Pith Number

pith:U4SHCCXZ

pith:2017:U4SHCCXZEPIT6AJQKQTBMKKQS2

not attested not anchored not stored refs pending

Volume Rigidity of Principal Circle Bundles over the Complex Projective Space

Paul W.Y. Lee

arxiv:1712.03683 v1 · 2017-12-11 · 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{U4SHCCXZEPIT6AJQKQTBMKKQS2}

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	2026-05-18T00:28:20.403040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a724710af923d13f013054261629509690b7d57f660e4aef2f6c1c64dc2f0a1c

Aliases

arxiv: 1712.03683 · arxiv_version: 1712.03683v1 · doi: 10.48550/arxiv.1712.03683 · pith_short_12: U4SHCCXZEPIT · pith_short_16: U4SHCCXZEPIT6AJQ · pith_short_8: U4SHCCXZ

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/U4SHCCXZEPIT6AJQKQTBMKKQS2 \
  | 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: a724710af923d13f013054261629509690b7d57f660e4aef2f6c1c64dc2f0a1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40fffcf923c90d1b5c6cde97a72aa049b6119e0e6e88a46ae56268e7f5824805",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-12-11T09:13:41Z",
    "title_canon_sha256": "2c5f5eac0819bf3f9d5387d7a169a5ef164f97058d63c59a37e83d8aa85d1b46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.03683",
    "kind": "arxiv",
    "version": 1
  }
}