Pith Number

pith:TFEPA6FW

pith:2008:TFEPA6FWNQRWQ6MZICEFOH6P47

not attested not anchored not stored refs pending

Geometric entropy of geodesic currents on free groups

Ilya Kapovich, Tatiana Nagnibeda

arxiv:0810.4728 v2 · 2008-10-26 · math.GR · math.DS · 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{TFEPA6FWNQRWQ6MZICEFOH6P47}

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	2026-05-18T04:21:30.217369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9948f078b66c236879994088571fcfe7e11a4df0d9f620ca6daa2398307f69f7

Aliases

arxiv: 0810.4728 · arxiv_version: 0810.4728v2 · doi: 10.48550/arxiv.0810.4728 · pith_short_12: TFEPA6FWNQRW · pith_short_16: TFEPA6FWNQRWQ6MZ · pith_short_8: TFEPA6FW

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/TFEPA6FWNQRWQ6MZICEFOH6P47 \
  | 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: 9948f078b66c236879994088571fcfe7e11a4df0d9f620ca6daa2398307f69f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed71f67d3c26641d9b307e492043b5c7fb24355f5e5bfce83faa88cc76d5cc76",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-10-26T23:22:19Z",
    "title_canon_sha256": "c7e9ab00fa11179f1daa5b8b9cbb59ac4380528b777b4e57b217e729754acd0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.4728",
    "kind": "arxiv",
    "version": 2
  }
}