Pith Number

pith:GNQTPDUD

pith:2010:GNQTPDUDADP2DGL7SADV4FH6LF

not attested not anchored not stored refs pending

The `Real' Schwarz Lemma

David A. Thompson, Steven J. Miller

arxiv:1012.0585 v1 · 2010-12-02 · math.HO · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GNQTPDUDADP2DGL7SADV4FH6LF}

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	2026-05-18T04:34:09.699945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3361378e8300dfa1997f90075e14fe595c1760a43060a9f186da030597dd089f

Aliases

arxiv: 1012.0585 · arxiv_version: 1012.0585v1 · doi: 10.48550/arxiv.1012.0585 · pith_short_12: GNQTPDUDADP2 · pith_short_16: GNQTPDUDADP2DGL7 · pith_short_8: GNQTPDUD

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/GNQTPDUDADP2DGL7SADV4FH6LF \
  | 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: 3361378e8300dfa1997f90075e14fe595c1760a43060a9f186da030597dd089f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23de968517d5631df48233631e82914d84aac74f97543efd03ba3c6587cd768d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2010-12-02T21:33:36Z",
    "title_canon_sha256": "c4bfac0e7eec747def32832221e4a7e2bc9c23382d5bf69326079e2c5e69fdb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0585",
    "kind": "arxiv",
    "version": 1
  }
}