Pith Number

pith:PGFENEBR

pith:2013:PGFENEBRU2TPMMC6VMQLCKZSR2

not attested not anchored not stored refs pending

Equivalent trace sets for arithmetic Fuchsian groups

Grant S. Lakeland

arxiv:1312.7771 v3 · 2013-12-30 · 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{PGFENEBRU2TPMMC6VMQLCKZSR2}

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	2026-05-18T01:18:23.634295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

798a469031a6a6f6305eab20b12b328ebce18706aa00a1c9cc0f1c28b8d22e2a

Aliases

arxiv: 1312.7771 · arxiv_version: 1312.7771v3 · doi: 10.48550/arxiv.1312.7771 · pith_short_12: PGFENEBRU2TP · pith_short_16: PGFENEBRU2TPMMC6 · pith_short_8: PGFENEBR

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/PGFENEBRU2TPMMC6VMQLCKZSR2 \
  | 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: 798a469031a6a6f6305eab20b12b328ebce18706aa00a1c9cc0f1c28b8d22e2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f16d12ee130e478bd1af0a6b3aca2b0a9cfcb1c2901a37030632c973efddaffd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-12-30T16:35:57Z",
    "title_canon_sha256": "b4d1d1c1d393628b05f543a2a9717f53f121c3cadae23e92d8dde70f96acdead"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7771",
    "kind": "arxiv",
    "version": 3
  }
}