Pith Number

pith:VDCKBNV6

pith:2011:VDCKBNV6G65I5LMURQXA6AL45W

not attested not anchored not stored refs pending

Properties and applications of the prime detecting function: infinitude of twin primes, asymptotic law of distribution of prime pairs differing by an even number

R. M. Abrarov, S. M. Abrarov

arxiv:1109.6557 v1 · 2011-09-29 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDCKBNV6G65I5LMURQXA6AL45W}

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	2026-05-18T04:12:01.340562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8c4a0b6be37ba8ead948c2e0f017ced816b539e58c970e2095caea6340ee646

Aliases

arxiv: 1109.6557 · arxiv_version: 1109.6557v1 · doi: 10.48550/arxiv.1109.6557 · pith_short_12: VDCKBNV6G65I · pith_short_16: VDCKBNV6G65I5LMU · pith_short_8: VDCKBNV6

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/VDCKBNV6G65I5LMURQXA6AL45W \
  | 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: a8c4a0b6be37ba8ead948c2e0f017ced816b539e58c970e2095caea6340ee646

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18fae4434bb06396c39de1f0c532b30475ccb6ec7f3ef827da3691aa1d3dca28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2011-09-29T15:27:36Z",
    "title_canon_sha256": "81471262b6bb0fce7c21c8222224fd0402957edb422a72e835d7cc01aaccfb12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6557",
    "kind": "arxiv",
    "version": 1
  }
}