypGGaMRuScwxB5OrUeGjJdENNzHG18Jp97ShAY68GTktDV5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:39:03.519044Z"},"content_sha256":"68cff47b8884e3f26f84c38b5e7e7715fb8780db092a104d17c581058f1b2aad","schema_version":"1.0","event_id":"sha256:68cff47b8884e3f26f84c38b5e7e7715fb8780db092a104d17c581058f1b2aad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/bundle.json","state_url":"https://pith.science/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/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":"2026-06-24T04:39:03Z","links":{"resolver":"https://pith.science/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW","bundle":"https://pith.science/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/bundle.json","state":"https://pith.science/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTUXQNXZ473UZ2NI2BHQ4QVZHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QTUXQNXZ473UZ2NI2BHQ4QVZHW","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":"02a1adec824646245e140bd139244219a2a99ddc8bf7f2d0a51574d9996e5fc1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-28T06:22:04Z","title_canon_sha256":"edc02fc676184843936f9c5846d70a02a289155907a29ee5ef4e974be057878c"},"schema_version":"1.0","source":{"id":"1307.7336","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7336","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7336v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7336","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"QTUXQNXZ473U","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QTUXQNXZ473UZ2NI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QTUXQNXZ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:68cff47b8884e3f26f84c38b5e7e7715fb8780db092a104d17c581058f1b2aad","target":"graph","created_at":"2026-05-18T03:17:23Z","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 this paper we introduce a canonical method of constructing simple uniform semifield extensions of uniform layered semifields introduced by Izhakian Knebusch and Rowen in the paper 'Layered tropical mathematics'. Our construction includes a decomposition of a uniform extension of a uniformly layered (uniform) semifield to the bipotent semifield extension of its $\\nu$-values semifield and a cancellative semifields extension of its layers (sorting) semifield. We give a characterization of these two types of semifields extensions in the first two sections of the paper. The third section glues t","authors_text":"Tal Perri","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-28T06:22:04Z","title":"Uniform extensions of layered semifields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7336","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":"sha256:20af4bf3b731afc3323d3681567456561555482142e043f309034347afc227df","target":"record","created_at":"2026-05-18T03:17:23Z","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":"02a1adec824646245e140bd139244219a2a99ddc8bf7f2d0a51574d9996e5fc1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-28T06:22:04Z","title_canon_sha256":"edc02fc676184843936f9c5846d70a02a289155907a29ee5ef4e974be057878c"},"schema_version":"1.0","source":{"id":"1307.7336","kind":"arxiv","version":1}},"canonical_sha256":"84e97836f9e7f74ce9a8d04f0e42b93d8779e3484e4354c0c583a5aeecc2a684","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e97836f9e7f74ce9a8d04f0e42b93d8779e3484e4354c0c583a5aeecc2a684","first_computed_at":"2026-05-18T03:17:23.525894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:23.525894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KVsR6tLbCeTPseqR2ByL4U//W/xnhl8fDpC1lnA2HGY/yizgudFAaNZneih+Y8ZwRb2Kp6F4MQoVVIHfv9PKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:23.526531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20af4bf3b731afc3323d3681567456561555482142e043f309034347afc227df","sha256:68cff47b8884e3f26f84c38b5e7e7715fb8780db092a104d17c581058f1b2aad"],"state_sha256":"c354043ac9aa9df3bd6e2b74d19a8d400c1c1281c6376897b74f7619dc062da1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQrx/gyUO0Zjmqe3pQT0hAgMMuaJ0CvShL22lIjGa+adZondtVL0i5G2cGdlLdWeqaFdvumTt8imyd0NofTHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:39:03.520890Z","bundle_sha256":"59dd393384a7a8adf5ec8e32469298044871cabd9783b97bcc38b4d7ef4b38e3"}}