Pith Number

pith:D4ORI4HH

pith:2004:D4ORI4HHXA64PNP6EAKGXIYV2D

not attested not anchored not stored refs pending

On Generalized Knot Groups

Sam Nelson, Xiao-Song Lin

arxiv:math/0407050 v4 · 2004-07-04 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D4ORI4HHXA64PNP6EAKGXIYV2D}

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	2026-07-04T15:13:33.520325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f1d1470e7b83dc7b5fe20146ba315d0da73cf032eeff8075ebba99da80cf88c

Aliases

arxiv: math/0407050 · arxiv_version: math/0407050v4 · doi: 10.48550/arxiv.math/0407050 · pith_short_12: D4ORI4HHXA64 · pith_short_16: D4ORI4HHXA64PNP6 · pith_short_8: D4ORI4HH

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/D4ORI4HHXA64PNP6EAKGXIYV2D \
  | 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: 1f1d1470e7b83dc7b5fe20146ba315d0da73cf032eeff8075ebba99da80cf88c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8edf0e894c8e38300e9e344eae372637d65dd27a02ad635289d379255a77419",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-07-04T18:45:03Z",
    "title_canon_sha256": "50c7ef485b3edc41afb48ce8cee82f7db99b6bd8934e8e9bd257ce9abf04d35b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407050",
    "kind": "arxiv",
    "version": 4
  }
}