Pith Number

pith:PHKQLWNP

pith:2011:PHKQLWNPN76E2GBD4GH7GYNRXP

not attested not anchored not stored refs pending

Directed animals, quadratic and rewriting systems

Jean-Fran\c{c}ois Marckert

arxiv:1112.0910 v2 · 2011-12-05 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHKQLWNPN76E2GBD4GH7GYNRXP}

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	2026-05-18T02:21:28.044081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79d505d9af6ffc4d1823e18ff361b1bbe592d3164569f775e3e32faa04910607

Aliases

arxiv: 1112.0910 · arxiv_version: 1112.0910v2 · doi: 10.48550/arxiv.1112.0910 · pith_short_12: PHKQLWNPN76E · pith_short_16: PHKQLWNPN76E2GBD · pith_short_8: PHKQLWNP

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/PHKQLWNPN76E2GBD4GH7GYNRXP \
  | 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: 79d505d9af6ffc4d1823e18ff361b1bbe592d3164569f775e3e32faa04910607

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25c52d862bbc94916cc39a18a362ca817906c00bdcb58b1bb74396f34a9d5687",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-05T12:59:30Z",
    "title_canon_sha256": "2e48ba33d9a84afb4eaf60a1862778f4f66a613b50ef6e77bde843c9dec12798"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0910",
    "kind": "arxiv",
    "version": 2
  }
}