Pith Number

pith:PGK54UJ3

pith:2011:PGK54UJ3CFHOBNRIF3JDIK5PJM

not attested not anchored not stored refs pending

Smooth metric measure spaces, quasi-Einstein metrics, and tractors

Jeffrey S. Case

arxiv:1110.3009 v3 · 2011-10-13 · 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{PGK54UJ3CFHOBNRIF3JDIK5PJM}

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	2026-05-18T03:49:59.821451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7995de513b114ee0b6282ed2342baf4b1d47338de8ee62c7f560b407f1fcab79

Aliases

arxiv: 1110.3009 · arxiv_version: 1110.3009v3 · doi: 10.48550/arxiv.1110.3009 · pith_short_12: PGK54UJ3CFHO · pith_short_16: PGK54UJ3CFHOBNRI · pith_short_8: PGK54UJ3

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/PGK54UJ3CFHOBNRIF3JDIK5PJM \
  | 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: 7995de513b114ee0b6282ed2342baf4b1d47338de8ee62c7f560b407f1fcab79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf5d060e828d2ad996af897b5576f8f73f4a54db1609bb9d6eba3792e80f3664",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-10-13T17:46:28Z",
    "title_canon_sha256": "ceb79a46d1c12d5990102f347cbd2b19e0fed75212f1f32808d59f0fac613052"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3009",
    "kind": "arxiv",
    "version": 3
  }
}