Pith Number

pith:SN54M32P

pith:2007:SN54M32PS3HORLT3YVFRBBCRPK

not attested not anchored not stored refs pending

Geometric Intersection Number and analogues of the Curve Complex for free groups

Ilya Kapovich, Martin Lustig

arxiv:0711.3806 v4 · 2007-11-24 · 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{SN54M32PS3HORLT3YVFRBBCRPK}

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	2026-05-18T02:38:19.307816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

937bc66f4f96cee8ae7bc54b1084517ab9f0c893cbbc1d480d1067e3c1b72d13

Aliases

arxiv: 0711.3806 · arxiv_version: 0711.3806v4 · doi: 10.48550/arxiv.0711.3806 · pith_short_12: SN54M32PS3HO · pith_short_16: SN54M32PS3HORLT3 · pith_short_8: SN54M32P

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/SN54M32PS3HORLT3YVFRBBCRPK \
  | 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: 937bc66f4f96cee8ae7bc54b1084517ab9f0c893cbbc1d480d1067e3c1b72d13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ea5ae1be64fceda1cca9deac010521349eb7c173ee5d4da2ea47a9d07114203",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-11-24T01:43:24Z",
    "title_canon_sha256": "098f93073f32dd45ad6c08b257c95ff1b4f35834643a9547b3b5b52e736710be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.3806",
    "kind": "arxiv",
    "version": 4
  }
}