Pith Number

pith:WPZ5YMLZ

pith:2011:WPZ5YMLZQ7WE2ZQUR2K4XJH2IU

not attested not anchored not stored refs pending

Homogeneity and projective equivalence of differential equation fields

D. J. Saunders, M. Crampin

arxiv:1109.3640 v1 · 2011-09-16 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPZ5YMLZQ7WE2ZQUR2K4XJH2IU}

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	2026-05-18T04:12:55.425557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3f3dc317987ec4d66148e95cba4fa45333b01fcddb978c4aebaece002faa3d0

Aliases

arxiv: 1109.3640 · arxiv_version: 1109.3640v1 · doi: 10.48550/arxiv.1109.3640 · pith_short_12: WPZ5YMLZQ7WE · pith_short_16: WPZ5YMLZQ7WE2ZQU · pith_short_8: WPZ5YMLZ

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/WPZ5YMLZQ7WE2ZQUR2K4XJH2IU \
  | 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: b3f3dc317987ec4d66148e95cba4fa45333b01fcddb978c4aebaece002faa3d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f1d8df7c34ccb9b3cece461d704cc0004718863cfbd3b170b6a23952831e7c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-09-16T15:01:36Z",
    "title_canon_sha256": "223e8b01a060b59934cfc6453d5a6433058d0dbbdc00547cb6c5389101280987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3640",
    "kind": "arxiv",
    "version": 1
  }
}