Pith Number

pith:27JO2HN3

pith:2022:27JO2HN3DGY2O5R7KCJZGXCZ55

not attested not anchored not stored refs pending

A combinatorial higher-rank hyperbolicity condition

Martina J{\o}rgensen, Urs Lang

arxiv:2206.08153 v3 · 2022-06-16 · math.MG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27JO2HN3DGY2O5R7KCJZGXCZ55}

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	2026-07-05T06:56:29.259489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7d2ed1dbb19b1a7763f5093935c59ef69169d2ee3424f89c05c31b46e333e12

Aliases

arxiv: 2206.08153 · arxiv_version: 2206.08153v3 · doi: 10.48550/arxiv.2206.08153 · pith_short_12: 27JO2HN3DGY2 · pith_short_16: 27JO2HN3DGY2O5R7 · pith_short_8: 27JO2HN3

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/27JO2HN3DGY2O5R7KCJZGXCZ55 \
  | 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: d7d2ed1dbb19b1a7763f5093935c59ef69169d2ee3424f89c05c31b46e333e12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aa13a42040970face2555de5b5f5ccd26571aeea446efd651752667da949916",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2022-06-16T13:17:07Z",
    "title_canon_sha256": "7f94a0c3bb244ca93011b0fb1b0341fc6c6bb0f7bd00b9f7f81758b43006ed79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.08153",
    "kind": "arxiv",
    "version": 3
  }
}