Pith Number

pith:F5JIU4VI

pith:2016:F5JIU4VI6W5ONY3LNL5KG3GTVC

not attested not anchored not stored refs pending

$L^2$-Euler characteristics and the Thurston norm

Stefan Friedl, Wolfgang L\"uck

arxiv:1609.07805 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{F5JIU4VI6W5ONY3LNL5KG3GTVC}

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	2026-05-18T00:04:17.934076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f528a72a8f5bae6e36b6afaa36cd3a8a93213c0ae9076afb52d407e5d1e5852

Aliases

arxiv: 1609.07805 · arxiv_version: 1609.07805v2 · doi: 10.48550/arxiv.1609.07805 · pith_short_12: F5JIU4VI6W5O · pith_short_16: F5JIU4VI6W5ONY3L · pith_short_8: F5JIU4VI

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/F5JIU4VI6W5ONY3LNL5KG3GTVC \
  | 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: 2f528a72a8f5bae6e36b6afaa36cd3a8a93213c0ae9076afb52d407e5d1e5852

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49606fda991750c5c1f7c854c3f8fededad07e8722953fc0075978294d94dd4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-25T21:28:33Z",
    "title_canon_sha256": "45a5b3e285324f84676feeb577a45e744f90529125d992933f97fe757d05ebe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07805",
    "kind": "arxiv",
    "version": 2
  }
}