Pith Number

pith:VK4IWP7H

pith:2004:VK4IWP7H4PFXM7KBJEZ5FYDTWH

not attested not anchored not stored refs pending

Automorphisms of free groups with boundaries

Craig A. Jensen, Nathalie Wahl

arxiv:math/0402166 v2 · 2004-02-11 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VK4IWP7H4PFXM7KBJEZ5FYDTWH}

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	2026-05-18T02:41:32.515747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aab88b3fe7e3cb767d414933d2e073b1d33524950327e80ce3780710a759201b

Aliases

arxiv: math/0402166 · arxiv_version: math/0402166v2 · doi: 10.48550/arxiv.math/0402166 · pith_short_12: VK4IWP7H4PFX · pith_short_16: VK4IWP7H4PFXM7KB · pith_short_8: VK4IWP7H

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/VK4IWP7H4PFXM7KBJEZ5FYDTWH \
  | 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: aab88b3fe7e3cb767d414933d2e073b1d33524950327e80ce3780710a759201b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "206745dd7a2fd0cdb84fa0001df09eb0cbca65f6c341dc5714cd21fd73647b8c",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-02-11T00:36:32Z",
    "title_canon_sha256": "c3a6ddb13c103706b13d5d061827e9b179333e6b5468b8587185c4ae087067ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0402166",
    "kind": "arxiv",
    "version": 2
  }
}