Pith Number

pith:ACIHSEDZ

pith:2005:ACIHSEDZDTV7DJW6GE7WFFVUEY

not attested not anchored not stored refs pending

The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

Guo-An Diao, Mark Feighn

arxiv:math/0510198 v1 · 2005-10-10 · 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{ACIHSEDZDTV7DJW6GE7WFFVUEY}

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	2026-05-18T02:37:59.707306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00907910791cebf1a6de313f6296b42623cfbb5dc29322727e627ec6307de0c5

Aliases

arxiv: math/0510198 · arxiv_version: math/0510198v1 · doi: 10.48550/arxiv.math/0510198 · pith_short_12: ACIHSEDZDTV7 · pith_short_16: ACIHSEDZDTV7DJW6 · pith_short_8: ACIHSEDZ

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/ACIHSEDZDTV7DJW6GE7WFFVUEY \
  | 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: 00907910791cebf1a6de313f6296b42623cfbb5dc29322727e627ec6307de0c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09ec3b7549d05aed215ca2e44f0d121d02ff14cd4ad44e1ff0646aebb3a1c1ec",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-10-10T16:47:25Z",
    "title_canon_sha256": "ccbe0fafe9543bbf5fbdbbc37550675997e2aa772590d0abdb00bceed73bf389"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0510198",
    "kind": "arxiv",
    "version": 1
  }
}