Pith Number

pith:GXY65SH7

pith:2008:GXY65SH73QTXMSV6WIKG5VVRO5

not attested not anchored not stored refs pending

Growth of intersection numbers for free group automorphisms

Jason Behrstock, Matt Clay, Mladen Bestvina

arxiv:0806.4975 v3 · 2008-06-30 · 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{GXY65SH73QTXMSV6WIKG5VVRO5}

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	2026-05-18T02:58:11.382166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35f1eec8ffdc27764abeb2146ed6b1776d0fc8d05bc8035eac1e68e8398fa245

Aliases

arxiv: 0806.4975 · arxiv_version: 0806.4975v3 · doi: 10.48550/arxiv.0806.4975 · pith_short_12: GXY65SH73QTX · pith_short_16: GXY65SH73QTXMSV6 · pith_short_8: GXY65SH7

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/GXY65SH73QTXMSV6WIKG5VVRO5 \
  | 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: 35f1eec8ffdc27764abeb2146ed6b1776d0fc8d05bc8035eac1e68e8398fa245

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4d1541d91640742fb99ba7572c804b3898cfb055666c4de12f890f5fc06bb78",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-06-30T19:31:05Z",
    "title_canon_sha256": "cdf7a09da3376413ce91f07db4af64700bcd37c20dfa93c0e94ccaea3d427c61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.4975",
    "kind": "arxiv",
    "version": 3
  }
}