Pith Number

pith:QMEES26W

pith:2012:QMEES26WTOEDZTTDLMO5AR4Q6C

not attested not anchored not stored refs pending

Bounding the gap between a free group (outer) automorphism and its inverse

Enric Ventura, Manuel Ladra, Pedro V. Silva

arxiv:1212.6749 v3 · 2012-12-30 · 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{QMEES26WTOEDZTTDLMO5AR4Q6C}

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	2026-05-18T02:27:57.395838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8308496bd69b883cce635b1dd04790f090856e39cb20552e82ae2f4cc49d227f

Aliases

arxiv: 1212.6749 · arxiv_version: 1212.6749v3 · doi: 10.48550/arxiv.1212.6749 · pith_short_12: QMEES26WTOED · pith_short_16: QMEES26WTOEDZTTD · pith_short_8: QMEES26W

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/QMEES26WTOEDZTTDLMO5AR4Q6C \
  | 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: 8308496bd69b883cce635b1dd04790f090856e39cb20552e82ae2f4cc49d227f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb2cf59e589d996d3602dd0714a5a6e7505b49d4c1e8b0839d48e7bdef07fbef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-30T17:17:41Z",
    "title_canon_sha256": "54d3b62d144bfb3e6f62fbc9c65e2ead3f5b2c3c631565aca1536ca4a76a439d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6749",
    "kind": "arxiv",
    "version": 3
  }
}