Pith Number

pith:BYK7UBAC

pith:2019:BYK7UBACVXUCWG7JVNIPTITFT7

not attested not anchored not stored refs pending

Large prime gaps and probabilistic models

Kevin Ford, Terence Tao, William Banks

arxiv:1908.08613 v3 · 2019-08-22 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BYK7UBACVXUCWG7JVNIPTITFT7}

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.

Cited by

1 paper in Pith

The Poisson Tail Conjecture for Primes in Short Intervals

Receipt and verification

First computed	2026-07-05T11:52:10.631637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e15fa0402ade82b1be9ab50f9a2659fe9c88a0c607ca2c0c01f33cdb4089439

Aliases

arxiv: 1908.08613 · arxiv_version: 1908.08613v3 · doi: 10.48550/arxiv.1908.08613 · pith_short_12: BYK7UBACVXUC · pith_short_16: BYK7UBACVXUCWG7J · pith_short_8: BYK7UBAC

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/BYK7UBACVXUCWG7JVNIPTITFT7 \
  | 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: 0e15fa0402ade82b1be9ab50f9a2659fe9c88a0c607ca2c0c01f33cdb4089439

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4039df26e3dd2ffd8b3f5f2195c5cc5d4fb39ecb72ef6e743b70143e23255ba",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-08-22T22:33:17Z",
    "title_canon_sha256": "787e9bbf07aeddd555dbf097a242c90c2457031e9ae3897d93b2484156046aea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08613",
    "kind": "arxiv",
    "version": 3
  }
}