Pith Number

pith:6XE2J2VZ

pith:2016:6XE2J2VZMFWSZTC7D2NPJGVYTL

not attested not anchored not stored refs pending

Uniform congruence counting for Schottky semigroups in $\mathrm{SL}_2(\mathbf{Z})$

Dale Winter, Hee Oh, Michael Magee

arxiv:1601.03705 v3 · 2016-01-14 · math.NT · 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{6XE2J2VZMFWSZTC7D2NPJGVYTL}

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	2026-05-18T00:35:51.891254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5c9a4eab9616d2ccc5f1e9af49ab89afc7567cab9ec8b514844142dcebd157a

Aliases

arxiv: 1601.03705 · arxiv_version: 1601.03705v3 · doi: 10.48550/arxiv.1601.03705 · pith_short_12: 6XE2J2VZMFWS · pith_short_16: 6XE2J2VZMFWSZTC7 · pith_short_8: 6XE2J2VZ

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/6XE2J2VZMFWSZTC7D2NPJGVYTL \
  | 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: f5c9a4eab9616d2ccc5f1e9af49ab89afc7567cab9ec8b514844142dcebd157a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32c080b2ea534dc6d7bdcc77d28d1b02da43f4e635b9237ece959d9a49df12fd",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-14T19:31:38Z",
    "title_canon_sha256": "de7eb87b36603ca1e631655b5cf8f266e010317d9166907a39215405531078ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03705",
    "kind": "arxiv",
    "version": 3
  }
}