Pith Number

pith:DCGSYSSA

pith:2012:DCGSYSSAQJG7KI46CF7EWPGMU6

not attested not anchored not stored refs pending

A simplification of Ap\'ery's proof of the irrationality of \zeta(3)

Krishnan Rajkumar

arxiv:1212.5881 v1 · 2012-12-24 · math.NT · math.CO · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DCGSYSSAQJG7KI46CF7EWPGMU6}

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	2026-05-18T03:37:51.101583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

188d2c4a40824df5239e117e4b3ccca7b7e59d009b919dd16f885deea2b0859e

Aliases

arxiv: 1212.5881 · arxiv_version: 1212.5881v1 · doi: 10.48550/arxiv.1212.5881 · pith_short_12: DCGSYSSAQJG7 · pith_short_16: DCGSYSSAQJG7KI46 · pith_short_8: DCGSYSSA

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/DCGSYSSAQJG7KI46CF7EWPGMU6 \
  | 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: 188d2c4a40824df5239e117e4b3ccca7b7e59d009b919dd16f885deea2b0859e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fe6a60d005f7eb6f78d931faa3e03c7b8bedf4758266b179ce2a378d30c2a9a",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-24T09:34:50Z",
    "title_canon_sha256": "03a5bd5a5208d534093c20e588efec819466ce9d7c9f1cdb0c9fb38abea9a73d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5881",
    "kind": "arxiv",
    "version": 1
  }
}