Pith Number

pith:I2LQKCGW

pith:2008:I2LQKCGW5GZVSLORFJMCFKVLHV

not attested not anchored not stored refs pending

Explicit double shuffle relations and a generalization of Euler's decomposition formula

Bingyong Xie, Li Guo

arxiv:0808.2618 v1 · 2008-08-19 · math.NT · math.AC · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I2LQKCGW5GZVSLORFJMCFKVLHV}

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	2026-05-18T02:41:09.408890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46970508d6e9b3592dd12a5822aaab3d6f51d3aeef317a7180e23da6d5669152

Aliases

arxiv: 0808.2618 · arxiv_version: 0808.2618v1 · doi: 10.48550/arxiv.0808.2618 · pith_short_12: I2LQKCGW5GZV · pith_short_16: I2LQKCGW5GZVSLOR · pith_short_8: I2LQKCGW

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/I2LQKCGW5GZVSLORFJMCFKVLHV \
  | 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: 46970508d6e9b3592dd12a5822aaab3d6f51d3aeef317a7180e23da6d5669152

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71fb27ec28b506b92a0ef0ae586a99cf63e1f57fa45241aa38e78951d7f784d2",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-08-19T19:46:22Z",
    "title_canon_sha256": "39a89fb5b26a4c5aac26ff93f23a6116b7a9d05699e431f4ac6a5fec543ad7f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2618",
    "kind": "arxiv",
    "version": 1
  }
}