Pith Number

pith:2JXGRWOD

pith:2012:2JXGRWOD6OCGSAROK7H4Y5H5O4

not attested not anchored not stored refs pending

Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions

Miao-Kun Wang, Ye-ping Jiang, Yu-Ming Chu

arxiv:1210.6126 v1 · 2012-10-23 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2JXGRWOD6OCGSAROK7H4Y5H5O4}

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	2026-05-18T03:41:42.402969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d26e68d9c3f38469022e57cfcc74fd770b6f8b99f4219029b6ccc5bdb25b241d

Aliases

arxiv: 1210.6126 · arxiv_version: 1210.6126v1 · doi: 10.48550/arxiv.1210.6126 · pith_short_12: 2JXGRWOD6OCG · pith_short_16: 2JXGRWOD6OCGSARO · pith_short_8: 2JXGRWOD

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/2JXGRWOD6OCGSAROK7H4Y5H5O4 \
  | 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: d26e68d9c3f38469022e57cfcc74fd770b6f8b99f4219029b6ccc5bdb25b241d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "192803ba3978d0f4dc6a52c930498a8b62f63e1e038111f17223e0830c20cc52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-10-23T04:40:26Z",
    "title_canon_sha256": "a6f839ab7eff71419d2ef0449b2df53b8cc72b69060787e6a3c95fd14b724fed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6126",
    "kind": "arxiv",
    "version": 1
  }
}