Pith Number

pith:ELMVPUJ3

pith:2026:ELMVPUJ3OVIEBMSKTIAVFIJ5NB

not attested not anchored not stored refs pending

A decades-long breakthrough in zero-density estimates and primes in short intervals

Caroline L. Turnage-Butterbaugh

arxiv:2607.04632 v1 · 2026-07-06 · 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{ELMVPUJ3OVIEBMSKTIAVFIJ5NB}

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	2026-07-07T02:19:28.422214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22d957d13b755040b24a9a0152a13d684e0b56c5647c0484e795813a6abbbc42

Aliases

arxiv: 2607.04632 · arxiv_version: 2607.04632v1 · doi: 10.48550/arxiv.2607.04632 · pith_short_12: ELMVPUJ3OVIE · pith_short_16: ELMVPUJ3OVIEBMSK · pith_short_8: ELMVPUJ3

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/ELMVPUJ3OVIEBMSKTIAVFIJ5NB \
  | 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: 22d957d13b755040b24a9a0152a13d684e0b56c5647c0484e795813a6abbbc42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f4201a821b8e038d324e5eb39066b2eba0b3239c4a1bcec649a6ceb8de306b1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-06T03:32:22Z",
    "title_canon_sha256": "4cec6353ea06ff609a24a404a613df9b9282cd9ca6fca6ae8ce903d3e9fe29c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04632",
    "kind": "arxiv",
    "version": 1
  }
}