{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U2YMBMTPB73OSMNC3PQV435VB4","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":"f4322c7c0eaa4259eeff19f99615b53002cdad42c48b4497f0fd79766a4e718c","cross_cats_sorted":["math.MP","physics.hist-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-02-03T00:18:50Z","title_canon_sha256":"9e82907ee4d8c9736528ae38202596f09c9f91ced9d0e9719fcab790fd382d6f"},"schema_version":"1.0","source":{"id":"2502.00967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00967","created_at":"2026-07-05T10:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00967v1","created_at":"2026-07-05T10:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00967","created_at":"2026-07-05T10:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"U2YMBMTPB73O","created_at":"2026-07-05T10:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"U2YMBMTPB73OSMNC","created_at":"2026-07-05T10:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"U2YMBMTP","created_at":"2026-07-05T10:08:40Z"}],"graph_snapshots":[{"event_id":"sha256:7c4d3d9399673049a11aa8ebb9d823c02fb4aa578478f211f4fd01f92fbc4066","target":"graph","created_at":"2026-07-05T10:08:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.00967/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a \"partially additive field\" share many similarities with physical quantities. In particular, they form subsets of mutually summable elements (similar to physical dimensions), dimensionless elements (those summable with 1) form a field, and every element can be uniquely represented as a product of a dimensionless element and any non-zero element of the same dimension (a unit). We also discuss the conditions for the existence of a coherent unit system. In contrast to previous works","authors_text":"Georgy Alymov","cross_cats":["math.MP","physics.hist-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-02-03T00:18:50Z","title":"Physical quantities as a partially additive field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00967","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:d28bfdea4599769fad0522949351f7c7934c1dbd98092344581221773542afb4","target":"record","created_at":"2026-07-05T10:08:40Z","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":"f4322c7c0eaa4259eeff19f99615b53002cdad42c48b4497f0fd79766a4e718c","cross_cats_sorted":["math.MP","physics.hist-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-02-03T00:18:50Z","title_canon_sha256":"9e82907ee4d8c9736528ae38202596f09c9f91ced9d0e9719fcab790fd382d6f"},"schema_version":"1.0","source":{"id":"2502.00967","kind":"arxiv","version":1}},"canonical_sha256":"a6b0c0b26f0ff6e931a2dbe15e6fb50f1f806a5a144165cb2deae2d1c4ba3471","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6b0c0b26f0ff6e931a2dbe15e6fb50f1f806a5a144165cb2deae2d1c4ba3471","first_computed_at":"2026-07-05T10:08:40.808410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:08:40.808410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nndqEd2Ky88cp0G1eFBw32kn3ogX6u++qVrsVo6chkhuJSpI6Lp+6L3PPxpSn1Ar4XXLD7bs3NJ4sabi5zRDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:08:40.808822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.00967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d28bfdea4599769fad0522949351f7c7934c1dbd98092344581221773542afb4","sha256:7c4d3d9399673049a11aa8ebb9d823c02fb4aa578478f211f4fd01f92fbc4066"],"state_sha256":"e2ed77e8fc162a77e9e5adfddfe84cd637b3e840730a9a18ae66812ea72c0f14"}