Pith Number

pith:3WHX5TQ2

pith:2012:3WHX5TQ253YUIJ3ZBNLCA3ZPWE

not attested not anchored not stored refs pending

Riemannian Submersions Need Not Preserve Positive Ricci Curvature

Curtis Pro, Frederick Wilhelm

arxiv:1206.3766 v1 · 2012-06-17 · 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{3WHX5TQ253YUIJ3ZBNLCA3ZPWE}

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	2026-05-18T03:53:18.793624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd8f7ece1aeef14427790b56206f2fb1039344063bedff9c46db0a2fc2c56417

Aliases

arxiv: 1206.3766 · arxiv_version: 1206.3766v1 · doi: 10.48550/arxiv.1206.3766 · pith_short_12: 3WHX5TQ253YU · pith_short_16: 3WHX5TQ253YUIJ3Z · pith_short_8: 3WHX5TQ2

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/3WHX5TQ253YUIJ3ZBNLCA3ZPWE \
  | 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: dd8f7ece1aeef14427790b56206f2fb1039344063bedff9c46db0a2fc2c56417

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc0feff79e69f35a396ce8776b5a2421db842ad8316307e003a6140c7916f151",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-06-17T16:35:46Z",
    "title_canon_sha256": "2bb2ee090dbed0be13250c1195f5f194cdbcc70d60ac141ed9ee5a29df698d07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3766",
    "kind": "arxiv",
    "version": 1
  }
}