Pith Number

pith:6VZORWGL

pith:2008:6VZORWGL3PXABR2ZNC73MMAIJH

not attested not anchored not stored refs pending

A simple formula for the Casson-Walker invariant

Michael Polyak, Sergei Matveev

arxiv:0811.0606 v2 · 2008-11-04 · 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{6VZORWGL3PXABR2ZNC73MMAIJH}

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	2026-05-18T04:15:04.922299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f572e8d8cbdbee00c75968bfb6300849eeb9565f87a236b0eb9c0adef2d016f4

Aliases

arxiv: 0811.0606 · arxiv_version: 0811.0606v2 · doi: 10.48550/arxiv.0811.0606 · pith_short_12: 6VZORWGL3PXA · pith_short_16: 6VZORWGL3PXABR2Z · pith_short_8: 6VZORWGL

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/6VZORWGL3PXABR2ZNC73MMAIJH \
  | 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: f572e8d8cbdbee00c75968bfb6300849eeb9565f87a236b0eb9c0adef2d016f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4902c45aa9edfd791b81d2a36e59ce4c9116e6a0c840fcbed07ef7cbb406dc5a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-11-04T20:48:48Z",
    "title_canon_sha256": "a8676ac7068f4c4cea27192a9293bd7a06237477fa5ba37cb11c7136706116d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.0606",
    "kind": "arxiv",
    "version": 2
  }
}