Pith Number

pith:K4B54SKL

pith:2011:K4B54SKLIMVNAFXNDZ4LJDAQSI

not attested not anchored not stored refs pending

Twisted Alexander polynomials of hyperbolic knots

Nathan M. Dunfield, Nicholas Jackson, Stefan Friedl

arxiv:1108.3045 v3 · 2011-08-15 · 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{K4B54SKLIMVNAFXNDZ4LJDAQSI}

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	2026-05-18T02:46:15.290148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5703de494b432ad016ed1e78b48c10921ef4fdf31ef2b318b6250ead331ca5d9

Aliases

arxiv: 1108.3045 · arxiv_version: 1108.3045v3 · doi: 10.48550/arxiv.1108.3045 · pith_short_12: K4B54SKLIMVN · pith_short_16: K4B54SKLIMVNAFXN · pith_short_8: K4B54SKL

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/K4B54SKLIMVNAFXNDZ4LJDAQSI \
  | 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: 5703de494b432ad016ed1e78b48c10921ef4fdf31ef2b318b6250ead331ca5d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37e31908700ec8ec065ce936f1fd7fee9ba4a999489ed19e2eb6f0927b805627",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-15T18:20:28Z",
    "title_canon_sha256": "5d473c8e2f60decec889cbdbee0e6166fc4dcc22a84fdae9a479a73742aba206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3045",
    "kind": "arxiv",
    "version": 3
  }
}