Pith Number

pith:2UGRUNSP

pith:2015:2UGRUNSPRWQ3PHHYUOM55PCQJI

not attested not anchored not stored refs pending

Tree-based language complexity of Thompson's group F

Jennifer Taback, Sharif Younes

arxiv:1501.04315 v2 · 2015-01-18 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UGRUNSPRWQ3PHHYUOM55PCQJI}

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	2026-05-18T02:29:02.284145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d50d1a364f8da1b79cf8a399debc504a08a985aa58e42c34234ab9c2a090f596

Aliases

arxiv: 1501.04315 · arxiv_version: 1501.04315v2 · doi: 10.48550/arxiv.1501.04315 · pith_short_12: 2UGRUNSPRWQ3 · pith_short_16: 2UGRUNSPRWQ3PHHY · pith_short_8: 2UGRUNSP

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/2UGRUNSPRWQ3PHHYUOM55PCQJI \
  | 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: d50d1a364f8da1b79cf8a399debc504a08a985aa58e42c34234ab9c2a090f596

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f35cf537a06085d03ff154290249a577d967fcfeae405135449ea0caf371e9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-18T15:21:43Z",
    "title_canon_sha256": "3747156b55aaeab4c1eec95d2dedc2d4820da8f6edf3991cf2745c2f3fa6dbdb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04315",
    "kind": "arxiv",
    "version": 2
  }
}