Pith Number

pith:TYSFWLRF

pith:2011:TYSFWLRF22ELLCNLO4IQ5SZBH7

not attested not anchored not stored refs pending

Distribution on elements of cosets of small subgroups and applications

Igor Shparlinski, Jean Bourgain, Sergei Konyagin

arxiv:1103.0567 v1 · 2011-03-02 · 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{TYSFWLRF22ELLCNLO4IQ5SZBH7}

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	2026-05-18T04:27:27.783191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e245b2e25d688b589ab77110ecb213ff96257a78f995cbf150f3314e07d1b22

Aliases

arxiv: 1103.0567 · arxiv_version: 1103.0567v1 · doi: 10.48550/arxiv.1103.0567 · pith_short_12: TYSFWLRF22EL · pith_short_16: TYSFWLRF22ELLCNL · pith_short_8: TYSFWLRF

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/TYSFWLRF22ELLCNLO4IQ5SZBH7 \
  | 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: 9e245b2e25d688b589ab77110ecb213ff96257a78f995cbf150f3314e07d1b22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5948dfae2078f1f8a60dc100a211d68ef529a6e24caabfe272161fb420258a07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-02T21:45:00Z",
    "title_canon_sha256": "28945509317400ca0df3b2cfc93922214a4bf4c53ceaf77500c90876f9fdc734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0567",
    "kind": "arxiv",
    "version": 1
  }
}