{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:COY2HEYNORMSVPV5V74K4JIKK4","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":"78ab80d41311153dfa1ea493e5152dd4df3138c718ac8df380e21f4b1d6d7fba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T05:10:43Z","title_canon_sha256":"de3f62fe4d796848db10f23619cd5799d40e0a5b082ecdbaa1a9bae41a0d1fcd"},"schema_version":"1.0","source":{"id":"2505.04951","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04951","created_at":"2026-07-05T11:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04951v3","created_at":"2026-07-05T11:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04951","created_at":"2026-07-05T11:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"COY2HEYNORMS","created_at":"2026-07-05T11:37:44Z"},{"alias_kind":"pith_short_16","alias_value":"COY2HEYNORMSVPV5","created_at":"2026-07-05T11:37:44Z"},{"alias_kind":"pith_short_8","alias_value":"COY2HEYN","created_at":"2026-07-05T11:37:44Z"}],"graph_snapshots":[{"event_id":"sha256:3fd0243fbdc0fa50ebc16fbc55dc354468d8602aab0f2381c02dc69be3089af3","target":"graph","created_at":"2026-07-05T11:37:44Z","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/2505.04951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The arithmetic average of the first $n$ primes, $\\bar p_n = {1\\over n} \\sum_{i=1}^n p_i$, exhibits very many interesting and subtle properties. Since the transformation from $p_n \\to \\bar p_n$ is extremely easy to invert, $p_n = n\\bar p_n - (n-1)\\bar p_{n-1}$, it is clear that these two sequences $p_n \\longleftrightarrow \\bar p_n$ must ultimately carry exactly the same information. But the averaged sequence $\\bar p_n$, while very closely correlated with the primes, ($\\bar p_n \\sim {1\\over2} p_n$), is much \"smoother'', and much better behaved. Using extensions of various standard results I shal","authors_text":"Matt Visser (Victoria University of Wellington)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T05:10:43Z","title":"On the arithmetic average of the first $n$ primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04951","kind":"arxiv","version":3},"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:dd5d19799c03415071bf94e1751622cb761f96c7098e9f96b6c76b654e225494","target":"record","created_at":"2026-07-05T11:37:44Z","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":"78ab80d41311153dfa1ea493e5152dd4df3138c718ac8df380e21f4b1d6d7fba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-08T05:10:43Z","title_canon_sha256":"de3f62fe4d796848db10f23619cd5799d40e0a5b082ecdbaa1a9bae41a0d1fcd"},"schema_version":"1.0","source":{"id":"2505.04951","kind":"arxiv","version":3}},"canonical_sha256":"13b1a3930d74592abebdaff8ae250a57331d5fe0b5bbd2d0c88210aa65f6ca1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b1a3930d74592abebdaff8ae250a57331d5fe0b5bbd2d0c88210aa65f6ca1c","first_computed_at":"2026-07-05T11:37:44.672865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:44.672865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hKYbwj8svUsGka77plx37eWQ9hiDh6KrWoS3t91N+lBWAZt9SBA7kGG4RfL/g1o0IPHsd9J4wTqsChUAbkuBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:44.673424Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.04951","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd5d19799c03415071bf94e1751622cb761f96c7098e9f96b6c76b654e225494","sha256:3fd0243fbdc0fa50ebc16fbc55dc354468d8602aab0f2381c02dc69be3089af3"],"state_sha256":"7f327b54f03a9b3c8ca80a88486a2e7d1cd0247ecbc446138e4df49060518343"}