Pith Number

pith:75PMCRJ3

pith:2014:75PMCRJ3RFQ57DIFUVCSD5SVDT

not attested not anchored not stored refs pending

Exponential sums over primes in short intervals and an application to the Waring--Goldbach problem

Bingrong Huang

arxiv:1412.2743 v2 · 2014-12-06 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{75PMCRJ3RFQ57DIFUVCSD5SVDT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:13:28.776830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff5ec1453b8961df8d05a54521f6551cd90e82493c979042e802cc4df10250b1

Aliases

arxiv: 1412.2743 · arxiv_version: 1412.2743v2 · doi: 10.48550/arxiv.1412.2743 · pith_short_12: 75PMCRJ3RFQ5 · pith_short_16: 75PMCRJ3RFQ57DIF · pith_short_8: 75PMCRJ3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/75PMCRJ3RFQ57DIFUVCSD5SVDT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ff5ec1453b8961df8d05a54521f6551cd90e82493c979042e802cc4df10250b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cb6eeb006c3591cad91fef9f6962e3c3ed9941c41392483e89529511af975df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-06T14:04:34Z",
    "title_canon_sha256": "a9b7e0e192b956237af2f7f416f2a28245ea7ab068f636b77cf244b7fb954964"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2743",
    "kind": "arxiv",
    "version": 2
  }
}