Pith Number

pith:AAHZAH5L

pith:2009:AAHZAH5LVJ65HTZRD7FEDYPJBO

not attested not anchored not stored refs pending

Bounding the residual finiteness of free groups

Francesco Matucci, Martin Kassabov

arxiv:0912.2368 v2 · 2009-12-11 · 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{AAHZAH5LVJ65HTZRD7FEDYPJBO}

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	2026-05-18T04:21:53.135355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

000f901fabaa7dd3cf311fca41e1e90badd82da124e569cda1456a9e49e74fd5

Aliases

arxiv: 0912.2368 · arxiv_version: 0912.2368v2 · doi: 10.48550/arxiv.0912.2368 · pith_short_12: AAHZAH5LVJ65 · pith_short_16: AAHZAH5LVJ65HTZR · pith_short_8: AAHZAH5L

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/AAHZAH5LVJ65HTZRD7FEDYPJBO \
  | 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: 000f901fabaa7dd3cf311fca41e1e90badd82da124e569cda1456a9e49e74fd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa72cfdaf3cd33ed3632ec525fc5ec9296ada815bf035de1e3cde287889d56be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-12-11T22:10:12Z",
    "title_canon_sha256": "c964f236d2cdaec1c5aba371fe650bc050839e4336b5ccc8b3e5a02acf931fcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2368",
    "kind": "arxiv",
    "version": 2
  }
}