Pith Number

pith:N36S2HSH

pith:2010:N36S2HSHMZRZ2ZM6PMLNWZLFCY

not attested not anchored not stored refs pending

Lipschitz retraction and distortion for subgroups of Out(F_n)

Lee Mosher, Michael Handel

arxiv:1009.5018 v3 · 2010-09-25 · math.GR · 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{N36S2HSHMZRZ2ZM6PMLNWZLFCY}

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	2026-05-18T02:38:18.400722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6efd2d1e4766639d659e7b16db656516328677abbc654615acb6de92576eb2e8

Aliases

arxiv: 1009.5018 · arxiv_version: 1009.5018v3 · doi: 10.48550/arxiv.1009.5018 · pith_short_12: N36S2HSHMZRZ · pith_short_16: N36S2HSHMZRZ2ZM6 · pith_short_8: N36S2HSH

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/N36S2HSHMZRZ2ZM6PMLNWZLFCY \
  | 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: 6efd2d1e4766639d659e7b16db656516328677abbc654615acb6de92576eb2e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "844e42e9d7934fd69c09049277c9048f5f8812bf77a247e616427c8b056a1dda",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-25T15:36:21Z",
    "title_canon_sha256": "ab93815e6c9afbdf984a42050be05326ca4b4f146c9b08c14aa4c5d12d5e4bc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5018",
    "kind": "arxiv",
    "version": 3
  }
}