Pith Number

pith:Y6XNGTJB

pith:2014:Y6XNGTJBBXLZXQ5X6SFGETLK5M

not attested not anchored not stored refs pending

Volume entropy for minimal presentations of surface groups in all ranks

David Juher, Francesc Ma\~nosas, J\'er\^ome Los, Llu\'is Alsed\`a

arxiv:1407.1648 v1 · 2014-07-07 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y6XNGTJBBXLZXQ5X6SFGETLK5M}

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	2026-05-18T02:48:10.799299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7aed34d210dd79bc3b7f48a624d6aeb2a06f71711f63101b52dc531933a8a6c

Aliases

arxiv: 1407.1648 · arxiv_version: 1407.1648v1 · doi: 10.48550/arxiv.1407.1648 · pith_short_12: Y6XNGTJBBXLZ · pith_short_16: Y6XNGTJBBXLZXQ5X · pith_short_8: Y6XNGTJB

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/Y6XNGTJBBXLZXQ5X6SFGETLK5M \
  | 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: c7aed34d210dd79bc3b7f48a624d6aeb2a06f71711f63101b52dc531933a8a6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4169fbb068e9f8a9f41ef8412465b66e3d85dd05c8ec8209641817174a1c09e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-07-07T10:05:14Z",
    "title_canon_sha256": "039b2a3d3865212c75101f73433af5130f3fd169526d90fbcf3c1e469f84f55c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.1648",
    "kind": "arxiv",
    "version": 1
  }
}