Pith Number

pith:H7AFXA3W

pith:2012:H7AFXA3WBDCOIMACJPIHR2CTDM

not attested not anchored not stored refs pending

On Eigenvalues of Free Group Endomorphisms

Daniel S. Silver, Susan G. Williams

arxiv:1206.4926 v2 · 2012-06-21 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H7AFXA3WBDCOIMACJPIHR2CTDM}

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	2026-05-18T03:52:41.084099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3fc05b837608c4e430024bd078e8531b06cfe265c443f70420b06834f30c26f7

Aliases

arxiv: 1206.4926 · arxiv_version: 1206.4926v2 · doi: 10.48550/arxiv.1206.4926 · pith_short_12: H7AFXA3WBDCO · pith_short_16: H7AFXA3WBDCOIMAC · pith_short_8: H7AFXA3W

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/H7AFXA3WBDCOIMACJPIHR2CTDM \
  | 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: 3fc05b837608c4e430024bd078e8531b06cfe265c443f70420b06834f30c26f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe17d0b09d41949e373bdfd4f01d9e8a12cff88cacb8d218eff91fab35ce5ba4",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-21T16:07:18Z",
    "title_canon_sha256": "2e29668a4cff04e55fd0824aca837797822a56f686fa85f977a052911c2f6fa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4926",
    "kind": "arxiv",
    "version": 2
  }
}