Pith Number

pith:SYGMAH4K

pith:2002:SYGMAH4KGAF6WEXUVC2P4E3FTD

not attested not anchored not stored refs pending

The fine structure of 321 avoiding permutations

Michael H. Albert

arxiv:math/0212163 v2 · 2002-12-11 · 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{SYGMAH4KGAF6WEXUVC2P4E3FTD}

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	2026-05-18T01:35:42.436688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

960cc01f8a300beb12f4a8b4fe136598c7b20ad511238f93c95102fbe2880f28

Aliases

arxiv: math/0212163 · arxiv_version: math/0212163v2 · doi: 10.48550/arxiv.math/0212163 · pith_short_12: SYGMAH4KGAF6 · pith_short_16: SYGMAH4KGAF6WEXU · pith_short_8: SYGMAH4K

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/SYGMAH4KGAF6WEXUVC2P4E3FTD \
  | 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: 960cc01f8a300beb12f4a8b4fe136598c7b20ad511238f93c95102fbe2880f28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b82ac103db063a9ccfdf817e1d21b6e3e14085941445baccff5351d886aaedd2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2002-12-11T22:13:05Z",
    "title_canon_sha256": "8be16d0cf3650e53ca21846800e7031e74dad44cd92285fb014c746d6e08dc8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212163",
    "kind": "arxiv",
    "version": 2
  }
}