Pith Number

pith:3L3UGORT

pith:2011:3L3UGORTBDDJGQ44OMQRUIPMJO

not attested not anchored not stored refs pending

On the Modular Behaviour of the Infinite Product $(1-x)(1-xq)(1-xq^2)(1-xq^3)...$

Changgui Zhang

arxiv:1112.4979 v1 · 2011-12-21 · math.NT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3L3UGORTBDDJGQ44OMQRUIPMJO}

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	2026-05-18T04:05:56.632735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daf7433a3308c693439c73211a21ec4bbbcabb82cb16b97e07f1c1e555d9022c

Aliases

arxiv: 1112.4979 · arxiv_version: 1112.4979v1 · doi: 10.48550/arxiv.1112.4979 · pith_short_12: 3L3UGORTBDDJ · pith_short_16: 3L3UGORTBDDJGQ44 · pith_short_8: 3L3UGORT

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/3L3UGORTBDDJGQ44OMQRUIPMJO \
  | 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: daf7433a3308c693439c73211a21ec4bbbcabb82cb16b97e07f1c1e555d9022c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d079d19ea20e16480e163c2251e30c9d492071ecf26ece408abc28fcde6cf96",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-21T10:34:31Z",
    "title_canon_sha256": "7d9b4a8ea650e4fca01fa16cdbc70d1566b1788b5843e0b88bc9905c8587411f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4979",
    "kind": "arxiv",
    "version": 1
  }
}