Pith Number

pith:PRAIYX2D

pith:2009:PRAIYX2D2BSKBKUPQP4RHTI7HY

not attested not anchored not stored refs pending

Twisted exponential sums of polynomials in one variable

Chunlei Liu, Wenxin Liu

arxiv:0912.1929 v1 · 2009-12-10 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PRAIYX2D2BSKBKUPQP4RHTI7HY}

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	2026-05-18T02:10:24.997879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c408c5f43d064a0aa8f83f913cd1f3e232366d02b888352a0cd3fa1a507acd0

Aliases

arxiv: 0912.1929 · arxiv_version: 0912.1929v1 · doi: 10.48550/arxiv.0912.1929 · pith_short_12: PRAIYX2D2BSK · pith_short_16: PRAIYX2D2BSKBKUP · pith_short_8: PRAIYX2D

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/PRAIYX2D2BSKBKUPQP4RHTI7HY \
  | 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: 7c408c5f43d064a0aa8f83f913cd1f3e232366d02b888352a0cd3fa1a507acd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbbf01206b26d11d048440fcb8ed017115688f978c963a3dbbad2575dcd5a9ea",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-12-10T07:49:32Z",
    "title_canon_sha256": "de16a1d46167b10031232c4e54e6e1fd38d3770d2f0e899f4528624b6680ca75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1929",
    "kind": "arxiv",
    "version": 1
  }
}