Pith Number

pith:R67E2M3M

pith:2012:R67E2M3MXGIFQWEBELEYNJFDKT

not attested not anchored not stored refs pending

Unbalanced subtrees in binary rooted ordered and un-ordered trees

Filippo Disanto

arxiv:1202.5668 v4 · 2012-02-25 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R67E2M3MXGIFQWEBELEYNJFDKT}

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	2026-05-18T03:31:30.839927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fbe4d336cb99058588122c986a4a354cd6b50b5d1d493c82febb31caf09bd9b

Aliases

arxiv: 1202.5668 · arxiv_version: 1202.5668v4 · doi: 10.48550/arxiv.1202.5668 · pith_short_12: R67E2M3MXGIF · pith_short_16: R67E2M3MXGIFQWEB · pith_short_8: R67E2M3M

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/R67E2M3MXGIFQWEBELEYNJFDKT \
  | 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: 8fbe4d336cb99058588122c986a4a354cd6b50b5d1d493c82febb31caf09bd9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2a1baee625a63e58d60f8fc576e08a5dd692ac7a4e41d6ec91885de329af14b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-25T17:00:18Z",
    "title_canon_sha256": "2ce1b2332cf926c53d8dd1c521b53d4c254cb64a1a656edf2a8fd0926a8ce9ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5668",
    "kind": "arxiv",
    "version": 4
  }
}