Pith Number

pith:LGMZNZ5L

pith:2016:LGMZNZ5L62HSPFIRL2X6M5DH5Y

not attested not anchored not stored refs pending

Commutative hairy graphs and representations of $Out(F_r)$

Thomas Willwacher, Victor Turchin

arxiv:1603.08855 v1 · 2016-03-29 · math.AT · math.QA · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LGMZNZ5L62HSPFIRL2X6M5DH5Y}

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	2026-05-18T00:45:06.619183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d

Aliases

arxiv: 1603.08855 · arxiv_version: 1603.08855v1 · doi: 10.48550/arxiv.1603.08855 · pith_short_12: LGMZNZ5L62HS · pith_short_16: LGMZNZ5L62HSPFIR · pith_short_8: LGMZNZ5L

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/LGMZNZ5L62HSPFIRL2X6M5DH5Y \
  | 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: 599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be1237122c0eb215cd14a68387cddbf604361214e18a31d1ad45ce5f0462f12b",
    "cross_cats_sorted": [
      "math.QA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-03-29T17:32:13Z",
    "title_canon_sha256": "f5fd0d01192238ae5366bf14ce6f1e87b7cb3623e651601bb651b3141ce39688"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08855",
    "kind": "arxiv",
    "version": 1
  }
}