Pith Number

pith:Y67IN3ZU

pith:2006:Y67IN3ZUYUP3TUX75PBRYXZGAP

not attested not anchored not stored refs pending

Horocyclic products of trees

Laurent Bartholdi, Markus Neuhauser, Wolfgang Woess

arxiv:math/0601417 v1 · 2006-01-17 · math.GR · math.CO · 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{Y67IN3ZUYUP3TUX75PBRYXZGAP}

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	2026-05-18T01:11:52.181530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7be86ef34c51fb9d2ffebc31c5f2603fa76499e7c3fc3f84a12ca6eb1667ede

Aliases

arxiv: math/0601417 · arxiv_version: math/0601417v1 · doi: 10.48550/arxiv.math/0601417 · pith_short_12: Y67IN3ZUYUP3 · pith_short_16: Y67IN3ZUYUP3TUX7 · pith_short_8: Y67IN3ZU

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/Y67IN3ZUYUP3TUX75PBRYXZGAP \
  | 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: c7be86ef34c51fb9d2ffebc31c5f2603fa76499e7c3fc3f84a12ca6eb1667ede

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9caa1532b2a4b4dc873233c5d1cba9ecb716b427cb622408f771ceb4abe4f95",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-01-17T16:24:23Z",
    "title_canon_sha256": "8bf402500b0fd70f878ac4b3514cec97ffa30e53ba9fe8a5f7fcd773b63d9da7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601417",
    "kind": "arxiv",
    "version": 1
  }
}