Pith Number

pith:J7DRGGWL

pith:2025:J7DRGGWLJQUJN3MRMULK24AC5S

not attested not anchored not stored refs pending

Refinements for primes in short arithmetic progressions

Michael Harm

arxiv:2507.15334 v2 · 2025-07-21 · 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{J7DRGGWLJQUJN3MRMULK24AC5S}

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

2 papers in Pith

Binomial coefficients with divisors avoiding an interval

On the Goldbach problem with restricted primes

Receipt and verification

First computed	2026-05-20T01:04:56.190279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8

Aliases

arxiv: 2507.15334 · arxiv_version: 2507.15334v2 · doi: 10.48550/arxiv.2507.15334 · pith_short_12: J7DRGGWLJQUJ · pith_short_16: J7DRGGWLJQUJN3MR · pith_short_8: J7DRGGWL

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/J7DRGGWLJQUJN3MRMULK24AC5S \
  | 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: 4fc7131acb4c2896ed916516ad7002ec95c8a37fd342d4afce52d5e5cfec0ee8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "469e950ab35a2a419c01842ff2151efd1a6643810d40cb927523f02d7ea8f567",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-21T07:47:54Z",
    "title_canon_sha256": "b273b1883a136015682a35e7956df61f79ab11e8f8faa54385eec68583fc7152"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15334",
    "kind": "arxiv",
    "version": 2
  }
}