Pith Number

pith:ESA2QN23

pith:2025:ESA2QN23A2ZZDNU5I6Q5MB5COR

not attested not anchored not stored refs pending

Reduction theory for Fuchsian groups with cusps

Adam Abrams, Ilie Ugarcovici, Svetlana Katok

arxiv:2507.16958 v2 · 2025-07-22 · 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{ESA2QN23A2ZZDNU5I6Q5MB5COR}

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	2026-07-05T11:54:49.552070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2481a8375b06b391b69d47a1d607a274539ef6aaa5265976599c2c7407ced954

Aliases

arxiv: 2507.16958 · arxiv_version: 2507.16958v2 · doi: 10.48550/arxiv.2507.16958 · pith_short_12: ESA2QN23A2ZZ · pith_short_16: ESA2QN23A2ZZDNU5 · pith_short_8: ESA2QN23

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/ESA2QN23A2ZZDNU5I6Q5MB5COR \
  | 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: 2481a8375b06b391b69d47a1d607a274539ef6aaa5265976599c2c7407ced954

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c5969e48b0d9c1ab4f24218fcfb90c6f24482a31c0b8e299f1c3ab33d0b6905",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-07-22T18:58:52Z",
    "title_canon_sha256": "572b6ebf8cfe88a2a6999c044fd05a917b60391b85894d365123d03ecc6d1c3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16958",
    "kind": "arxiv",
    "version": 2
  }
}