Pith Number

pith:DSK3KRZB

pith:2026:DSK3KRZBHFSHTWMORSDJ4J5BLT

not attested not anchored not stored refs pending

A coarse Menger theorem for hyperbolic graphs, finitely presented groups, and more

Sandra Albrechtsen

arxiv:2606.17605 v1 · 2026-06-16 · math.CO · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DSK3KRZBHFSHTWMORSDJ4J5BLT}

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	2026-06-19T16:10:17.110021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c95b54721396479d98e8c869e27a15cfae478284b24817692d88328bf7e36f8

Aliases

arxiv: 2606.17605 · arxiv_version: 2606.17605v1 · doi: 10.48550/arxiv.2606.17605 · pith_short_12: DSK3KRZBHFSH · pith_short_16: DSK3KRZBHFSHTWMO · pith_short_8: DSK3KRZB

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/DSK3KRZBHFSHTWMORSDJ4J5BLT \
  | 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: 1c95b54721396479d98e8c869e27a15cfae478284b24817692d88328bf7e36f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "974431af750aa596f0d0ea15cf87cb70a036593e92fd1f5ff61d52db934cfb21",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-16T07:10:58Z",
    "title_canon_sha256": "e557cc18c587ec96636d8bb1c618c2683243a157ddfc50dfbfc75feb75d91f21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17605",
    "kind": "arxiv",
    "version": 1
  }
}