{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6EX27I2GCOLEAR6QHJCMYMBVO7","short_pith_number":"pith:6EX27I2G","schema_version":"1.0","canonical_sha256":"f12fafa34613964047d03a44cc303577de0929d198d127aea4e23ad4498da4bb","source":{"kind":"arxiv","id":"2507.18908","version":1},"attestation_state":"computed","paper":{"title":"Blocks in Finite Hyperfields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Hobby","submitted_at":"2025-07-25T03:00:54Z","abstract_excerpt":"This paper studies the structure of finite hyperfields $H$, and finds a subtle pattern in their addition operation. Consider the class $\\mathcal{H}$ of all hyperfields with a given multiplicative group on $H^\\times = H - \\{0\\}$ and given value of $-1$. Then the addition of hyperfields in this class is determined by the set of pairs $(x,y)$ with $y \\in x+1$ for $x,y \\in H^\\times$. There are blocks of such pairs, where $(x_0,y_0)$ and $(x_1,y_1)$ are in the same block iff every hyperfield with $y_0 \\in x_0 + 1$ also has $y_1 \\in x_1 + 1$. The theory of these blocks is developed, they can easily "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.18908","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-25T03:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"1e5d060666b044505b03154c64aef0558d1d746b9ae3cc8b7d0dec009df2bae4","abstract_canon_sha256":"11ed12150a1978f65f4d806a92552f12fbaa9d594e21d55638499c55c4147cd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:15.989629Z","signature_b64":"8bpzRT7iysDE+oG3GRelowypRI/VaQNGnlamyhwXN6+/HFD6QraKTUkNgAvGxHGwBkZc80MqnZLsvWLJDowJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f12fafa34613964047d03a44cc303577de0929d198d127aea4e23ad4498da4bb","last_reissued_at":"2026-07-05T11:43:15.989093Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:15.989093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blocks in Finite Hyperfields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Hobby","submitted_at":"2025-07-25T03:00:54Z","abstract_excerpt":"This paper studies the structure of finite hyperfields $H$, and finds a subtle pattern in their addition operation. Consider the class $\\mathcal{H}$ of all hyperfields with a given multiplicative group on $H^\\times = H - \\{0\\}$ and given value of $-1$. Then the addition of hyperfields in this class is determined by the set of pairs $(x,y)$ with $y \\in x+1$ for $x,y \\in H^\\times$. There are blocks of such pairs, where $(x_0,y_0)$ and $(x_1,y_1)$ are in the same block iff every hyperfield with $y_0 \\in x_0 + 1$ also has $y_1 \\in x_1 + 1$. The theory of these blocks is developed, they can easily "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.18908","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.18908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.18908","created_at":"2026-07-05T11:43:15.989160+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.18908v1","created_at":"2026-07-05T11:43:15.989160+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.18908","created_at":"2026-07-05T11:43:15.989160+00:00"},{"alias_kind":"pith_short_12","alias_value":"6EX27I2GCOLE","created_at":"2026-07-05T11:43:15.989160+00:00"},{"alias_kind":"pith_short_16","alias_value":"6EX27I2GCOLEAR6Q","created_at":"2026-07-05T11:43:15.989160+00:00"},{"alias_kind":"pith_short_8","alias_value":"6EX27I2G","created_at":"2026-07-05T11:43:15.989160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7","json":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7.json","graph_json":"https://pith.science/api/pith-number/6EX27I2GCOLEAR6QHJCMYMBVO7/graph.json","events_json":"https://pith.science/api/pith-number/6EX27I2GCOLEAR6QHJCMYMBVO7/events.json","paper":"https://pith.science/paper/6EX27I2G"},"agent_actions":{"view_html":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7","download_json":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7.json","view_paper":"https://pith.science/paper/6EX27I2G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.18908&json=true","fetch_graph":"https://pith.science/api/pith-number/6EX27I2GCOLEAR6QHJCMYMBVO7/graph.json","fetch_events":"https://pith.science/api/pith-number/6EX27I2GCOLEAR6QHJCMYMBVO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7/action/storage_attestation","attest_author":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7/action/author_attestation","sign_citation":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7/action/citation_signature","submit_replication":"https://pith.science/pith/6EX27I2GCOLEAR6QHJCMYMBVO7/action/replication_record"}},"created_at":"2026-07-05T11:43:15.989160+00:00","updated_at":"2026-07-05T11:43:15.989160+00:00"}