Pith Number

pith:PVC6GPRG

pith:2015:PVC6GPRGHAOJ6FIUVTK42T7CHI

not attested not anchored not stored refs pending

On the arithmetic dimension of triangle groups

John Voight, Steve Nugent

arxiv:1510.04637 v2 · 2015-10-15 · math.NT · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PVC6GPRGHAOJ6FIUVTK42T7CHI}

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	2026-05-18T01:22:00.731561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d45e33e26381c9f1514acd5cd4fe23a0cb2dc4840099ca2ab2cbfd23c23a81a

Aliases

arxiv: 1510.04637 · arxiv_version: 1510.04637v2 · doi: 10.48550/arxiv.1510.04637 · pith_short_12: PVC6GPRGHAOJ · pith_short_16: PVC6GPRGHAOJ6FIU · pith_short_8: PVC6GPRG

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/PVC6GPRGHAOJ6FIUVTK42T7CHI \
  | 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: 7d45e33e26381c9f1514acd5cd4fe23a0cb2dc4840099ca2ab2cbfd23c23a81a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85e5cc4c382bb7b89b48fa74e47a12c3adfff7f1711df20b32b03440d9adc888",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-15T17:26:48Z",
    "title_canon_sha256": "ec2a1ff364cf7a88375dfd6316403c9cf885d198d5d2326163f111cbc51c01fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04637",
    "kind": "arxiv",
    "version": 2
  }
}