Pith Number

pith:PS4VHU3V

pith:2013:PS4VHU3VD4CKAF6LP767LMKJCQ

not attested not anchored not stored refs pending

Explicit formulae for primes in arithmetic progressions, II

Tomohiro Yamada

arxiv:1309.5798 v3 · 2013-09-23 · 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{PS4VHU3VD4CKAF6LP767LMKJCQ}

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	2026-05-18T02:58:56.801513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cb953d3751f04a017cb7ffdf5b1491438d64601c723b14ff696a9ade42a68c8

Aliases

arxiv: 1309.5798 · arxiv_version: 1309.5798v3 · doi: 10.48550/arxiv.1309.5798 · pith_short_12: PS4VHU3VD4CK · pith_short_16: PS4VHU3VD4CKAF6L · pith_short_8: PS4VHU3V

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/PS4VHU3VD4CKAF6LP767LMKJCQ \
  | 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: 7cb953d3751f04a017cb7ffdf5b1491438d64601c723b14ff696a9ade42a68c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8404e3161276fb41619da871e5084399075dcdd8ae1a76af93df4da8566bc865",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-23T13:28:39Z",
    "title_canon_sha256": "c066827bb5b528e1a023ce2f0c0b149b9eb78042929911834693f156ad219f20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5798",
    "kind": "arxiv",
    "version": 3
  }
}