Pith Number

pith:YKJWKMRD

pith:2009:YKJWKMRDR5QUTMN7742CYNLR4I

not attested not anchored not stored refs pending

On the procongruence completion of the Teichm\"uller modular group

Marco Boggi

arxiv:0910.4305 v5 · 2009-10-22 · math.AG · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YKJWKMRDR5QUTMN7742CYNLR4I}

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	2026-05-18T03:36:06.760459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2936532238f6149b1bfff342c3571e20ddba5f06d9ebffaf05238a43d28ed47

Aliases

arxiv: 0910.4305 · arxiv_version: 0910.4305v5 · doi: 10.48550/arxiv.0910.4305 · pith_short_12: YKJWKMRDR5QU · pith_short_16: YKJWKMRDR5QUTMN7 · pith_short_8: YKJWKMRD

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/YKJWKMRDR5QUTMN7742CYNLR4I \
  | 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: c2936532238f6149b1bfff342c3571e20ddba5f06d9ebffaf05238a43d28ed47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87d9c349a8eeb91d26c9b0800c40122017c10ea662cef7060722c332765f36f3",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-10-22T12:39:04Z",
    "title_canon_sha256": "5d8a619c2bf2ec4e64e002ad881ef6478906cf28cb4f9ebd92ff4a33dcf828b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.4305",
    "kind": "arxiv",
    "version": 5
  }
}