Pith Number

pith:GLKFFA5E

pith:2000:GLKFFA5EZVZFHUZZ3PNVL4C3JF

not attested not anchored not stored refs pending

Noncommutative Rational Functions and Farber's Invariants of Boundary Links

Arkady Vaintrob, Christophe Reutenauer, Vladimir Retakh

arxiv:math/0004112 v1 · 2000-04-17 · 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{GLKFFA5EZVZFHUZZ3PNVL4C3JF}

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	2026-07-04T14:34:27.870372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32d45283a4cd7253d339dbdb55f05b4965e5f861a3fe9a6493a0a91dccd53c62

Aliases

arxiv: math/0004112 · arxiv_version: math/0004112v1 · doi: 10.48550/arxiv.math/0004112 · pith_short_12: GLKFFA5EZVZF · pith_short_16: GLKFFA5EZVZFHUZZ · pith_short_8: GLKFFA5E

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/GLKFFA5EZVZFHUZZ3PNVL4C3JF \
  | 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: 32d45283a4cd7253d339dbdb55f05b4965e5f861a3fe9a6493a0a91dccd53c62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb436ac231e41a289099bdfacc0f7fb221b571d1b70e026bfc490fa0b733b404",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-04-17T15:23:47Z",
    "title_canon_sha256": "f50d6662eab5ffc2f30902fbb0fad07dc5fff80dd4fc2742712131caa9661b27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0004112",
    "kind": "arxiv",
    "version": 1
  }
}