Pith Number

pith:MDEF3DDR

pith:2009:MDEF3DDRGN7WHGFCK3CRNGSHTH

not attested not anchored not stored refs pending

Virtually geometric words and Whitehead's algorithm

Jason Fox Manning

arxiv:0904.0724 v3 · 2009-04-04 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDEF3DDRGN7WHGFCK3CRNGSHTH}

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	2026-05-18T04:34:09.027930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d

Aliases

arxiv: 0904.0724 · arxiv_version: 0904.0724v3 · doi: 10.48550/arxiv.0904.0724 · pith_short_12: MDEF3DDRGN7W · pith_short_16: MDEF3DDRGN7WHGFC · pith_short_8: MDEF3DDR

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/MDEF3DDRGN7WHGFCK3CRNGSHTH \
  | 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: 60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc6a0350b1eaf758d5ad736be9bd4cb4908806dfdc6629156f282da5c0424ed3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-04-04T15:46:58Z",
    "title_canon_sha256": "de560a521771850e7f6a47f21906b3078d4a7235e9d1e2745826d5b692f4274c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0724",
    "kind": "arxiv",
    "version": 3
  }
}