{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UOHTIG3MMDXHIFJAVN4KZH6QGS","short_pith_number":"pith:UOHTIG3M","schema_version":"1.0","canonical_sha256":"a38f341b6c60ee741520ab78ac9fd034866332407c603c3e65756eb46151fc33","source":{"kind":"arxiv","id":"2605.21876","version":1},"attestation_state":"computed","paper":{"title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel R. Johnston, Michael Harm","submitted_at":"2026-05-21T01:38:50Z","abstract_excerpt":"We prove new results on the additive theory of reversed primes $\\overleftarrow{p}$; that is, primes $p$ which are written backwards in a fixed base $b\\geq 2$. In particular, we study a variant of Goldbach's conjecture, looking at representations of integers as the sum of primes and reversed primes. We show that:\n  (1) Every large odd integer is the sum of a prime and two reversed primes ($N=p_1+\\overleftarrow{p_2}+\\overleftarrow{p_3}$).\n  (2) Every large odd integer is the sum of two primes and a reversed prime ($N=p_1+p_2+\\overleftarrow{p_3}$).\n  (3) Almost all even integers are the sum of a "},"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":"2605.21876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T01:38:50Z","cross_cats_sorted":[],"title_canon_sha256":"20608201c343dd690db59b0fa4571ed9e9c1559362e5bfaad9f98a687f575cb3","abstract_canon_sha256":"d59c94ad55c08b4155efc92159fce335984c49eabee31ec2213cafa74f08a49e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:12.582114Z","signature_b64":"6uQt7fduvAVOK8t+wANS2baemedzaVFFWTGKgOLHv0jHenfhGb9er/ZY1Wh6wDPd8XD0Uqhzql1D66i/pMuQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a38f341b6c60ee741520ab78ac9fd034866332407c603c3e65756eb46151fc33","last_reissued_at":"2026-05-22T01:04:12.581305Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:12.581305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel R. Johnston, Michael Harm","submitted_at":"2026-05-21T01:38:50Z","abstract_excerpt":"We prove new results on the additive theory of reversed primes $\\overleftarrow{p}$; that is, primes $p$ which are written backwards in a fixed base $b\\geq 2$. In particular, we study a variant of Goldbach's conjecture, looking at representations of integers as the sum of primes and reversed primes. We show that:\n  (1) Every large odd integer is the sum of a prime and two reversed primes ($N=p_1+\\overleftarrow{p_2}+\\overleftarrow{p_3}$).\n  (2) Every large odd integer is the sum of two primes and a reversed prime ($N=p_1+p_2+\\overleftarrow{p_3}$).\n  (3) Almost all even integers are the sum of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21876","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/2605.21876/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":"2605.21876","created_at":"2026-05-22T01:04:12.581451+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21876v1","created_at":"2026-05-22T01:04:12.581451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21876","created_at":"2026-05-22T01:04:12.581451+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOHTIG3MMDXH","created_at":"2026-05-22T01:04:12.581451+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOHTIG3MMDXHIFJA","created_at":"2026-05-22T01:04:12.581451+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOHTIG3M","created_at":"2026-05-22T01:04:12.581451+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/UOHTIG3MMDXHIFJAVN4KZH6QGS","json":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS.json","graph_json":"https://pith.science/api/pith-number/UOHTIG3MMDXHIFJAVN4KZH6QGS/graph.json","events_json":"https://pith.science/api/pith-number/UOHTIG3MMDXHIFJAVN4KZH6QGS/events.json","paper":"https://pith.science/paper/UOHTIG3M"},"agent_actions":{"view_html":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS","download_json":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS.json","view_paper":"https://pith.science/paper/UOHTIG3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21876&json=true","fetch_graph":"https://pith.science/api/pith-number/UOHTIG3MMDXHIFJAVN4KZH6QGS/graph.json","fetch_events":"https://pith.science/api/pith-number/UOHTIG3MMDXHIFJAVN4KZH6QGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS/action/storage_attestation","attest_author":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS/action/author_attestation","sign_citation":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS/action/citation_signature","submit_replication":"https://pith.science/pith/UOHTIG3MMDXHIFJAVN4KZH6QGS/action/replication_record"}},"created_at":"2026-05-22T01:04:12.581451+00:00","updated_at":"2026-05-22T01:04:12.581451+00:00"}