Pith Number

pith:KL2V74NL

pith:2016:KL2V74NLG2PA7M2CAI6GBCZDMR

not attested not anchored not stored refs pending

Universal $L^2$-torsion, polytopes and applications to $3$-manifolds

Stefan Friedl, Wolfgang L\"uck

arxiv:1609.07809 v2 · 2016-09-25 · 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{KL2V74NLG2PA7M2CAI6GBCZDMR}

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	2026-05-18T00:45:06.376373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52f55ff1ab369e0fb342023c608b2364450f1d9206b519764f728282238e58e7

Aliases

arxiv: 1609.07809 · arxiv_version: 1609.07809v2 · doi: 10.48550/arxiv.1609.07809 · pith_short_12: KL2V74NLG2PA · pith_short_16: KL2V74NLG2PA7M2C · pith_short_8: KL2V74NL

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/KL2V74NLG2PA7M2CAI6GBCZDMR \
  | 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: 52f55ff1ab369e0fb342023c608b2364450f1d9206b519764f728282238e58e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aacf435b8feb7826fc3e541311576349a60750f4999fc05042273385a77feb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-25T21:39:57Z",
    "title_canon_sha256": "8ea0050f8261dff2dc0790a4cdb779c196989c42deacb93ed34569a2078bd44b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07809",
    "kind": "arxiv",
    "version": 2
  }
}