Pith Number

pith:BO32ZG2Q

pith:2006:BO32ZG2QBSUPBBKYBS6LG7E43B

not attested not anchored not stored refs pending

Hard Unknots and Collapsing Tangles

Louis H. Kauffman, Sofia Lambropoulou

arxiv:math/0601525 v5 · 2006-01-22 · 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{BO32ZG2QBSUPBBKYBS6LG7E43B}

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	2026-05-18T02:46:22.981505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bb7ac9b500ca8f085580cbcb37c9cd86c6f58aec1e2bdfc5a0c9c0c5b27c578

Aliases

arxiv: math/0601525 · arxiv_version: math/0601525v5 · doi: 10.48550/arxiv.math/0601525 · pith_short_12: BO32ZG2QBSUP · pith_short_16: BO32ZG2QBSUPBBKY · pith_short_8: BO32ZG2Q

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/BO32ZG2QBSUPBBKYBS6LG7E43B \
  | 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: 0bb7ac9b500ca8f085580cbcb37c9cd86c6f58aec1e2bdfc5a0c9c0c5b27c578

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36ed18c1376b4a31a987d813b85e4cd9287ca885d4ab4638ad5d7f5c9f7abf10",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2006-01-22T04:32:02Z",
    "title_canon_sha256": "b228a01d83c47c0ba0fb914b2557c9cb3ad6eb644dab68da8b610b7bc8377ade"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601525",
    "kind": "arxiv",
    "version": 5
  }
}