Pith Number

pith:4UATXETG

pith:2013:4UATXETGSM5JULW4N6UEXJRJW7

not attested not anchored not stored refs pending

Examples of expanding endomorphisms on fake tori

Andrey Gogolev, F. Thomas Farrell

arxiv:1307.3223 v2 · 2013-07-11 · math.DS · 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{4UATXETGSM5JULW4N6UEXJRJW7}

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	2026-05-18T00:44:29.656145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5013b9266933a9a2edc6fa84ba629b7eeaac44b817f5b7d3bd511866e852937

Aliases

arxiv: 1307.3223 · arxiv_version: 1307.3223v2 · doi: 10.48550/arxiv.1307.3223 · pith_short_12: 4UATXETGSM5J · pith_short_16: 4UATXETGSM5JULW4 · pith_short_8: 4UATXETG

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/4UATXETGSM5JULW4N6UEXJRJW7 \
  | 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: e5013b9266933a9a2edc6fa84ba629b7eeaac44b817f5b7d3bd511866e852937

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0847e925c4656c4dff35c43709fcd651b15f3e338f81d309df219e26e55d9293",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-07-11T19:27:12Z",
    "title_canon_sha256": "e4bfadb7b1ebb1f05ec69de21ac0521f2794bf521522e95b351490dc08cb60b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3223",
    "kind": "arxiv",
    "version": 2
  }
}