{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UOHTIG3MMDXHIFJAVN4KZH6QGS","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":"d59c94ad55c08b4155efc92159fce335984c49eabee31ec2213cafa74f08a49e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T01:38:50Z","title_canon_sha256":"20608201c343dd690db59b0fa4571ed9e9c1559362e5bfaad9f98a687f575cb3"},"schema_version":"1.0","source":{"id":"2605.21876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21876","created_at":"2026-05-22T01:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21876v1","created_at":"2026-05-22T01:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21876","created_at":"2026-05-22T01:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"UOHTIG3MMDXH","created_at":"2026-05-22T01:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"UOHTIG3MMDXHIFJA","created_at":"2026-05-22T01:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"UOHTIG3M","created_at":"2026-05-22T01:04:12Z"}],"graph_snapshots":[{"event_id":"sha256:c9af72cff8188ec0de429927b865bafe4f12d74eaa2f0832ec3336d049f58f0a","target":"graph","created_at":"2026-05-22T01:04:12Z","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/2605.21876/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Daniel R. Johnston, Michael Harm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T01:38:50Z","title":"The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21876","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":"sha256:2f8982ec22e43f001d3e5fffe4af47509b981ccced28a6e94363afa442a94db6","target":"record","created_at":"2026-05-22T01:04:12Z","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":"d59c94ad55c08b4155efc92159fce335984c49eabee31ec2213cafa74f08a49e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T01:38:50Z","title_canon_sha256":"20608201c343dd690db59b0fa4571ed9e9c1559362e5bfaad9f98a687f575cb3"},"schema_version":"1.0","source":{"id":"2605.21876","kind":"arxiv","version":1}},"canonical_sha256":"a38f341b6c60ee741520ab78ac9fd034866332407c603c3e65756eb46151fc33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a38f341b6c60ee741520ab78ac9fd034866332407c603c3e65756eb46151fc33","first_computed_at":"2026-05-22T01:04:12.581305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:12.581305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6uQt7fduvAVOK8t+wANS2baemedzaVFFWTGKgOLHv0jHenfhGb9er/ZY1Wh6wDPd8XD0Uqhzql1D66i/pMuQCw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:12.582114Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f8982ec22e43f001d3e5fffe4af47509b981ccced28a6e94363afa442a94db6","sha256:c9af72cff8188ec0de429927b865bafe4f12d74eaa2f0832ec3336d049f58f0a"],"state_sha256":"7d2d53e9dad16458c7d13a82947afbd925950d63107b60066ca129e634ab3791"}