Pith Number

pith:MAWMJH7R

pith:2009:MAWMJH7RH7T5DHKPXMPUMD5CK4

not attested not anchored not stored refs pending

Domains of proper discontinuity on the boundary of Outer space

Ilya Kapovich, Martin Lustig

arxiv:0902.4263 v3 · 2009-02-25 · 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{MAWMJH7RH7T5DHKPXMPUMD5CK4}

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	2026-05-18T04:20:51.406608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

602cc49ff13fe7d19d4fbb1f460fa2573104fbfd73501dbf8225482c46a7a2c4

Aliases

arxiv: 0902.4263 · arxiv_version: 0902.4263v3 · doi: 10.48550/arxiv.0902.4263 · pith_short_12: MAWMJH7RH7T5 · pith_short_16: MAWMJH7RH7T5DHKP · pith_short_8: MAWMJH7R

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/MAWMJH7RH7T5DHKPXMPUMD5CK4 \
  | 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: 602cc49ff13fe7d19d4fbb1f460fa2573104fbfd73501dbf8225482c46a7a2c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34697e7b11700a3eae2c2c2e8581245f1441640f11a14007ac86a9fc1f940be3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-25T20:09:56Z",
    "title_canon_sha256": "7286eece2eaac8ab807cf3057dfb26cc5e61005cc5a589a4e5d8e41c70209dd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.4263",
    "kind": "arxiv",
    "version": 3
  }
}