Pith Number

pith:4ZESAWVR

pith:2025:4ZESAWVRXHRSSXTY33TG4JJ5TE

not attested not anchored not stored refs pending

On the number of exceptional intervals to the prime number theorem in short intervals

Ayla Gafni, Terence Tao

arxiv:2505.24017 v1 · 2025-05-29 · 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{4ZESAWVRXHRSSXTY33TG4JJ5TE}

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

Products of consecutive integers with unusual anatomy

Receipt and verification

First computed	2026-05-27T14:06:37.128444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e649205ab1b9e3295e78dee66e253d9923eb9291d99eec28f6b692af3ac5c1fc

Aliases

arxiv: 2505.24017 · arxiv_version: 2505.24017v1 · doi: 10.48550/arxiv.2505.24017 · pith_short_12: 4ZESAWVRXHRS · pith_short_16: 4ZESAWVRXHRSSXTY · pith_short_8: 4ZESAWVR

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/4ZESAWVRXHRSSXTY33TG4JJ5TE \
  | 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: e649205ab1b9e3295e78dee66e253d9923eb9291d99eec28f6b692af3ac5c1fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e378e50678fcfa988c93967cebe49e69df8d536f55c12ed8c8ed11c4a52b09",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-05-29T21:36:29Z",
    "title_canon_sha256": "85c54938f1037424b3b7c1a4331cbbbcc79cbce8237139e6e6f8148fab998e4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24017",
    "kind": "arxiv",
    "version": 1
  }
}