Pith Number

pith:AL6KS5OP

pith:2011:AL6KS5OPKFDDYZWVEZ5UL7TNH5

not attested not anchored not stored refs pending

$p$-adic estimates for multiplicative character sums

Alan Adolphson, Steven Sperber

arxiv:1103.5513 v1 · 2011-03-29 · 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{AL6KS5OPKFDDYZWVEZ5UL7TNH5}

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	2026-05-18T04:25:37.417077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02fca975cf51463c66d5267b45fe6d3f6d54c7ecdac12af97c322b4d356cd208

Aliases

arxiv: 1103.5513 · arxiv_version: 1103.5513v1 · doi: 10.48550/arxiv.1103.5513 · pith_short_12: AL6KS5OPKFDD · pith_short_16: AL6KS5OPKFDDYZWV · pith_short_8: AL6KS5OP

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/AL6KS5OPKFDDYZWVEZ5UL7TNH5 \
  | 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: 02fca975cf51463c66d5267b45fe6d3f6d54c7ecdac12af97c322b4d356cd208

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2060c426f9fd37a12ddd79910b28468f0e77d291ffdb8a33bc4d9fb02cc0717",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-29T00:02:22Z",
    "title_canon_sha256": "95be03c1a1780e7d7ebe87679f3b4ea2ff8d8ea1674aa8be2805c0491017ea4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5513",
    "kind": "arxiv",
    "version": 1
  }
}