Pith Number

pith:R32E3P5X

pith:2026:R32E3P5XFV7OVNNWVUV26VEYLF

not attested not anchored not stored refs pending

The exceptional set of the Goldbach problem

Gautami Bhowmik, Lasse Grimmelt

arxiv:2607.27282 v1 · 2026-07-29 · 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{R32E3P5XFV7OVNNWVUV26VEYLF}

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	2026-07-31T00:10:29.768547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

8ef44dbfb72d7eeab5b6ad2baf54985975ca2f6601b5025a8f51097d8e23f5b9

Aliases

arxiv: 2607.27282 · arxiv_version: 2607.27282v1 · doi: 10.48550/arxiv.2607.27282 · pith_short_12: R32E3P5XFV7O · pith_short_16: R32E3P5XFV7OVNNW · pith_short_8: R32E3P5X

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/R32E3P5XFV7OVNNWVUV26VEYLF \
  | 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: 8ef44dbfb72d7eeab5b6ad2baf54985975ca2f6601b5025a8f51097d8e23f5b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "218f7e11a158df652a456f3a4c87d6018d5a59aab3049436981b014d1a8e3eda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-29T13:54:38Z",
    "title_canon_sha256": "abdc941d9a7528d7927e8bbbd2b93a9ed6f3e483fe8204926c14aef8cc4b1caa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27282",
    "kind": "arxiv",
    "version": 1
  }
}