Pith Number

pith:4X4ELS4J

pith:2012:4X4ELS4J2AMVQTJ375IYNIVGFP

not attested not anchored not stored refs pending

Flows on rooted trees and the Narayana idempotents

Fr\'ed\'eric Chapoton (ICJ)

arxiv:1203.1780 v1 · 2012-03-08 · 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{4X4ELS4J2AMVQTJ375IYNIVGFP}

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	2026-05-18T04:00:36.972936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5f845cb89d019584d3bff5186a2a62be3a2dbe8142bb5d243de78929263230a

Aliases

arxiv: 1203.1780 · arxiv_version: 1203.1780v1 · doi: 10.48550/arxiv.1203.1780 · pith_short_12: 4X4ELS4J2AMV · pith_short_16: 4X4ELS4J2AMVQTJ3 · pith_short_8: 4X4ELS4J

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/4X4ELS4J2AMVQTJ375IYNIVGFP \
  | 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: e5f845cb89d019584d3bff5186a2a62be3a2dbe8142bb5d243de78929263230a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8fb0a5084623a85e716ac4c257cf3c99e1866efeeed902b2b7bdf32a2cde59a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-03-08T12:56:26Z",
    "title_canon_sha256": "70fab1a2ae5cae2a5175bffff040a7f0ca154d34cefe0f3f55d2f8426bb05fc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1780",
    "kind": "arxiv",
    "version": 1
  }
}