Pith Number

pith:GZP5BBEJ

pith:2012:GZP5BBEJ6E6UJHEOEYD7G36PTZ

not attested not anchored not stored refs pending

Fixed points of endomorphisms of virtually free groups

Pedro V. Silva

arxiv:1203.1355 v2 · 2012-03-07 · math.GR · cs.FL · 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{GZP5BBEJ6E6UJHEOEYD7G36PTZ}

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	2026-05-18T04:00:26.228412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

365fd08489f13d449c8e2607f36fcf9e778c2222fd4599176cc2070bdf00841b

Aliases

arxiv: 1203.1355 · arxiv_version: 1203.1355v2 · doi: 10.48550/arxiv.1203.1355 · pith_short_12: GZP5BBEJ6E6U · pith_short_16: GZP5BBEJ6E6UJHEO · pith_short_8: GZP5BBEJ

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/GZP5BBEJ6E6UJHEOEYD7G36PTZ \
  | 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: 365fd08489f13d449c8e2607f36fcf9e778c2222fd4599176cc2070bdf00841b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bfb374c76047e238cdafce4d44ae29d7a2c52dfcb3246b9c234f46e6d8f53f1",
    "cross_cats_sorted": [
      "cs.FL",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-03-07T00:19:48Z",
    "title_canon_sha256": "3db05fb2eb61d015f18f17ebf9adc5e21f54232b757bb618538318277830a85b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1355",
    "kind": "arxiv",
    "version": 2
  }
}