Pith Number

pith:FNY2LBES

pith:2012:FNY2LBESQDZJ2KQLTLUS4LZANQ

not attested not anchored not stored refs pending

On Character Sums and Exponential Sums over Generalized Arithmetic Progressions

Xuancheng Shao

arxiv:1206.0521 v2 · 2012-06-04 · 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{FNY2LBESQDZJ2KQLTLUS4LZANQ}

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	2026-05-18T02:57:53.515206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b71a5849280f29d2a0b9ae92e2f206c381933f7fe0083da191c0f8b4b3bf270

Aliases

arxiv: 1206.0521 · arxiv_version: 1206.0521v2 · doi: 10.48550/arxiv.1206.0521 · pith_short_12: FNY2LBESQDZJ · pith_short_16: FNY2LBESQDZJ2KQL · pith_short_8: FNY2LBES

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/FNY2LBESQDZJ2KQLTLUS4LZANQ \
  | 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: 2b71a5849280f29d2a0b9ae92e2f206c381933f7fe0083da191c0f8b4b3bf270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "151bac1eb3ce65df48663f76e85c475ae84680bfb83c51650ed7373004f29275",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-04T05:22:05Z",
    "title_canon_sha256": "5eb71dc28e96923266dbd7e104445f38ea3210cd17f320d9c69afa80dc18d869"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0521",
    "kind": "arxiv",
    "version": 2
  }
}