Pith Number

pith:LVFRHUHX

pith:2013:LVFRHUHXGSGHVPGUTQRP7ELHB6

not attested not anchored not stored refs pending

Explicit Formula for Witten-Kontsevich Tau-Function

Jian Zhou

arxiv:1306.5429 v1 · 2013-06-23 · math.AG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LVFRHUHXGSGHVPGUTQRP7ELHB6}

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	2026-05-18T03:20:08.133321Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d4b13d0f7348c7abcd49c22ff91670f868acd135f94c054bccdd12b4916fc7a

Aliases

arxiv: 1306.5429 · arxiv_version: 1306.5429v1 · doi: 10.48550/arxiv.1306.5429 · pith_short_12: LVFRHUHXGSGH · pith_short_16: LVFRHUHXGSGHVPGU · pith_short_8: LVFRHUHX

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/LVFRHUHXGSGHVPGUTQRP7ELHB6 \
  | 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: 5d4b13d0f7348c7abcd49c22ff91670f868acd135f94c054bccdd12b4916fc7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b7f8f311642f4f356d0b13ff517326821fab631ae10defc12dc2278bab5a87c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-06-23T16:03:49Z",
    "title_canon_sha256": "e8a8c030e2f6d4a7502fb1f0b2a57e3ce91d8bb915e486ecac551b166a6a35c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5429",
    "kind": "arxiv",
    "version": 1
  }
}