Pith Number

pith:NEAB4I4T

pith:2013:NEAB4I4TOC74SAW32H4PGX37DE

not attested not anchored not stored refs pending

Explicit formulae for primes in arithmetic progressions, I

Tomohiro Yamada

arxiv:1306.5322 v4 · 2013-06-22 · 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{NEAB4I4TOC74SAW32H4PGX37DE}

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	2026-05-18T01:27:29.012221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69001e239370bfc902dbd1f8f35f7f191df65f8f9e14a610216c0c2b082aed68

Aliases

arxiv: 1306.5322 · arxiv_version: 1306.5322v4 · doi: 10.48550/arxiv.1306.5322 · pith_short_12: NEAB4I4TOC74 · pith_short_16: NEAB4I4TOC74SAW3 · pith_short_8: NEAB4I4T

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/NEAB4I4TOC74SAW32H4PGX37DE \
  | 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: 69001e239370bfc902dbd1f8f35f7f191df65f8f9e14a610216c0c2b082aed68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d717fe35fdb3827099e69e9be065d8d9866dbcdae50479cc9d30af42665c8de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-06-22T13:27:17Z",
    "title_canon_sha256": "7357e808fc397d337da750f3ca3c451c167f09b3877d30bd713fb8845a82a546"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5322",
    "kind": "arxiv",
    "version": 4
  }
}