Pith Number

pith:GZMNRRP4

pith:2011:GZMNRRP45UM37O6RDI4TYWFUBM

not attested not anchored not stored refs pending

Permutation Complexity and the Letter Doubling Map

Steven Widmer

arxiv:1102.5527 v1 · 2011-02-27 · 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{GZMNRRP45UM37O6RDI4TYWFUBM}

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	2026-05-18T04:27:46.681918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3658d8c5fced19bfbbd11a393c58b40b0f8e82a5fc9dd2808494644c3597b666

Aliases

arxiv: 1102.5527 · arxiv_version: 1102.5527v1 · doi: 10.48550/arxiv.1102.5527 · pith_short_12: GZMNRRP45UM3 · pith_short_16: GZMNRRP45UM37O6R · pith_short_8: GZMNRRP4

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/GZMNRRP45UM37O6RDI4TYWFUBM \
  | 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: 3658d8c5fced19bfbbd11a393c58b40b0f8e82a5fc9dd2808494644c3597b666

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13839042ae30ba1ab692f68162a6adcc78a758f450ac29e8e1b0128112b4e9fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-27T17:46:21Z",
    "title_canon_sha256": "34d9599313f4a194d604b0f09adec43616e2310bf24525ed10b310594ccdb498"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5527",
    "kind": "arxiv",
    "version": 1
  }
}