Pith Number

pith:DMPAAYIP

pith:2014:DMPAAYIPJHFGEFBLUFLYZHH27O

not attested not anchored not stored refs pending

Gaps between fractional parts, and additive combinatorics

Andrew Granville, Antal Balog, Jozsef Solymosi

arxiv:1410.8404 v1 · 2014-10-30 · 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{DMPAAYIPJHFGEFBLUFLYZHH27O}

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	2026-05-18T02:38:59.989455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b1e00610f49ca62142ba1578c9cfafbb25a5983e7428cf27b6544646708526a

Aliases

arxiv: 1410.8404 · arxiv_version: 1410.8404v1 · doi: 10.48550/arxiv.1410.8404 · pith_short_12: DMPAAYIPJHFG · pith_short_16: DMPAAYIPJHFGEFBL · pith_short_8: DMPAAYIP

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/DMPAAYIPJHFGEFBLUFLYZHH27O \
  | 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: 1b1e00610f49ca62142ba1578c9cfafbb25a5983e7428cf27b6544646708526a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "335e45d3bb3afbecbf37a725493bb30bbe85f2493abbc62f726170db3d0806c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-30T15:22:46Z",
    "title_canon_sha256": "b801bc18e5e5d0be5744dd4177232adf721064f631b86f32dba913f00785143d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.8404",
    "kind": "arxiv",
    "version": 1
  }
}