Pith Number

pith:MDBP3FZL

pith:2010:MDBP3FZLJQPEHBCZKZGZXF4G4Y

not attested not anchored not stored refs pending

Estimates for exponential sums with a large automorphism group

Antonio Rojas-Le\'on

arxiv:1010.0120 v1 · 2010-10-01 · 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{MDBP3FZLJQPEHBCZKZGZXF4G4Y}

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	2026-05-18T04:40:00.247818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902

Aliases

arxiv: 1010.0120 · arxiv_version: 1010.0120v1 · doi: 10.48550/arxiv.1010.0120 · pith_short_12: MDBP3FZLJQPE · pith_short_16: MDBP3FZLJQPEHBCZ · pith_short_8: MDBP3FZL

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/MDBP3FZLJQPEHBCZKZGZXF4G4Y \
  | 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: 60c2fd972b4c1e438459564d9b9786e608bc5e7cd158f23760f53f9e0b3f7902

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f586cfead1a04c552468967bd0d58ea96a86709d4d7296c85442e7974420c09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-01T10:56:04Z",
    "title_canon_sha256": "869b46a2dd89866ac10c57c2a34cbae1038b993b6567948cdbbc7ec508615b9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0120",
    "kind": "arxiv",
    "version": 1
  }
}