Pith Number

pith:P4M7TMW7

pith:2016:P4M7TMW7LG2GFBT6NHYIKZM2X6

not attested not anchored not stored refs pending

Pulling back stability with applications to Out($F_n$) and relatively hyperbolic groups

Matthew Gentry Durham, Samuel J. Taylor, Tarik Aougab

arxiv:1609.06698 v2 · 2016-09-21 · math.GT · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4M7TMW7LG2GFBT6NHYIKZM2X6}

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	2026-05-18T00:34:52.664772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f19f9b2df59b462867e69f085659abfb9fcd751d027503dfd511dd427d0e976

Aliases

arxiv: 1609.06698 · arxiv_version: 1609.06698v2 · doi: 10.48550/arxiv.1609.06698 · pith_short_12: P4M7TMW7LG2G · pith_short_16: P4M7TMW7LG2GFBT6 · pith_short_8: P4M7TMW7

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/P4M7TMW7LG2GFBT6NHYIKZM2X6 \
  | 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: 7f19f9b2df59b462867e69f085659abfb9fcd751d027503dfd511dd427d0e976

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca0cb92c6210692e25163084353ef28b3d6224256df1c00bdf355655215f4bbf",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-21T19:41:12Z",
    "title_canon_sha256": "e8aeab625871de3f69ebd8e4e2d5256530fc8ed9d7e144d226be25c24a47cc86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06698",
    "kind": "arxiv",
    "version": 2
  }
}