Pith Number

pith:CPR2CW64

pith:2007:CPR2CW64KDHQPMOADJRLUTBQKU

not attested not anchored not stored refs pending

On the sum of the series formed from the prime numbers where the prime numbers of the form $4n-1$ have a positive sign and those of the form $4n+1$ a negative sign

Leonhard Euler

arxiv:0708.2564 v3 · 2007-08-19 · math.HO · 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{CPR2CW64KDHQPMOADJRLUTBQKU}

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	2026-05-18T00:29:54.215376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13e3a15bdc50cf07b1c01a62ba4c305508300335d5545fc13a2500668ac3a616

Aliases

arxiv: 0708.2564 · arxiv_version: 0708.2564v3 · doi: 10.48550/arxiv.0708.2564 · pith_short_12: CPR2CW64KDHQ · pith_short_16: CPR2CW64KDHQPMOA · pith_short_8: CPR2CW64

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/CPR2CW64KDHQPMOADJRLUTBQKU \
  | 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: 13e3a15bdc50cf07b1c01a62ba4c305508300335d5545fc13a2500668ac3a616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a54041e4435bd73d77dcb9c64a413f74b0b79a5176f914fc46010b6761a6e5b3",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2007-08-19T22:08:24Z",
    "title_canon_sha256": "5a1853668580160d453fad209911c75b93f99693fd8e09878e84c2d43505c072"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.2564",
    "kind": "arxiv",
    "version": 3
  }
}