Pith Number

pith:W5RHVSZS

pith:2008:W5RHVSZSCQXKBQK656MLM35TWE

not attested not anchored not stored refs pending

The Fundamental Crossed Module of the Complement of a Knotted Surface

Jo\~ao Faria Martins

arxiv:0801.3921 v1 · 2008-01-25 · math.GT · hep-th · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W5RHVSZSCQXKBQK656MLM35TWE}

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	2026-05-18T00:44:10.574015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7627acb32142ea0c15eef98b66fb3b13ea290a2360143135232185e4a2d602f

Aliases

arxiv: 0801.3921 · arxiv_version: 0801.3921v1 · doi: 10.48550/arxiv.0801.3921 · pith_short_12: W5RHVSZSCQXK · pith_short_16: W5RHVSZSCQXKBQK6 · pith_short_8: W5RHVSZS

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/W5RHVSZSCQXKBQK656MLM35TWE \
  | 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: b7627acb32142ea0c15eef98b66fb3b13ea290a2360143135232185e4a2d602f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2b5a537c467a4f1c294c175dd564c9230491b0697bf9924de424468b9e68810",
    "cross_cats_sorted": [
      "hep-th",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2008-01-25T14:21:10Z",
    "title_canon_sha256": "1705c84054ad1f8b5f46dc70b2142098c8af6fc0cb78d8d34f913935d1e6ff30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.3921",
    "kind": "arxiv",
    "version": 1
  }
}