Pith Number

pith:PBQZCGAM

pith:2011:PBQZCGAM3VXS7BEEZFG3PQMNPL

not attested not anchored not stored refs pending

Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

Bruce C. Berndt, George Lamb, Mathew Rogers

arxiv:1108.4980 v2 · 2011-08-25 · math.CA · math.NT

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

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	2026-05-18T04:14:44.720761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

786191180cdd6f2f8484c94db7c18d7ac23f7173bb0e98d16e976dd97c8abd2f

Aliases

arxiv: 1108.4980 · arxiv_version: 1108.4980v2 · doi: 10.48550/arxiv.1108.4980 · pith_short_12: PBQZCGAM3VXS · pith_short_16: PBQZCGAM3VXS7BEE · pith_short_8: PBQZCGAM

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/PBQZCGAM3VXS7BEEZFG3PQMNPL \
  | 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: 786191180cdd6f2f8484c94db7c18d7ac23f7173bb0e98d16e976dd97c8abd2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0ac02da9a1c93bfeeae583dfbe7e1ac9ddbd587fba00311e2f0b44f4b7e7573",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-08-25T01:14:31Z",
    "title_canon_sha256": "1775e2398d9bf763a0493ebb7770dab874f1cdfbe44a846af80b22e46158f946"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4980",
    "kind": "arxiv",
    "version": 2
  }
}