Pith Number

pith:VCTGTFMD

pith:2011:VCTGTFMDBZUS5NZP24KDBMSPHB

not attested not anchored not stored refs pending

Sequences of Integers with Missing Quotients and Dense Points Without Neighbors

Sergei Konyagin, Tanya Khovanova

arxiv:1104.0441 v1 · 2011-04-04 · math.CO · 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{VCTGTFMDBZUS5NZP24KDBMSPHB}

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	2026-05-18T03:20:18.969671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8a66995830e692eb72fd71430b24f3843a62474d0a387c803554b94de1e4552

Aliases

arxiv: 1104.0441 · arxiv_version: 1104.0441v1 · doi: 10.48550/arxiv.1104.0441 · pith_short_12: VCTGTFMDBZUS · pith_short_16: VCTGTFMDBZUS5NZP · pith_short_8: VCTGTFMD

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/VCTGTFMDBZUS5NZP24KDBMSPHB \
  | 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: a8a66995830e692eb72fd71430b24f3843a62474d0a387c803554b94de1e4552

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dc4320947ef89f802f3d784d424d16bee93301446a2e714925a3a0d06984124",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-04-04T00:20:34Z",
    "title_canon_sha256": "4a41eec3ae7b45dc041e1756f1400f65c1685c01a474ddb335b07232c81e9725"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0441",
    "kind": "arxiv",
    "version": 1
  }
}