Pith Number

pith:U45KXOIB

pith:2014:U45KXOIB7OKQZDNSKP5JHVMKIL

not attested not anchored not stored refs pending

The horoboundary of outer space, and growth under random automorphisms

Camille Horbez

arxiv:1407.3608 v1 · 2014-07-14 · math.GR · math.GT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U45KXOIB7OKQZDNSKP5JHVMKIL}

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	2026-05-18T02:47:42.385980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a73aabb901fb950c8db253fa93d58a42f1cd078aca020b41ca2beaf6497deecf

Aliases

arxiv: 1407.3608 · arxiv_version: 1407.3608v1 · doi: 10.48550/arxiv.1407.3608 · pith_short_12: U45KXOIB7OKQ · pith_short_16: U45KXOIB7OKQZDNS · pith_short_8: U45KXOIB

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/U45KXOIB7OKQZDNSKP5JHVMKIL \
  | 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: a73aabb901fb950c8db253fa93d58a42f1cd078aca020b41ca2beaf6497deecf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570c21d4e4ced3a0853ed4ce7598fbbb5a937bdd76d6e789453e7fef5a77b3ac",
    "cross_cats_sorted": [
      "math.GT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-07-14T11:22:24Z",
    "title_canon_sha256": "5afff8eccf7ef44bb8cc37f206ffe1448243c1f5ae208235fa9075254484275c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3608",
    "kind": "arxiv",
    "version": 1
  }
}