Pith Number

pith:WKJR2GFF

pith:2008:WKJR2GFFGGHOX4U2MLWEWIMWLO

not attested not anchored not stored refs pending

Elementary combinatorics of the HOMFLYPT polynomial

Michael Polyak, Sergei Chmutov

arxiv:0810.4105 v2 · 2008-10-22 · math.GT · 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{WKJR2GFFGGHOX4U2MLWEWIMWLO}

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	2026-05-18T04:15:04.931700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2931d18a5318eebf29a62ec4b21965b974d8e105c98571ab350afbbe1f96f5a

Aliases

arxiv: 0810.4105 · arxiv_version: 0810.4105v2 · doi: 10.48550/arxiv.0810.4105 · pith_short_12: WKJR2GFFGGHO · pith_short_16: WKJR2GFFGGHOX4U2 · pith_short_8: WKJR2GFF

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/WKJR2GFFGGHOX4U2MLWEWIMWLO \
  | 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: b2931d18a5318eebf29a62ec4b21965b974d8e105c98571ab350afbbe1f96f5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d45012fa92ae0c243015ca49b4569828b86842f18cf7a812ab2ef1578230286b",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-10-22T16:36:51Z",
    "title_canon_sha256": "7523695997e2556b9edc9779dd1eb2b49298e68d5dd1a9fb21e607cb8faeac94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4105",
    "kind": "arxiv",
    "version": 2
  }
}