Pith Number

pith:WWPBJDKN

pith:2009:WWPBJDKN2P5ZJZ4Q4VWEFGUHTZ

not attested not anchored not stored refs pending

Twisted Alexander invariant and non-abelian Reidemeister torsion for hyperbolic three-dimensional manifolds with cusps

J\'er\^ome Dubois, Yoshikazu Yamaguchi

arxiv:0906.1500 v4 · 2009-06-08 · 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{WWPBJDKN2P5ZJZ4Q4VWEFGUHTZ}

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	2026-05-18T04:04:42.775790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b59e148d4dd3fb94e790e56c429a879e792bc5c9d02dbed56143d2e12519e94a

Aliases

arxiv: 0906.1500 · arxiv_version: 0906.1500v4 · doi: 10.48550/arxiv.0906.1500 · pith_short_12: WWPBJDKN2P5Z · pith_short_16: WWPBJDKN2P5ZJZ4Q · pith_short_8: WWPBJDKN

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/WWPBJDKN2P5ZJZ4Q4VWEFGUHTZ \
  | 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: b59e148d4dd3fb94e790e56c429a879e792bc5c9d02dbed56143d2e12519e94a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3283773cdd4dd1e37f0bbe50c571e46162c8cd155e46ad0e8a8f85188259ab5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-06-08T14:33:03Z",
    "title_canon_sha256": "eba1d48106fd33d0c1f4331655deaf4ec6c94d462eb1daa059425d39f88a91bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1500",
    "kind": "arxiv",
    "version": 4
  }
}