Pith Number

pith:ODUA7WUL

pith:2008:ODUA7WULPLAMIZ5VDUDRSB7F2I

not attested not anchored not stored refs pending

Plumbers' knots

Chad Giusti

arxiv:0811.2215 v3 · 2008-11-13 · math.AT · 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{ODUA7WULPLAMIZ5VDUDRSB7F2I}

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	2026-05-18T02:26:32.151862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70e80fda8b7ac0c467b51d071907e5d2384e7769338bf25eed500d7c46b2bf20

Aliases

arxiv: 0811.2215 · arxiv_version: 0811.2215v3 · doi: 10.48550/arxiv.0811.2215 · pith_short_12: ODUA7WULPLAM · pith_short_16: ODUA7WULPLAMIZ5V · pith_short_8: ODUA7WUL

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/ODUA7WULPLAMIZ5VDUDRSB7F2I \
  | 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: 70e80fda8b7ac0c467b51d071907e5d2384e7769338bf25eed500d7c46b2bf20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f28e02061f65c3a2f1f83896fa4ae8e8acd237843bc4ffc56db8b20ab204f7fa",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-11-13T20:59:25Z",
    "title_canon_sha256": "ca4232aeaca61c55fe4ec82bf0cb01e8e3928b0147ebf2fdc12576eea1f62394"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.2215",
    "kind": "arxiv",
    "version": 3
  }
}