Pith Number

pith:73N4AXKF

pith:2010:73N4AXKF4M64SRGYNXYBO3JGWV

not attested not anchored not stored refs pending

A state-sum formula for the Alexander polynomial

Samson Black

arxiv:1002.4860 v2 · 2010-02-25 · math.GT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{73N4AXKF4M64SRGYNXYBO3JGWV}

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	2026-05-18T03:16:06.727755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fedbc05d45e33dc944d86df0176d26b554dc18b67dbc7301065561d2c857d05c

Aliases

arxiv: 1002.4860 · arxiv_version: 1002.4860v2 · doi: 10.48550/arxiv.1002.4860 · pith_short_12: 73N4AXKF4M64 · pith_short_16: 73N4AXKF4M64SRGY · pith_short_8: 73N4AXKF

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/73N4AXKF4M64SRGYNXYBO3JGWV \
  | 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: fedbc05d45e33dc944d86df0176d26b554dc18b67dbc7301065561d2c857d05c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c34be1cfd2dd5702cf046aa77a964f4d655535d7c1f1aa75912145745e71a7c",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-02-25T20:30:50Z",
    "title_canon_sha256": "dd11b7440f48c430f64e17f46073071acc9b6adf7df24ffb59bf7a194e664488"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4860",
    "kind": "arxiv",
    "version": 2
  }
}