Pith Number

pith:IZNRLBQ4

pith:2018:IZNRLBQ4TL7Q5WKPQJSQZQOE46

not attested not anchored not stored refs pending

Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below

Aaron Naber, Jeff Cheeger, Wenshuai Jiang

arxiv:1805.07988 v1 · 2018-05-21 · 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{IZNRLBQ4TL7Q5WKPQJSQZQOE46}

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	2026-05-18T00:15:31.957115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

465b15861c9aff0ed94f82650cc1c4e7b451ca6f9528c472061060be416b7b03

Aliases

arxiv: 1805.07988 · arxiv_version: 1805.07988v1 · doi: 10.48550/arxiv.1805.07988 · pith_short_12: IZNRLBQ4TL7Q · pith_short_16: IZNRLBQ4TL7Q5WKP · pith_short_8: IZNRLBQ4

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/IZNRLBQ4TL7Q5WKPQJSQZQOE46 \
  | 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: 465b15861c9aff0ed94f82650cc1c4e7b451ca6f9528c472061060be416b7b03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50c7140a0cbc25f3b63444703e6e86bc75ef216bcd502eeb7708be714f8d0cb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-05-21T11:09:55Z",
    "title_canon_sha256": "565f9286de8127ab7bd7d0a8fc74794faf3156aae08dd983d10cf0189887a328"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.07988",
    "kind": "arxiv",
    "version": 1
  }
}